9 """Z3 is a high performance theorem prover developed at Microsoft Research.
11 Z3 is used in many applications such as: software/hardware verification and testing,
12 constraint solving, analysis of hybrid systems, security, biology (in silico analysis),
13 and geometrical problems.
16 Please send feedback, comments and/or corrections on the Issue tracker for
17 https://github.com/Z3prover/z3.git. Your comments are very valuable.
38 ... x = BitVec('x', 32)
40 ... # the expression x + y is type incorrect
42 ... except Z3Exception as ex:
43 ... print("failed: %s" % ex)
48 from .z3types
import *
49 from .z3consts
import *
50 from .z3printer
import *
51 from fractions
import Fraction
56 if sys.version_info.major >= 3:
57 from typing
import Iterable
67 if sys.version_info.major < 3:
69 return isinstance(v, (int, long))
72 return isinstance(v, int)
84 major = ctypes.c_uint(0)
85 minor = ctypes.c_uint(0)
86 build = ctypes.c_uint(0)
87 rev = ctypes.c_uint(0)
89 return "%s.%s.%s" % (major.value, minor.value, build.value)
93 major = ctypes.c_uint(0)
94 minor = ctypes.c_uint(0)
95 build = ctypes.c_uint(0)
96 rev = ctypes.c_uint(0)
98 return (major.value, minor.value, build.value, rev.value)
105 def _z3_assert(cond, msg):
107 raise Z3Exception(msg)
110 def _z3_check_cint_overflow(n, name):
111 _z3_assert(ctypes.c_int(n).value == n, name +
" is too large")
115 """Log interaction to a file. This function must be invoked immediately after init(). """
120 """Append user-defined string to interaction log. """
125 """Convert an integer or string into a Z3 symbol."""
132 def _symbol2py(ctx, s):
133 """Convert a Z3 symbol back into a Python object. """
146 if len(args) == 1
and (isinstance(args[0], tuple)
or isinstance(args[0], list)):
148 elif len(args) == 1
and (isinstance(args[0], set)
or isinstance(args[0], AstVector)):
149 return [arg
for arg
in args[0]]
158 def _get_args_ast_list(args):
160 if isinstance(args, (set, AstVector, tuple)):
161 return [arg
for arg
in args]
168 def _to_param_value(val):
169 if isinstance(val, bool):
170 return "true" if val
else "false"
181 """A Context manages all other Z3 objects, global configuration options, etc.
183 Z3Py uses a default global context. For most applications this is sufficient.
184 An application may use multiple Z3 contexts. Objects created in one context
185 cannot be used in another one. However, several objects may be "translated" from
186 one context to another. It is not safe to access Z3 objects from multiple threads.
187 The only exception is the method `interrupt()` that can be used to interrupt() a long
189 The initialization method receives global configuration options for the new context.
194 _z3_assert(len(args) % 2 == 0,
"Argument list must have an even number of elements.")
213 if Z3_del_context
is not None and self.
owner:
219 """Return a reference to the actual C pointer to the Z3 context."""
223 """Interrupt a solver performing a satisfiability test, a tactic processing a goal, or simplify functions.
225 This method can be invoked from a thread different from the one executing the
226 interruptible procedure.
231 """Return the global parameter description set."""
240 """Return a reference to the global Z3 context.
243 >>> x.ctx == main_ctx()
248 >>> x2 = Real('x', c)
255 if _main_ctx
is None:
272 """Set Z3 global (or module) parameters.
274 >>> set_param(precision=10)
277 _z3_assert(len(args) % 2 == 0,
"Argument list must have an even number of elements.")
281 if not set_pp_option(k, v):
296 """Reset all global (or module) parameters.
302 """Alias for 'set_param' for backward compatibility.
308 """Return the value of a Z3 global (or module) parameter
310 >>> get_param('nlsat.reorder')
313 ptr = (ctypes.c_char_p * 1)()
315 r = z3core._to_pystr(ptr[0])
317 raise Z3Exception(
"failed to retrieve value for '%s'" % name)
329 """Superclass for all Z3 objects that have support for pretty printing."""
334 def _repr_html_(self):
335 in_html = in_html_mode()
338 set_html_mode(in_html)
343 """AST are Direct Acyclic Graphs (DAGs) used to represent sorts, declarations and expressions."""
351 if self.ctx.ref()
is not None and self.
ast is not None and Z3_dec_ref
is not None:
356 return _to_ast_ref(self.
ast, self.
ctx)
359 return obj_to_string(self)
362 return obj_to_string(self)
365 return self.
eq(other)
378 elif is_eq(self)
and self.num_args() == 2:
379 return self.arg(0).
eq(self.arg(1))
381 raise Z3Exception(
"Symbolic expressions cannot be cast to concrete Boolean values.")
384 """Return a string representing the AST node in s-expression notation.
387 >>> ((x + 1)*x).sexpr()
393 """Return a pointer to the corresponding C Z3_ast object."""
397 """Return unique identifier for object. It can be used for hash-tables and maps."""
401 """Return a reference to the C context where this AST node is stored."""
402 return self.ctx.ref()
405 """Return `True` if `self` and `other` are structurally identical.
412 >>> n1 = simplify(n1)
413 >>> n2 = simplify(n2)
418 _z3_assert(
is_ast(other),
"Z3 AST expected")
422 """Translate `self` to the context `target`. That is, return a copy of `self` in the context `target`.
428 >>> # Nodes in different contexts can't be mixed.
429 >>> # However, we can translate nodes from one context to another.
430 >>> x.translate(c2) + y
434 _z3_assert(isinstance(target, Context),
"argument must be a Z3 context")
441 """Return a hashcode for the `self`.
443 >>> n1 = simplify(Int('x') + 1)
444 >>> n2 = simplify(2 + Int('x') - 1)
445 >>> n1.hash() == n2.hash()
452 """Return `True` if `a` is an AST node.
456 >>> is_ast(IntVal(10))
460 >>> is_ast(BoolSort())
462 >>> is_ast(Function('f', IntSort(), IntSort()))
469 return isinstance(a, AstRef)
473 """Return `True` if `a` and `b` are structurally identical AST nodes.
483 >>> eq(simplify(x + 1), simplify(1 + x))
491 def _ast_kind(ctx, a):
497 def _ctx_from_ast_arg_list(args, default_ctx=None):
505 _z3_assert(ctx == a.ctx,
"Context mismatch")
511 def _ctx_from_ast_args(*args):
512 return _ctx_from_ast_arg_list(args)
515 def _to_func_decl_array(args):
517 _args = (FuncDecl * sz)()
519 _args[i] = args[i].as_func_decl()
523 def _to_ast_array(args):
527 _args[i] = args[i].as_ast()
531 def _to_ref_array(ref, args):
535 _args[i] = args[i].as_ast()
539 def _to_ast_ref(a, ctx):
540 k = _ast_kind(ctx, a)
542 return _to_sort_ref(a, ctx)
543 elif k == Z3_FUNC_DECL_AST:
544 return _to_func_decl_ref(a, ctx)
546 return _to_expr_ref(a, ctx)
555 def _sort_kind(ctx, s):
560 """A Sort is essentially a type. Every Z3 expression has a sort. A sort is an AST node."""
569 """Return the Z3 internal kind of a sort.
570 This method can be used to test if `self` is one of the Z3 builtin sorts.
573 >>> b.kind() == Z3_BOOL_SORT
575 >>> b.kind() == Z3_INT_SORT
577 >>> A = ArraySort(IntSort(), IntSort())
578 >>> A.kind() == Z3_ARRAY_SORT
580 >>> A.kind() == Z3_INT_SORT
583 return _sort_kind(self.
ctx, self.
ast)
586 """Return `True` if `self` is a subsort of `other`.
588 >>> IntSort().subsort(RealSort())
594 """Try to cast `val` as an element of sort `self`.
596 This method is used in Z3Py to convert Python objects such as integers,
597 floats, longs and strings into Z3 expressions.
600 >>> RealSort().cast(x)
604 _z3_assert(
is_expr(val),
"Z3 expression expected")
605 _z3_assert(self.
eq(val.sort()),
"Sort mismatch")
609 """Return the name (string) of sort `self`.
611 >>> BoolSort().name()
613 >>> ArraySort(IntSort(), IntSort()).name()
619 """Return `True` if `self` and `other` are the same Z3 sort.
622 >>> p.sort() == BoolSort()
624 >>> p.sort() == IntSort()
632 """Return `True` if `self` and `other` are not the same Z3 sort.
635 >>> p.sort() != BoolSort()
637 >>> p.sort() != IntSort()
644 return AstRef.__hash__(self)
648 """Return `True` if `s` is a Z3 sort.
650 >>> is_sort(IntSort())
652 >>> is_sort(Int('x'))
654 >>> is_expr(Int('x'))
657 return isinstance(s, SortRef)
660 def _to_sort_ref(s, ctx):
662 _z3_assert(isinstance(s, Sort),
"Z3 Sort expected")
663 k = _sort_kind(ctx, s)
664 if k == Z3_BOOL_SORT:
666 elif k == Z3_INT_SORT
or k == Z3_REAL_SORT:
668 elif k == Z3_BV_SORT:
670 elif k == Z3_ARRAY_SORT:
672 elif k == Z3_DATATYPE_SORT:
674 elif k == Z3_FINITE_DOMAIN_SORT:
676 elif k == Z3_FLOATING_POINT_SORT:
678 elif k == Z3_ROUNDING_MODE_SORT:
680 elif k == Z3_RE_SORT:
682 elif k == Z3_SEQ_SORT:
684 elif k == Z3_CHAR_SORT:
686 elif k == Z3_TYPE_VAR:
692 return _to_sort_ref(
Z3_get_sort(ctx.ref(), a), ctx)
696 """Create a new uninterpreted sort named `name`.
698 If `ctx=None`, then the new sort is declared in the global Z3Py context.
700 >>> A = DeclareSort('A')
701 >>> a = Const('a', A)
702 >>> b = Const('b', A)
714 """Type variable reference"""
724 """Create a new type variable named `name`.
726 If `ctx=None`, then the new sort is declared in the global Z3Py context.
741 """Function declaration. Every constant and function have an associated declaration.
743 The declaration assigns a name, a sort (i.e., type), and for function
744 the sort (i.e., type) of each of its arguments. Note that, in Z3,
745 a constant is a function with 0 arguments.
758 """Return the name of the function declaration `self`.
760 >>> f = Function('f', IntSort(), IntSort())
763 >>> isinstance(f.name(), str)
769 """Return the number of arguments of a function declaration.
770 If `self` is a constant, then `self.arity()` is 0.
772 >>> f = Function('f', IntSort(), RealSort(), BoolSort())
779 """Return the sort of the argument `i` of a function declaration.
780 This method assumes that `0 <= i < self.arity()`.
782 >>> f = Function('f', IntSort(), RealSort(), BoolSort())
791 """Return the sort of the range of a function declaration.
792 For constants, this is the sort of the constant.
794 >>> f = Function('f', IntSort(), RealSort(), BoolSort())
801 """Return the internal kind of a function declaration.
802 It can be used to identify Z3 built-in functions such as addition, multiplication, etc.
805 >>> d = (x + 1).decl()
806 >>> d.kind() == Z3_OP_ADD
808 >>> d.kind() == Z3_OP_MUL
816 result = [
None for i
in range(n)]
819 if k == Z3_PARAMETER_INT:
821 elif k == Z3_PARAMETER_DOUBLE:
823 elif k == Z3_PARAMETER_RATIONAL:
825 elif k == Z3_PARAMETER_SYMBOL:
827 elif k == Z3_PARAMETER_SORT:
829 elif k == Z3_PARAMETER_AST:
831 elif k == Z3_PARAMETER_FUNC_DECL:
838 """Create a Z3 application expression using the function `self`, and the given arguments.
840 The arguments must be Z3 expressions. This method assumes that
841 the sorts of the elements in `args` match the sorts of the
842 domain. Limited coercion is supported. For example, if
843 args[0] is a Python integer, and the function expects a Z3
844 integer, then the argument is automatically converted into a
847 >>> f = Function('f', IntSort(), RealSort(), BoolSort())
855 args = _get_args(args)
857 _args = (Ast * num)()
862 tmp = self.
domain(i).cast(args[i])
864 _args[i] = tmp.as_ast()
869 """Return `True` if `a` is a Z3 function declaration.
871 >>> f = Function('f', IntSort(), IntSort())
878 return isinstance(a, FuncDeclRef)
882 """Create a new Z3 uninterpreted function with the given sorts.
884 >>> f = Function('f', IntSort(), IntSort())
890 _z3_assert(len(sig) > 0,
"At least two arguments expected")
894 _z3_assert(
is_sort(rng),
"Z3 sort expected")
895 dom = (Sort * arity)()
896 for i
in range(arity):
898 _z3_assert(
is_sort(sig[i]),
"Z3 sort expected")
905 """Create a new fresh Z3 uninterpreted function with the given sorts.
909 _z3_assert(len(sig) > 0,
"At least two arguments expected")
913 _z3_assert(
is_sort(rng),
"Z3 sort expected")
914 dom = (z3.Sort * arity)()
915 for i
in range(arity):
917 _z3_assert(
is_sort(sig[i]),
"Z3 sort expected")
923 def _to_func_decl_ref(a, ctx):
928 """Create a new Z3 recursive with the given sorts."""
931 _z3_assert(len(sig) > 0,
"At least two arguments expected")
935 _z3_assert(
is_sort(rng),
"Z3 sort expected")
936 dom = (Sort * arity)()
937 for i
in range(arity):
939 _z3_assert(
is_sort(sig[i]),
"Z3 sort expected")
946 """Set the body of a recursive function.
947 Recursive definitions can be simplified if they are applied to ground
950 >>> fac = RecFunction('fac', IntSort(ctx), IntSort(ctx))
951 >>> n = Int('n', ctx)
952 >>> RecAddDefinition(fac, n, If(n == 0, 1, n*fac(n-1)))
955 >>> s = Solver(ctx=ctx)
956 >>> s.add(fac(n) < 3)
959 >>> s.model().eval(fac(5))
965 args = _get_args(args)
969 _args[i] = args[i].ast
980 """Constraints, formulas and terms are expressions in Z3.
982 Expressions are ASTs. Every expression has a sort.
983 There are three main kinds of expressions:
984 function applications, quantifiers and bounded variables.
985 A constant is a function application with 0 arguments.
986 For quantifier free problems, all expressions are
987 function applications.
997 """Return the sort of expression `self`.
1009 """Shorthand for `self.sort().kind()`.
1011 >>> a = Array('a', IntSort(), IntSort())
1012 >>> a.sort_kind() == Z3_ARRAY_SORT
1014 >>> a.sort_kind() == Z3_INT_SORT
1017 return self.
sort().kind()
1020 """Return a Z3 expression that represents the constraint `self == other`.
1022 If `other` is `None`, then this method simply returns `False`.
1033 a, b = _coerce_exprs(self, other)
1038 return AstRef.__hash__(self)
1041 """Return a Z3 expression that represents the constraint `self != other`.
1043 If `other` is `None`, then this method simply returns `True`.
1054 a, b = _coerce_exprs(self, other)
1055 _args, sz = _to_ast_array((a, b))
1062 """Return the Z3 function declaration associated with a Z3 application.
1064 >>> f = Function('f', IntSort(), IntSort())
1073 _z3_assert(
is_app(self),
"Z3 application expected")
1077 """Return the number of arguments of a Z3 application.
1081 >>> (a + b).num_args()
1083 >>> f = Function('f', IntSort(), IntSort(), IntSort(), IntSort())
1089 _z3_assert(
is_app(self),
"Z3 application expected")
1093 """Return argument `idx` of the application `self`.
1095 This method assumes that `self` is a function application with at least `idx+1` arguments.
1099 >>> f = Function('f', IntSort(), IntSort(), IntSort(), IntSort())
1109 _z3_assert(
is_app(self),
"Z3 application expected")
1110 _z3_assert(idx < self.
num_args(),
"Invalid argument index")
1114 """Return a list containing the children of the given expression
1118 >>> f = Function('f', IntSort(), IntSort(), IntSort(), IntSort())
1138 """inverse function to the serialize method on ExprRef.
1139 It is made available to make it easier for users to serialize expressions back and forth between
1140 strings. Solvers can be serialized using the 'sexpr()' method.
1144 if len(s.assertions()) != 1:
1145 raise Z3Exception(
"single assertion expected")
1146 fml = s.assertions()[0]
1147 if fml.num_args() != 1:
1148 raise Z3Exception(
"dummy function 'F' expected")
1151 def _to_expr_ref(a, ctx):
1152 if isinstance(a, Pattern):
1156 if k == Z3_QUANTIFIER_AST:
1159 if sk == Z3_BOOL_SORT:
1161 if sk == Z3_INT_SORT:
1162 if k == Z3_NUMERAL_AST:
1165 if sk == Z3_REAL_SORT:
1166 if k == Z3_NUMERAL_AST:
1168 if _is_algebraic(ctx, a):
1171 if sk == Z3_BV_SORT:
1172 if k == Z3_NUMERAL_AST:
1176 if sk == Z3_ARRAY_SORT:
1178 if sk == Z3_DATATYPE_SORT:
1180 if sk == Z3_FLOATING_POINT_SORT:
1181 if k == Z3_APP_AST
and _is_numeral(ctx, a):
1184 return FPRef(a, ctx)
1185 if sk == Z3_FINITE_DOMAIN_SORT:
1186 if k == Z3_NUMERAL_AST:
1190 if sk == Z3_ROUNDING_MODE_SORT:
1192 if sk == Z3_SEQ_SORT:
1194 if sk == Z3_CHAR_SORT:
1196 if sk == Z3_RE_SORT:
1197 return ReRef(a, ctx)
1201 def _coerce_expr_merge(s, a):
1214 _z3_assert(s1.ctx == s.ctx,
"context mismatch")
1215 _z3_assert(
False,
"sort mismatch")
1220 def _coerce_exprs(a, b, ctx=None):
1222 a = _py2expr(a, ctx)
1223 b = _py2expr(b, ctx)
1224 if isinstance(a, str)
and isinstance(b, SeqRef):
1226 if isinstance(b, str)
and isinstance(a, SeqRef):
1228 if isinstance(a, float)
and isinstance(b, ArithRef):
1230 if isinstance(b, float)
and isinstance(a, ArithRef):
1234 s = _coerce_expr_merge(s, a)
1235 s = _coerce_expr_merge(s, b)
1241 def _reduce(func, sequence, initial):
1243 for element
in sequence:
1244 result = func(result, element)
1248 def _coerce_expr_list(alist, ctx=None):
1255 alist = [_py2expr(a, ctx)
for a
in alist]
1256 s = _reduce(_coerce_expr_merge, alist,
None)
1257 return [s.cast(a)
for a
in alist]
1261 """Return `True` if `a` is a Z3 expression.
1268 >>> is_expr(IntSort())
1272 >>> is_expr(IntVal(1))
1275 >>> is_expr(ForAll(x, x >= 0))
1277 >>> is_expr(FPVal(1.0))
1280 return isinstance(a, ExprRef)
1284 """Return `True` if `a` is a Z3 function application.
1286 Note that, constants are function applications with 0 arguments.
1293 >>> is_app(IntSort())
1297 >>> is_app(IntVal(1))
1300 >>> is_app(ForAll(x, x >= 0))
1303 if not isinstance(a, ExprRef):
1305 k = _ast_kind(a.ctx, a)
1306 return k == Z3_NUMERAL_AST
or k == Z3_APP_AST
1310 """Return `True` if `a` is Z3 constant/variable expression.
1319 >>> is_const(IntVal(1))
1322 >>> is_const(ForAll(x, x >= 0))
1325 return is_app(a)
and a.num_args() == 0
1329 """Return `True` if `a` is variable.
1331 Z3 uses de-Bruijn indices for representing bound variables in
1339 >>> f = Function('f', IntSort(), IntSort())
1340 >>> # Z3 replaces x with bound variables when ForAll is executed.
1341 >>> q = ForAll(x, f(x) == x)
1347 >>> is_var(b.arg(1))
1350 return is_expr(a)
and _ast_kind(a.ctx, a) == Z3_VAR_AST
1354 """Return the de-Bruijn index of the Z3 bounded variable `a`.
1362 >>> f = Function('f', IntSort(), IntSort(), IntSort())
1363 >>> # Z3 replaces x and y with bound variables when ForAll is executed.
1364 >>> q = ForAll([x, y], f(x, y) == x + y)
1366 f(Var(1), Var(0)) == Var(1) + Var(0)
1370 >>> v1 = b.arg(0).arg(0)
1371 >>> v2 = b.arg(0).arg(1)
1376 >>> get_var_index(v1)
1378 >>> get_var_index(v2)
1382 _z3_assert(
is_var(a),
"Z3 bound variable expected")
1387 """Return `True` if `a` is an application of the given kind `k`.
1391 >>> is_app_of(n, Z3_OP_ADD)
1393 >>> is_app_of(n, Z3_OP_MUL)
1396 return is_app(a)
and a.decl().kind() == k
1399 def If(a, b, c, ctx=None):
1400 """Create a Z3 if-then-else expression.
1404 >>> max = If(x > y, x, y)
1410 if isinstance(a, Probe)
or isinstance(b, Tactic)
or isinstance(c, Tactic):
1411 return Cond(a, b, c, ctx)
1413 ctx = _get_ctx(_ctx_from_ast_arg_list([a, b, c], ctx))
1416 b, c = _coerce_exprs(b, c, ctx)
1418 _z3_assert(a.ctx == b.ctx,
"Context mismatch")
1419 return _to_expr_ref(
Z3_mk_ite(ctx.ref(), a.as_ast(), b.as_ast(), c.as_ast()), ctx)
1423 """Create a Z3 distinct expression.
1430 >>> Distinct(x, y, z)
1432 >>> simplify(Distinct(x, y, z))
1434 >>> simplify(Distinct(x, y, z), blast_distinct=True)
1435 And(Not(x == y), Not(x == z), Not(y == z))
1437 args = _get_args(args)
1438 ctx = _ctx_from_ast_arg_list(args)
1440 _z3_assert(ctx
is not None,
"At least one of the arguments must be a Z3 expression")
1441 args = _coerce_expr_list(args, ctx)
1442 _args, sz = _to_ast_array(args)
1446 def _mk_bin(f, a, b):
1449 _z3_assert(a.ctx == b.ctx,
"Context mismatch")
1450 args[0] = a.as_ast()
1451 args[1] = b.as_ast()
1452 return f(a.ctx.ref(), 2, args)
1456 """Create a constant of the given sort.
1458 >>> Const('x', IntSort())
1462 _z3_assert(isinstance(sort, SortRef),
"Z3 sort expected")
1468 """Create several constants of the given sort.
1470 `names` is a string containing the names of all constants to be created.
1471 Blank spaces separate the names of different constants.
1473 >>> x, y, z = Consts('x y z', IntSort())
1477 if isinstance(names, str):
1478 names = names.split(
" ")
1479 return [
Const(name, sort)
for name
in names]
1483 """Create a fresh constant of a specified sort"""
1484 ctx = _get_ctx(sort.ctx)
1489 """Create a Z3 free variable. Free variables are used to create quantified formulas.
1490 A free variable with index n is bound when it occurs within the scope of n+1 quantified
1493 >>> Var(0, IntSort())
1495 >>> eq(Var(0, IntSort()), Var(0, BoolSort()))
1499 _z3_assert(
is_sort(s),
"Z3 sort expected")
1500 return _to_expr_ref(
Z3_mk_bound(s.ctx_ref(), idx, s.ast), s.ctx)
1505 Create a real free variable. Free variables are used to create quantified formulas.
1506 They are also used to create polynomials.
1516 Create a list of Real free variables.
1517 The variables have ids: 0, 1, ..., n-1
1519 >>> x0, x1, x2, x3 = RealVarVector(4)
1536 """Try to cast `val` as a Boolean.
1538 >>> x = BoolSort().cast(True)
1548 if isinstance(val, bool):
1552 msg =
"True, False or Z3 Boolean expression expected. Received %s of type %s"
1553 _z3_assert(
is_expr(val), msg % (val, type(val)))
1554 if not self.
eq(val.sort()):
1555 _z3_assert(self.
eq(val.sort()),
"Value cannot be converted into a Z3 Boolean value")
1559 return isinstance(other, ArithSortRef)
1569 """All Boolean expressions are instances of this class."""
1575 if isinstance(other, BoolRef):
1576 other =
If(other, 1, 0)
1577 return If(self, 1, 0) + other
1586 """Create the Z3 expression `self * other`.
1588 if isinstance(other, int)
and other == 1:
1589 return If(self, 1, 0)
1590 if isinstance(other, int)
and other == 0:
1592 if isinstance(other, BoolRef):
1593 other =
If(other, 1, 0)
1594 return If(self, other, 0)
1597 return And(self, other)
1600 return Or(self, other)
1603 return Xor(self, other)
1612 """Return `True` if `a` is a Z3 Boolean expression.
1618 >>> is_bool(And(p, q))
1626 return isinstance(a, BoolRef)
1630 """Return `True` if `a` is the Z3 true expression.
1635 >>> is_true(simplify(p == p))
1640 >>> # True is a Python Boolean expression
1648 """Return `True` if `a` is the Z3 false expression.
1655 >>> is_false(BoolVal(False))
1662 """Return `True` if `a` is a Z3 and expression.
1664 >>> p, q = Bools('p q')
1665 >>> is_and(And(p, q))
1667 >>> is_and(Or(p, q))
1674 """Return `True` if `a` is a Z3 or expression.
1676 >>> p, q = Bools('p q')
1679 >>> is_or(And(p, q))
1686 """Return `True` if `a` is a Z3 implication expression.
1688 >>> p, q = Bools('p q')
1689 >>> is_implies(Implies(p, q))
1691 >>> is_implies(And(p, q))
1698 """Return `True` if `a` is a Z3 not expression.
1710 """Return `True` if `a` is a Z3 equality expression.
1712 >>> x, y = Ints('x y')
1720 """Return `True` if `a` is a Z3 distinct expression.
1722 >>> x, y, z = Ints('x y z')
1723 >>> is_distinct(x == y)
1725 >>> is_distinct(Distinct(x, y, z))
1732 """Return the Boolean Z3 sort. If `ctx=None`, then the global context is used.
1736 >>> p = Const('p', BoolSort())
1739 >>> r = Function('r', IntSort(), IntSort(), BoolSort())
1746 return BoolSortRef(Z3_mk_bool_sort(ctx.ref()), ctx)
1749 def BoolVal(val, ctx=None):
1750 """Return the Boolean value `
True`
or `
False`. If `ctx=
None`, then the
global context
is used.
1763 return BoolRef(Z3_mk_true(ctx.ref()), ctx)
1765 return BoolRef(Z3_mk_false(ctx.ref()), ctx)
1768 def Bool(name, ctx=None):
1769 """Return a Boolean constant named `name`. If `ctx=
None`, then the
global context
is used.
1777 return BoolRef(Z3_mk_const(ctx.ref(), to_symbol(name, ctx), BoolSort(ctx).ast), ctx)
1780 def Bools(names, ctx=None):
1781 """Return a tuple of Boolean constants.
1783 `names`
is a single string containing all names separated by blank spaces.
1784 If `ctx=
None`, then the
global context
is used.
1786 >>> p, q, r =
Bools(
'p q r')
1787 >>>
And(p,
Or(q, r))
1791 if isinstance(names, str):
1792 names = names.split(" ")
1793 return [Bool(name, ctx) for name in names]
1796 def BoolVector(prefix, sz, ctx=None):
1797 """Return a list of Boolean constants of size `sz`.
1799 The constants are named using the given prefix.
1800 If `ctx=
None`, then the
global context
is used.
1806 And(p__0, p__1, p__2)
1808 return [Bool("%s__%s" % (prefix, i)) for i in range(sz)]
1811 def FreshBool(prefix="b", ctx=None):
1812 """Return a fresh Boolean constant
in the given context using the given prefix.
1814 If `ctx=
None`, then the
global context
is used.
1822 return BoolRef(Z3_mk_fresh_const(ctx.ref(), prefix, BoolSort(ctx).ast), ctx)
1825 def Implies(a, b, ctx=None):
1826 """Create a Z3 implies expression.
1828 >>> p, q =
Bools(
'p q')
1832 ctx = _get_ctx(_ctx_from_ast_arg_list([a, b], ctx))
1836 return BoolRef(Z3_mk_implies(ctx.ref(), a.as_ast(), b.as_ast()), ctx)
1839 def Xor(a, b, ctx=None):
1840 """Create a Z3 Xor expression.
1842 >>> p, q =
Bools(
'p q')
1848 ctx = _get_ctx(_ctx_from_ast_arg_list([a, b], ctx))
1852 return BoolRef(Z3_mk_xor(ctx.ref(), a.as_ast(), b.as_ast()), ctx)
1855 def Not(a, ctx=None):
1856 """Create a Z3
not expression
or probe.
1864 ctx = _get_ctx(_ctx_from_ast_arg_list([a], ctx))
1866 # Not is also used to build probes
1867 return Probe(Z3_probe_not(ctx.ref(), a.probe), ctx)
1871 return BoolRef(Z3_mk_not(ctx.ref(), a.as_ast()), ctx)
1881 def _has_probe(args):
1882 """Return `
True`
if one of the elements of the given collection
is a Z3 probe.
"""
1890 """Create a Z3
and-expression
or and-probe.
1892 >>> p, q, r =
Bools(
'p q r')
1897 And(p__0, p__1, p__2, p__3, p__4)
1901 last_arg = args[len(args) - 1]
1902 if isinstance(last_arg, Context):
1903 ctx = args[len(args) - 1]
1904 args = args[:len(args) - 1]
1905 elif len(args) == 1 and isinstance(args[0], AstVector):
1907 args = [a for a in args[0]]
1910 args = _get_args(args)
1911 ctx = _get_ctx(_ctx_from_ast_arg_list(args, ctx))
1913 _z3_assert(ctx is not None, "At least one of the arguments must be a Z3 expression or probe")
1914 if _has_probe(args):
1915 return _probe_and(args, ctx)
1917 args = _coerce_expr_list(args, ctx)
1918 _args, sz = _to_ast_array(args)
1919 return BoolRef(Z3_mk_and(ctx.ref(), sz, _args), ctx)
1923 """Create a Z3
or-expression
or or-probe.
1925 >>> p, q, r =
Bools(
'p q r')
1930 Or(p__0, p__1, p__2, p__3, p__4)
1934 last_arg = args[len(args) - 1]
1935 if isinstance(last_arg, Context):
1936 ctx = args[len(args) - 1]
1937 args = args[:len(args) - 1]
1938 elif len(args) == 1 and isinstance(args[0], AstVector):
1940 args = [a for a in args[0]]
1943 args = _get_args(args)
1944 ctx = _get_ctx(_ctx_from_ast_arg_list(args, ctx))
1946 _z3_assert(ctx is not None, "At least one of the arguments must be a Z3 expression or probe")
1947 if _has_probe(args):
1948 return _probe_or(args, ctx)
1950 args = _coerce_expr_list(args, ctx)
1951 _args, sz = _to_ast_array(args)
1952 return BoolRef(Z3_mk_or(ctx.ref(), sz, _args), ctx)
1954 #########################################
1958 #########################################
1961 class PatternRef(ExprRef):
1962 """Patterns are hints
for quantifier instantiation.
1967 return Z3_pattern_to_ast(self.ctx_ref(), self.ast)
1970 return Z3_get_ast_id(self.ctx_ref(), self.as_ast())
1974 """Return `
True`
if `a`
is a Z3 pattern (hint
for quantifier instantiation.
1978 >>> q =
ForAll(x, f(x) == 0, patterns = [ f(x) ])
1981 >>> q.num_patterns()
1988 return isinstance(a, PatternRef)
1991 def MultiPattern(*args):
1992 """Create a Z3 multi-pattern using the given expressions `*args`
2000 >>> q.num_patterns()
2008 _z3_assert(len(args) > 0, "At least one argument expected")
2009 _z3_assert(all([is_expr(a) for a in args]), "Z3 expressions expected")
2011 args, sz = _to_ast_array(args)
2012 return PatternRef(Z3_mk_pattern(ctx.ref(), sz, args), ctx)
2015 def _to_pattern(arg):
2019 return MultiPattern(arg)
2021 #########################################
2025 #########################################
2028 class QuantifierRef(BoolRef):
2029 """Universally
and Existentially quantified formulas.
"""
2035 return Z3_get_ast_id(self.ctx_ref(), self.as_ast())
2038 """Return the Boolean sort
or sort of Lambda.
"""
2039 if self.is_lambda():
2040 return _sort(self.ctx, self.as_ast())
2041 return BoolSort(self.ctx)
2043 def is_forall(self):
2044 """Return `
True`
if `self`
is a universal quantifier.
2048 >>> q =
ForAll(x, f(x) == 0)
2051 >>> q =
Exists(x, f(x) != 0)
2055 return Z3_is_quantifier_forall(self.ctx_ref(), self.ast)
2057 def is_exists(self):
2058 """Return `
True`
if `self`
is an existential quantifier.
2062 >>> q =
ForAll(x, f(x) == 0)
2065 >>> q =
Exists(x, f(x) != 0)
2069 return Z3_is_quantifier_exists(self.ctx_ref(), self.ast)
2071 def is_lambda(self):
2072 """Return `
True`
if `self`
is a
lambda expression.
2079 >>> q =
Exists(x, f(x) != 0)
2083 return Z3_is_lambda(self.ctx_ref(), self.ast)
2085 def __getitem__(self, arg):
2086 """Return the Z3 expression `self[arg]`.
2089 _z3_assert(self.is_lambda(), "quantifier should be a lambda expression")
2090 return _array_select(self, arg)
2093 """Return the weight annotation of `self`.
2097 >>> q =
ForAll(x, f(x) == 0)
2100 >>> q =
ForAll(x, f(x) == 0, weight=10)
2104 return int(Z3_get_quantifier_weight(self.ctx_ref(), self.ast))
2106 def skolem_id(self):
2107 """Return the skolem id of `self`.
2109 return _symbol2py(self.ctx, Z3_get_quantifier_skolem_id(self.ctx_ref(), self.ast))
2112 """Return the quantifier id of `self`.
2114 return _symbol2py(self.ctx, Z3_get_quantifier_id(self.ctx_ref(), self.ast))
2116 def num_patterns(self):
2117 """Return the number of patterns (i.e., quantifier instantiation hints)
in `self`.
2122 >>> q =
ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
2123 >>> q.num_patterns()
2126 return int(Z3_get_quantifier_num_patterns(self.ctx_ref(), self.ast))
2128 def pattern(self, idx):
2129 """Return a pattern (i.e., quantifier instantiation hints)
in `self`.
2134 >>> q =
ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
2135 >>> q.num_patterns()
2143 _z3_assert(idx < self.num_patterns(), "Invalid pattern idx")
2144 return PatternRef(Z3_get_quantifier_pattern_ast(self.ctx_ref(), self.ast, idx), self.ctx)
2146 def num_no_patterns(self):
2147 """Return the number of no-patterns.
"""
2148 return Z3_get_quantifier_num_no_patterns(self.ctx_ref(), self.ast)
2150 def no_pattern(self, idx):
2151 """Return a no-pattern.
"""
2153 _z3_assert(idx < self.num_no_patterns(), "Invalid no-pattern idx")
2154 return _to_expr_ref(Z3_get_quantifier_no_pattern_ast(self.ctx_ref(), self.ast, idx), self.ctx)
2157 """Return the expression being quantified.
2161 >>> q =
ForAll(x, f(x) == 0)
2165 return _to_expr_ref(Z3_get_quantifier_body(self.ctx_ref(), self.ast), self.ctx)
2168 """Return the number of variables bounded by this quantifier.
2173 >>> q =
ForAll([x, y], f(x, y) >= x)
2177 return int(Z3_get_quantifier_num_bound(self.ctx_ref(), self.ast))
2179 def var_name(self, idx):
2180 """Return a string representing a name used when displaying the quantifier.
2185 >>> q =
ForAll([x, y], f(x, y) >= x)
2192 _z3_assert(idx < self.num_vars(), "Invalid variable idx")
2193 return _symbol2py(self.ctx, Z3_get_quantifier_bound_name(self.ctx_ref(), self.ast, idx))
2195 def var_sort(self, idx):
2196 """Return the sort of a bound variable.
2201 >>> q =
ForAll([x, y], f(x, y) >= x)
2208 _z3_assert(idx < self.num_vars(), "Invalid variable idx")
2209 return _to_sort_ref(Z3_get_quantifier_bound_sort(self.ctx_ref(), self.ast, idx), self.ctx)
2212 """Return a list containing a single element self.
body()
2216 >>> q =
ForAll(x, f(x) == 0)
2220 return [self.body()]
2223 def is_quantifier(a):
2224 """Return `
True`
if `a`
is a Z3 quantifier.
2228 >>> q =
ForAll(x, f(x) == 0)
2234 return isinstance(a, QuantifierRef)
2237 def _mk_quantifier(is_forall, vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[]):
2239 _z3_assert(is_bool(body) or is_app(vs) or (len(vs) > 0 and is_app(vs[0])), "Z3 expression expected")
2240 _z3_assert(is_const(vs) or (len(vs) > 0 and all([is_const(v) for v in vs])), "Invalid bounded variable(s)")
2241 _z3_assert(all([is_pattern(a) or is_expr(a) for a in patterns]), "Z3 patterns expected")
2242 _z3_assert(all([is_expr(p) for p in no_patterns]), "no patterns are Z3 expressions")
2248 if not is_expr(body):
2249 body = BoolVal(body, ctx)
2253 _vs = (Ast * num_vars)()
2254 for i in range(num_vars):
2255 # TODO: Check if is constant
2256 _vs[i] = vs[i].as_ast()
2257 patterns = [_to_pattern(p) for p in patterns]
2258 num_pats = len(patterns)
2259 _pats = (Pattern * num_pats)()
2260 for i in range(num_pats):
2261 _pats[i] = patterns[i].ast
2262 _no_pats, num_no_pats = _to_ast_array(no_patterns)
2263 qid = to_symbol(qid, ctx)
2264 skid = to_symbol(skid, ctx)
2265 return QuantifierRef(Z3_mk_quantifier_const_ex(ctx.ref(), is_forall, weight, qid, skid,
2268 num_no_pats, _no_pats,
2269 body.as_ast()), ctx)
2272 def ForAll(vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[]):
2273 """Create a Z3 forall formula.
2275 The parameters `weight`, `qid`, `skid`, `patterns`
and `no_patterns` are optional annotations.
2280 >>>
ForAll([x, y], f(x, y) >= x)
2281 ForAll([x, y], f(x, y) >= x)
2282 >>>
ForAll([x, y], f(x, y) >= x, patterns=[ f(x, y) ])
2283 ForAll([x, y], f(x, y) >= x)
2284 >>>
ForAll([x, y], f(x, y) >= x, weight=10)
2285 ForAll([x, y], f(x, y) >= x)
2287 return _mk_quantifier(True, vs, body, weight, qid, skid, patterns, no_patterns)
2290 def Exists(vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[]):
2291 """Create a Z3 exists formula.
2293 The parameters `weight`, `qif`, `skid`, `patterns`
and `no_patterns` are optional annotations.
2299 >>> q =
Exists([x, y], f(x, y) >= x, skid=
"foo")
2301 Exists([x, y], f(x, y) >= x)
2304 >>> r =
Tactic(
'nnf')(q).as_expr()
2308 return _mk_quantifier(False, vs, body, weight, qid, skid, patterns, no_patterns)
2311 def Lambda(vs, body):
2312 """Create a Z3
lambda expression.
2316 >>> lo, hi, e, i =
Ints(
'lo hi e i')
2317 >>> mem1 =
Lambda([i],
If(
And(lo <= i, i <= hi), e, mem0[i]))
2325 _vs = (Ast * num_vars)()
2326 for i in range(num_vars):
2327 # TODO: Check if is constant
2328 _vs[i] = vs[i].as_ast()
2329 return QuantifierRef(Z3_mk_lambda_const(ctx.ref(), num_vars, _vs, body.as_ast()), ctx)
2331 #########################################
2335 #########################################
2338 class ArithSortRef(SortRef):
2339 """Real
and Integer sorts.
"""
2342 """Return `
True`
if `self`
is of the sort Real.
2353 return self.kind() == Z3_REAL_SORT
2356 """Return `
True`
if `self`
is of the sort Integer.
2367 return self.kind() == Z3_INT_SORT
2372 def subsort(self, other):
2373 """Return `
True`
if `self`
is a subsort of `other`.
"""
2374 return self.is_int() and is_arith_sort(other) and other.is_real()
2376 def cast(self, val):
2377 """Try to cast `val`
as an Integer
or Real.
2392 _z3_assert(self.ctx == val.ctx, "Context mismatch")
2396 if val_s.is_int() and self.is_real():
2398 if val_s.is_bool() and self.is_int():
2399 return If(val, 1, 0)
2400 if val_s.is_bool() and self.is_real():
2401 return ToReal(If(val, 1, 0))
2403 _z3_assert(False, "Z3 Integer/Real expression expected")
2406 return IntVal(val, self.ctx)
2408 return RealVal(val, self.ctx)
2410 msg = "int, long, float, string (numeral), or Z3 Integer/Real expression expected. Got %s"
2411 _z3_assert(False, msg % self)
2414 def is_arith_sort(s):
2415 """Return `
True`
if s
is an arithmetical sort (type).
2423 >>> n =
Int(
'x') + 1
2427 return isinstance(s, ArithSortRef)
2430 class ArithRef(ExprRef):
2431 """Integer
and Real expressions.
"""
2434 """Return the sort (type) of the arithmetical expression `self`.
2441 return ArithSortRef(Z3_get_sort(self.ctx_ref(), self.as_ast()), self.ctx)
2444 """Return `
True`
if `self`
is an integer expression.
2455 return self.sort().is_int()
2458 """Return `
True`
if `self`
is an real expression.
2466 return self.sort().is_real()
2468 def __add__(self, other):
2469 """Create the Z3 expression `self + other`.
2478 a, b = _coerce_exprs(self, other)
2479 return ArithRef(_mk_bin(Z3_mk_add, a, b), self.ctx)
2481 def __radd__(self, other):
2482 """Create the Z3 expression `other + self`.
2488 a, b = _coerce_exprs(self, other)
2489 return ArithRef(_mk_bin(Z3_mk_add, b, a), self.ctx)
2491 def __mul__(self, other):
2492 """Create the Z3 expression `self * other`.
2501 if isinstance(other, BoolRef):
2502 return If(other, self, 0)
2503 a, b = _coerce_exprs(self, other)
2504 return ArithRef(_mk_bin(Z3_mk_mul, a, b), self.ctx)
2506 def __rmul__(self, other):
2507 """Create the Z3 expression `other * self`.
2513 a, b = _coerce_exprs(self, other)
2514 return ArithRef(_mk_bin(Z3_mk_mul, b, a), self.ctx)
2516 def __sub__(self, other):
2517 """Create the Z3 expression `self - other`.
2526 a, b = _coerce_exprs(self, other)
2527 return ArithRef(_mk_bin(Z3_mk_sub, a, b), self.ctx)
2529 def __rsub__(self, other):
2530 """Create the Z3 expression `other - self`.
2536 a, b = _coerce_exprs(self, other)
2537 return ArithRef(_mk_bin(Z3_mk_sub, b, a), self.ctx)
2539 def __pow__(self, other):
2540 """Create the Z3 expression `self**other` (**
is the power operator).
2550 a, b = _coerce_exprs(self, other)
2551 return ArithRef(Z3_mk_power(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2553 def __rpow__(self, other):
2554 """Create the Z3 expression `other**self` (**
is the power operator).
2564 a, b = _coerce_exprs(self, other)
2565 return ArithRef(Z3_mk_power(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
2567 def __div__(self, other):
2568 """Create the Z3 expression `other/self`.
2587 a, b = _coerce_exprs(self, other)
2588 return ArithRef(Z3_mk_div(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2590 def __truediv__(self, other):
2591 """Create the Z3 expression `other/self`.
"""
2592 return self.__div__(other)
2594 def __rdiv__(self, other):
2595 """Create the Z3 expression `other/self`.
2608 a, b = _coerce_exprs(self, other)
2609 return ArithRef(Z3_mk_div(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
2611 def __rtruediv__(self, other):
2612 """Create the Z3 expression `other/self`.
"""
2613 return self.__rdiv__(other)
2615 def __mod__(self, other):
2616 """Create the Z3 expression `other%self`.
2625 a, b = _coerce_exprs(self, other)
2627 _z3_assert(a.is_int(), "Z3 integer expression expected")
2628 return ArithRef(Z3_mk_mod(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2630 def __rmod__(self, other):
2631 """Create the Z3 expression `other%self`.
2637 a, b = _coerce_exprs(self, other)
2639 _z3_assert(a.is_int(), "Z3 integer expression expected")
2640 return ArithRef(Z3_mk_mod(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
2643 """Return an expression representing `-self`.
2651 return ArithRef(Z3_mk_unary_minus(self.ctx_ref(), self.as_ast()), self.ctx)
2662 def __le__(self, other):
2663 """Create the Z3 expression `other <= self`.
2665 >>> x, y =
Ints(
'x y')
2672 a, b = _coerce_exprs(self, other)
2673 return BoolRef(Z3_mk_le(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2675 def __lt__(self, other):
2676 """Create the Z3 expression `other < self`.
2678 >>> x, y =
Ints(
'x y')
2685 a, b = _coerce_exprs(self, other)
2686 return BoolRef(Z3_mk_lt(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2688 def __gt__(self, other):
2689 """Create the Z3 expression `other > self`.
2691 >>> x, y =
Ints(
'x y')
2698 a, b = _coerce_exprs(self, other)
2699 return BoolRef(Z3_mk_gt(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2701 def __ge__(self, other):
2702 """Create the Z3 expression `other >= self`.
2704 >>> x, y =
Ints(
'x y')
2711 a, b = _coerce_exprs(self, other)
2712 return BoolRef(Z3_mk_ge(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2716 """Return `
True`
if `a`
is an arithmetical expression.
2733 return isinstance(a, ArithRef)
2737 """Return `
True`
if `a`
is an integer expression.
2752 return is_arith(a) and a.is_int()
2756 """Return `
True`
if `a`
is a real expression.
2771 return is_arith(a) and a.is_real()
2774 def _is_numeral(ctx, a):
2775 return Z3_is_numeral_ast(ctx.ref(), a)
2778 def _is_algebraic(ctx, a):
2779 return Z3_is_algebraic_number(ctx.ref(), a)
2782 def is_int_value(a):
2783 """Return `
True`
if `a`
is an integer value of sort Int.
2791 >>> n =
Int(
'x') + 1
2803 return is_arith(a) and a.is_int() and _is_numeral(a.ctx, a.as_ast())
2806 def is_rational_value(a):
2807 """Return `
True`
if `a`
is rational value of sort Real.
2817 >>> n =
Real(
'x') + 1
2825 return is_arith(a) and a.is_real() and _is_numeral(a.ctx, a.as_ast())
2828 def is_algebraic_value(a):
2829 """Return `
True`
if `a`
is an algebraic value of sort Real.
2839 return is_arith(a) and a.is_real() and _is_algebraic(a.ctx, a.as_ast())
2843 """Return `
True`
if `a`
is an expression of the form b + c.
2845 >>> x, y =
Ints(
'x y')
2851 return is_app_of(a, Z3_OP_ADD)
2855 """Return `
True`
if `a`
is an expression of the form b * c.
2857 >>> x, y =
Ints(
'x y')
2863 return is_app_of(a, Z3_OP_MUL)
2867 """Return `
True`
if `a`
is an expression of the form b - c.
2869 >>> x, y =
Ints(
'x y')
2875 return is_app_of(a, Z3_OP_SUB)
2879 """Return `
True`
if `a`
is an expression of the form b / c.
2881 >>> x, y =
Reals(
'x y')
2886 >>> x, y =
Ints(
'x y')
2892 return is_app_of(a, Z3_OP_DIV)
2896 """Return `
True`
if `a`
is an expression of the form b div c.
2898 >>> x, y =
Ints(
'x y')
2904 return is_app_of(a, Z3_OP_IDIV)
2908 """Return `
True`
if `a`
is an expression of the form b % c.
2910 >>> x, y =
Ints(
'x y')
2916 return is_app_of(a, Z3_OP_MOD)
2920 """Return `
True`
if `a`
is an expression of the form b <= c.
2922 >>> x, y =
Ints(
'x y')
2928 return is_app_of(a, Z3_OP_LE)
2932 """Return `
True`
if `a`
is an expression of the form b < c.
2934 >>> x, y =
Ints(
'x y')
2940 return is_app_of(a, Z3_OP_LT)
2944 """Return `
True`
if `a`
is an expression of the form b >= c.
2946 >>> x, y =
Ints(
'x y')
2952 return is_app_of(a, Z3_OP_GE)
2956 """Return `
True`
if `a`
is an expression of the form b > c.
2958 >>> x, y =
Ints(
'x y')
2964 return is_app_of(a, Z3_OP_GT)
2968 """Return `
True`
if `a`
is an expression of the form
IsInt(b).
2976 return is_app_of(a, Z3_OP_IS_INT)
2980 """Return `
True`
if `a`
is an expression of the form
ToReal(b).
2991 return is_app_of(a, Z3_OP_TO_REAL)
2995 """Return `
True`
if `a`
is an expression of the form
ToInt(b).
3006 return is_app_of(a, Z3_OP_TO_INT)
3009 class IntNumRef(ArithRef):
3010 """Integer values.
"""
3013 """Return a Z3 integer numeral
as a Python long (bignum) numeral.
3022 _z3_assert(self.is_int(), "Integer value expected")
3023 return int(self.as_string())
3025 def as_string(self):
3026 """Return a Z3 integer numeral
as a Python string.
3031 return Z3_get_numeral_string(self.ctx_ref(), self.as_ast())
3033 def as_binary_string(self):
3034 """Return a Z3 integer numeral
as a Python binary string.
3036 >>> v.as_binary_string()
3039 return Z3_get_numeral_binary_string(self.ctx_ref(), self.as_ast())
3042 class RatNumRef(ArithRef):
3043 """Rational values.
"""
3045 def numerator(self):
3046 """ Return the numerator of a Z3 rational numeral.
3058 return IntNumRef(Z3_get_numerator(self.ctx_ref(), self.as_ast()), self.ctx)
3060 def denominator(self):
3061 """ Return the denominator of a Z3 rational numeral.
3069 return IntNumRef(Z3_get_denominator(self.ctx_ref(), self.as_ast()), self.ctx)
3071 def numerator_as_long(self):
3072 """ Return the numerator
as a Python long.
3079 >>> v.numerator_as_long() + 1 == 10000000001
3082 return self.numerator().as_long()
3084 def denominator_as_long(self):
3085 """ Return the denominator
as a Python long.
3090 >>> v.denominator_as_long()
3093 return self.denominator().as_long()
3101 def is_int_value(self):
3102 return self.denominator().is_int() and self.denominator_as_long() == 1
3105 _z3_assert(self.is_int_value(), "Expected integer fraction")
3106 return self.numerator_as_long()
3108 def as_decimal(self, prec):
3109 """ Return a Z3 rational value
as a string
in decimal notation using at most `prec` decimal places.
3118 return Z3_get_numeral_decimal_string(self.ctx_ref(), self.as_ast(), prec)
3120 def as_string(self):
3121 """Return a Z3 rational numeral
as a Python string.
3127 return Z3_get_numeral_string(self.ctx_ref(), self.as_ast())
3129 def as_fraction(self):
3130 """Return a Z3 rational
as a Python Fraction object.
3136 return Fraction(self.numerator_as_long(), self.denominator_as_long())
3139 class AlgebraicNumRef(ArithRef):
3140 """Algebraic irrational values.
"""
3142 def approx(self, precision=10):
3143 """Return a Z3 rational number that approximates the algebraic number `self`.
3144 The result `r`
is such that |r - self| <= 1/10^precision
3148 6838717160008073720548335/4835703278458516698824704
3152 return RatNumRef(Z3_get_algebraic_number_upper(self.ctx_ref(), self.as_ast(), precision), self.ctx)
3154 def as_decimal(self, prec):
3155 """Return a string representation of the algebraic number `self`
in decimal notation
3156 using `prec` decimal places.
3159 >>> x.as_decimal(10)
3161 >>> x.as_decimal(20)
3162 '1.41421356237309504880?'
3164 return Z3_get_numeral_decimal_string(self.ctx_ref(), self.as_ast(), prec)
3167 return AstVector(Z3_algebraic_get_poly(self.ctx_ref(), self.as_ast()), self.ctx)
3170 return Z3_algebraic_get_i(self.ctx_ref(), self.as_ast())
3173 def _py2expr(a, ctx=None):
3174 if isinstance(a, bool):
3175 return BoolVal(a, ctx)
3177 return IntVal(a, ctx)
3178 if isinstance(a, float):
3179 return RealVal(a, ctx)
3180 if isinstance(a, str):
3181 return StringVal(a, ctx)
3185 _z3_assert(False, "Python bool, int, long or float expected")
3188 def IntSort(ctx=None):
3189 """Return the integer sort
in the given context. If `ctx=
None`, then the
global context
is used.
3202 return ArithSortRef(Z3_mk_int_sort(ctx.ref()), ctx)
3205 def RealSort(ctx=None):
3206 """Return the real sort
in the given context. If `ctx=
None`, then the
global context
is used.
3219 return ArithSortRef(Z3_mk_real_sort(ctx.ref()), ctx)
3222 def _to_int_str(val):
3223 if isinstance(val, float):
3224 return str(int(val))
3225 elif isinstance(val, bool):
3234 def IntVal(val, ctx=None):
3235 """Return a Z3 integer value. If `ctx=
None`, then the
global context
is used.
3243 return IntNumRef(Z3_mk_numeral(ctx.ref(), _to_int_str(val), IntSort(ctx).ast), ctx)
3246 def RealVal(val, ctx=None):
3247 """Return a Z3 real value.
3249 `val` may be a Python int, long, float
or string representing a number
in decimal
or rational notation.
3250 If `ctx=
None`, then the
global context
is used.
3262 return RatNumRef(Z3_mk_numeral(ctx.ref(), str(val), RealSort(ctx).ast), ctx)
3265 def RatVal(a, b, ctx=None):
3266 """Return a Z3 rational a/b.
3268 If `ctx=
None`, then the
global context
is used.
3276 _z3_assert(_is_int(a) or isinstance(a, str), "First argument cannot be converted into an integer")
3277 _z3_assert(_is_int(b) or isinstance(b, str), "Second argument cannot be converted into an integer")
3278 return simplify(RealVal(a, ctx) / RealVal(b, ctx))
3281 def Q(a, b, ctx=None):
3282 """Return a Z3 rational a/b.
3284 If `ctx=
None`, then the
global context
is used.
3291 return simplify(RatVal(a, b, ctx=ctx))
3294 def Int(name, ctx=None):
3295 """Return an integer constant named `name`. If `ctx=
None`, then the
global context
is used.
3304 return ArithRef(Z3_mk_const(ctx.ref(), to_symbol(name, ctx), IntSort(ctx).ast), ctx)
3307 def Ints(names, ctx=None):
3308 """Return a tuple of Integer constants.
3310 >>> x, y, z =
Ints(
'x y z')
3315 if isinstance(names, str):
3316 names = names.split(" ")
3317 return [Int(name, ctx) for name in names]
3320 def IntVector(prefix, sz, ctx=None):
3321 """Return a list of integer constants of size `sz`.
3330 return [Int("%s__%s" % (prefix, i), ctx) for i in range(sz)]
3333 def FreshInt(prefix="x", ctx=None):
3334 """Return a fresh integer constant
in the given context using the given prefix.
3344 return ArithRef(Z3_mk_fresh_const(ctx.ref(), prefix, IntSort(ctx).ast), ctx)
3347 def Real(name, ctx=None):
3348 """Return a real constant named `name`. If `ctx=
None`, then the
global context
is used.
3357 return ArithRef(Z3_mk_const(ctx.ref(), to_symbol(name, ctx), RealSort(ctx).ast), ctx)
3360 def Reals(names, ctx=None):
3361 """Return a tuple of real constants.
3363 >>> x, y, z =
Reals(
'x y z')
3366 >>>
Sum(x, y, z).sort()
3370 if isinstance(names, str):
3371 names = names.split(" ")
3372 return [Real(name, ctx) for name in names]
3375 def RealVector(prefix, sz, ctx=None):
3376 """Return a list of real constants of size `sz`.
3387 return [Real("%s__%s" % (prefix, i), ctx) for i in range(sz)]
3390 def FreshReal(prefix="b", ctx=None):
3391 """Return a fresh real constant
in the given context using the given prefix.
3401 return ArithRef(Z3_mk_fresh_const(ctx.ref(), prefix, RealSort(ctx).ast), ctx)
3405 """ Return the Z3 expression
ToReal(a).
3417 _z3_assert(a.is_int(), "Z3 integer expression expected.")
3419 return ArithRef(Z3_mk_int2real(ctx.ref(), a.as_ast()), ctx)
3423 """ Return the Z3 expression
ToInt(a).
3435 _z3_assert(a.is_real(), "Z3 real expression expected.")
3437 return ArithRef(Z3_mk_real2int(ctx.ref(), a.as_ast()), ctx)
3441 """ Return the Z3 predicate
IsInt(a).
3444 >>>
IsInt(x +
"1/2")
3448 >>>
solve(
IsInt(x +
"1/2"), x > 0, x < 1, x !=
"1/2")
3452 _z3_assert(a.is_real(), "Z3 real expression expected.")
3454 return BoolRef(Z3_mk_is_int(ctx.ref(), a.as_ast()), ctx)
3457 def Sqrt(a, ctx=None):
3458 """ Return a Z3 expression which represents the square root of a.
3470 def Cbrt(a, ctx=None):
3471 """ Return a Z3 expression which represents the cubic root of a.
3482 #########################################
3486 #########################################
3489 class BitVecSortRef(SortRef):
3490 """Bit-vector sort.
"""
3493 """Return the size (number of bits) of the bit-vector sort `self`.
3499 return int(Z3_get_bv_sort_size(self.ctx_ref(), self.ast))
3501 def subsort(self, other):
3502 return is_bv_sort(other) and self.size() < other.size()
3504 def cast(self, val):
3505 """Try to cast `val`
as a Bit-Vector.
3510 >>> b.cast(10).
sexpr()
3515 _z3_assert(self.ctx == val.ctx, "Context mismatch")
3516 # Idea: use sign_extend if sort of val is a bitvector of smaller size
3519 return BitVecVal(val, self)
3523 """Return
True if `s`
is a Z3 bit-vector sort.
3530 return isinstance(s, BitVecSortRef)
3533 class BitVecRef(ExprRef):
3534 """Bit-vector expressions.
"""
3537 """Return the sort of the bit-vector expression `self`.
3545 return BitVecSortRef(Z3_get_sort(self.ctx_ref(), self.as_ast()), self.ctx)
3548 """Return the number of bits of the bit-vector expression `self`.
3556 return self.sort().size()
3558 def __add__(self, other):
3559 """Create the Z3 expression `self + other`.
3568 a, b = _coerce_exprs(self, other)
3569 return BitVecRef(Z3_mk_bvadd(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
3571 def __radd__(self, other):
3572 """Create the Z3 expression `other + self`.
3578 a, b = _coerce_exprs(self, other)
3579 return BitVecRef(Z3_mk_bvadd(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
3581 def __mul__(self, other):
3582 """Create the Z3 expression `self * other`.
3591 a, b = _coerce_exprs(self, other)
3592 return BitVecRef(Z3_mk_bvmul(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
3594 def __rmul__(self, other):
3595 """Create the Z3 expression `other * self`.
3601 a, b = _coerce_exprs(self, other)
3602 return BitVecRef(Z3_mk_bvmul(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
3604 def __sub__(self, other):
3605 """Create the Z3 expression `self - other`.
3614 a, b = _coerce_exprs(self, other)
3615 return BitVecRef(Z3_mk_bvsub(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
3617 def __rsub__(self, other):
3618 """Create the Z3 expression `other - self`.
3624 a, b = _coerce_exprs(self, other)
3625 return BitVecRef(Z3_mk_bvsub(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
3627 def __or__(self, other):
3628 """Create the Z3 expression bitwise-
or `self | other`.
3637 a, b = _coerce_exprs(self, other)
3638 return BitVecRef(Z3_mk_bvor(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
3640 def __ror__(self, other):
3641 """Create the Z3 expression bitwise-
or `other | self`.
3647 a, b = _coerce_exprs(self, other)
3648 return BitVecRef(Z3_mk_bvor(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
3650 def __and__(self, other):
3651 """Create the Z3 expression bitwise-
and `self & other`.
3660 a, b = _coerce_exprs(self, other)
3661 return BitVecRef(Z3_mk_bvand(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
3663 def __rand__(self, other):
3664 """Create the Z3 expression bitwise-
or `other & self`.
3670 a, b = _coerce_exprs(self, other)
3671 return BitVecRef(Z3_mk_bvand(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
3673 def __xor__(self, other):
3674 """Create the Z3 expression bitwise-xor `self ^ other`.
3683 a, b = _coerce_exprs(self, other)
3684 return BitVecRef(Z3_mk_bvxor(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
3686 def __rxor__(self, other):
3687 """Create the Z3 expression bitwise-xor `other ^ self`.
3693 a, b = _coerce_exprs(self, other)
3694 return BitVecRef(Z3_mk_bvxor(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
3706 """Return an expression representing `-self`.
3714 return BitVecRef(Z3_mk_bvneg(self.ctx_ref(), self.as_ast()), self.ctx)
3716 def __invert__(self):
3717 """Create the Z3 expression bitwise-
not `~self`.
3725 return BitVecRef(Z3_mk_bvnot(self.ctx_ref(), self.as_ast()), self.ctx)
3727 def __div__(self, other):
3728 """Create the Z3 expression (signed) division `self / other`.
3730 Use the function
UDiv()
for unsigned division.
3743 a, b = _coerce_exprs(self, other)
3744 return BitVecRef(Z3_mk_bvsdiv(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
3746 def __truediv__(self, other):
3747 """Create the Z3 expression (signed) division `self / other`.
"""
3748 return self.__div__(other)
3750 def __rdiv__(self, other):
3751 """Create the Z3 expression (signed) division `other / self`.
3753 Use the function
UDiv()
for unsigned division.
3758 >>> (10 / x).
sexpr()
3759 '(bvsdiv #x0000000a x)'
3761 '(bvudiv #x0000000a x)'
3763 a, b = _coerce_exprs(self, other)
3764 return BitVecRef(Z3_mk_bvsdiv(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
3766 def __rtruediv__(self, other):
3767 """Create the Z3 expression (signed) division `other / self`.
"""
3768 return self.__rdiv__(other)
3770 def __mod__(self, other):
3771 """Create the Z3 expression (signed) mod `self % other`.
3773 Use the function
URem()
for unsigned remainder,
and SRem()
for signed remainder.
3788 a, b = _coerce_exprs(self, other)
3789 return BitVecRef(Z3_mk_bvsmod(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
3791 def __rmod__(self, other):
3792 """Create the Z3 expression (signed) mod `other % self`.
3794 Use the function
URem()
for unsigned remainder,
and SRem()
for signed remainder.
3799 >>> (10 % x).
sexpr()
3800 '(bvsmod #x0000000a x)'
3802 '(bvurem #x0000000a x)'
3804 '(bvsrem #x0000000a x)'
3806 a, b = _coerce_exprs(self, other)
3807 return BitVecRef(Z3_mk_bvsmod(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
3809 def __le__(self, other):
3810 """Create the Z3 expression (signed) `other <= self`.
3812 Use the function
ULE()
for unsigned less than
or equal to.
3817 >>> (x <= y).
sexpr()
3822 a, b = _coerce_exprs(self, other)
3823 return BoolRef(Z3_mk_bvsle(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
3825 def __lt__(self, other):
3826 """Create the Z3 expression (signed) `other < self`.
3828 Use the function
ULT()
for unsigned less than.
3838 a, b = _coerce_exprs(self, other)
3839 return BoolRef(Z3_mk_bvslt(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
3841 def __gt__(self, other):
3842 """Create the Z3 expression (signed) `other > self`.
3844 Use the function
UGT()
for unsigned greater than.
3854 a, b = _coerce_exprs(self, other)
3855 return BoolRef(Z3_mk_bvsgt(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
3857 def __ge__(self, other):
3858 """Create the Z3 expression (signed) `other >= self`.
3860 Use the function
UGE()
for unsigned greater than
or equal to.
3865 >>> (x >= y).
sexpr()
3870 a, b = _coerce_exprs(self, other)
3871 return BoolRef(Z3_mk_bvsge(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
3873 def __rshift__(self, other):
3874 """Create the Z3 expression (arithmetical) right shift `self >> other`
3876 Use the function
LShR()
for the right logical shift
3881 >>> (x >> y).
sexpr()
3900 a, b = _coerce_exprs(self, other)
3901 return BitVecRef(Z3_mk_bvashr(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
3903 def __lshift__(self, other):
3904 """Create the Z3 expression left shift `self << other`
3909 >>> (x << y).
sexpr()
3914 a, b = _coerce_exprs(self, other)
3915 return BitVecRef(Z3_mk_bvshl(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
3917 def __rrshift__(self, other):
3918 """Create the Z3 expression (arithmetical) right shift `other` >> `self`.
3920 Use the function
LShR()
for the right logical shift
3925 >>> (10 >> x).
sexpr()
3926 '(bvashr #x0000000a x)'
3928 a, b = _coerce_exprs(self, other)
3929 return BitVecRef(Z3_mk_bvashr(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
3931 def __rlshift__(self, other):
3932 """Create the Z3 expression left shift `other << self`.
3934 Use the function
LShR()
for the right logical shift
3939 >>> (10 << x).
sexpr()
3940 '(bvshl #x0000000a x)'
3942 a, b = _coerce_exprs(self, other)
3943 return BitVecRef(Z3_mk_bvshl(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
3946 class BitVecNumRef(BitVecRef):
3947 """Bit-vector values.
"""
3950 """Return a Z3 bit-vector numeral
as a Python long (bignum) numeral.
3955 >>> print(
"0x%.8x" % v.as_long())
3958 return int(self.as_string())
3960 def as_signed_long(self):
3961 """Return a Z3 bit-vector numeral
as a Python long (bignum) numeral.
3962 The most significant bit
is assumed to be the sign.
3976 val = self.as_long()
3977 if val >= 2**(sz - 1):
3979 if val < -2**(sz - 1):
3983 def as_string(self):
3984 return Z3_get_numeral_string(self.ctx_ref(), self.as_ast())
3986 def as_binary_string(self):
3987 return Z3_get_numeral_binary_string(self.ctx_ref(), self.as_ast())
3991 """Return `
True`
if `a`
is a Z3 bit-vector expression.
4001 return isinstance(a, BitVecRef)
4005 """Return `
True`
if `a`
is a Z3 bit-vector numeral value.
4016 return is_bv(a) and _is_numeral(a.ctx, a.as_ast())
4019 def BV2Int(a, is_signed=False):
4020 """Return the Z3 expression
BV2Int(a).
4028 >>> x >
BV2Int(b, is_signed=
False)
4030 >>> x >
BV2Int(b, is_signed=
True)
4036 _z3_assert(is_bv(a), "First argument must be a Z3 bit-vector expression")
4038 # investigate problem with bv2int
4039 return ArithRef(Z3_mk_bv2int(ctx.ref(), a.as_ast(), is_signed), ctx)
4042 def Int2BV(a, num_bits):
4043 """Return the z3 expression
Int2BV(a, num_bits).
4044 It
is a bit-vector of width num_bits
and represents the
4045 modulo of a by 2^num_bits
4048 return BitVecRef(Z3_mk_int2bv(ctx.ref(), num_bits, a.as_ast()), ctx)
4051 def BitVecSort(sz, ctx=None):
4052 """Return a Z3 bit-vector sort of the given size. If `ctx=
None`, then the
global context
is used.
4058 >>> x =
Const(
'x', Byte)
4063 return BitVecSortRef(Z3_mk_bv_sort(ctx.ref(), sz), ctx)
4066 def BitVecVal(val, bv, ctx=None):
4067 """Return a bit-vector value with the given number of bits. If `ctx=
None`, then the
global context
is used.
4072 >>> print(
"0x%.8x" % v.as_long())
4077 return BitVecNumRef(Z3_mk_numeral(ctx.ref(), _to_int_str(val), bv.ast), ctx)
4080 return BitVecNumRef(Z3_mk_numeral(ctx.ref(), _to_int_str(val), BitVecSort(bv, ctx).ast), ctx)
4083 def BitVec(name, bv, ctx=None):
4084 """Return a bit-vector constant named `name`. `bv` may be the number of bits of a bit-vector sort.
4085 If `ctx=
None`, then the
global context
is used.
4095 >>> x2 =
BitVec(
'x', word)
4099 if isinstance(bv, BitVecSortRef):
4103 bv = BitVecSort(bv, ctx)
4104 return BitVecRef(Z3_mk_const(ctx.ref(), to_symbol(name, ctx), bv.ast), ctx)
4107 def BitVecs(names, bv, ctx=None):
4108 """Return a tuple of bit-vector constants of size bv.
4110 >>> x, y, z =
BitVecs(
'x y z', 16)
4123 if isinstance(names, str):
4124 names = names.split(" ")
4125 return [BitVec(name, bv, ctx) for name in names]
4129 """Create a Z3 bit-vector concatenation expression.
4139 args = _get_args(args)
4142 _z3_assert(sz >= 2, "At least two arguments expected.")
4149 if is_seq(args[0]) or isinstance(args[0], str):
4150 args = [_coerce_seq(s, ctx) for s in args]
4152 _z3_assert(all([is_seq(a) for a in args]), "All arguments must be sequence expressions.")
4155 v[i] = args[i].as_ast()
4156 return SeqRef(Z3_mk_seq_concat(ctx.ref(), sz, v), ctx)
4160 _z3_assert(all([is_re(a) for a in args]), "All arguments must be regular expressions.")
4163 v[i] = args[i].as_ast()
4164 return ReRef(Z3_mk_re_concat(ctx.ref(), sz, v), ctx)
4167 _z3_assert(all([is_bv(a) for a in args]), "All arguments must be Z3 bit-vector expressions.")
4169 for i in range(sz - 1):
4170 r = BitVecRef(Z3_mk_concat(ctx.ref(), r.as_ast(), args[i + 1].as_ast()), ctx)
4174 def Extract(high, low, a):
4175 """Create a Z3 bit-vector extraction expression.
4176 Extract
is overloaded to also work on sequence extraction.
4177 The functions SubString
and SubSeq are redirected to Extract.
4178 For this case, the arguments are reinterpreted
as:
4179 high -
is a sequence (string)
4181 a -
is the length to be extracted
4191 if isinstance(high, str):
4192 high = StringVal(high)
4195 offset, length = _coerce_exprs(low, a, s.ctx)
4196 return SeqRef(Z3_mk_seq_extract(s.ctx_ref(), s.as_ast(), offset.as_ast(), length.as_ast()), s.ctx)
4198 _z3_assert(low <= high, "First argument must be greater than or equal to second argument")
4199 _z3_assert(_is_int(high) and high >= 0 and _is_int(low) and low >= 0,
4200 "First and second arguments must be non negative integers")
4201 _z3_assert(is_bv(a), "Third argument must be a Z3 bit-vector expression")
4202 return BitVecRef(Z3_mk_extract(a.ctx_ref(), high, low, a.as_ast()), a.ctx)
4205 def _check_bv_args(a, b):
4207 _z3_assert(is_bv(a) or is_bv(b), "First or second argument must be a Z3 bit-vector expression")
4211 """Create the Z3 expression (unsigned) `other <= self`.
4213 Use the operator <=
for signed less than
or equal to.
4218 >>> (x <= y).sexpr()
4220 >>>
ULE(x, y).sexpr()
4223 _check_bv_args(a, b)
4224 a, b = _coerce_exprs(a, b)
4225 return BoolRef(Z3_mk_bvule(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
4229 """Create the Z3 expression (unsigned) `other < self`.
4231 Use the operator <
for signed less than.
4238 >>>
ULT(x, y).sexpr()
4241 _check_bv_args(a, b)
4242 a, b = _coerce_exprs(a, b)
4243 return BoolRef(Z3_mk_bvult(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
4247 """Create the Z3 expression (unsigned) `other >= self`.
4249 Use the operator >=
for signed greater than
or equal to.
4254 >>> (x >= y).sexpr()
4256 >>>
UGE(x, y).sexpr()
4259 _check_bv_args(a, b)
4260 a, b = _coerce_exprs(a, b)
4261 return BoolRef(Z3_mk_bvuge(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
4265 """Create the Z3 expression (unsigned) `other > self`.
4267 Use the operator >
for signed greater than.
4274 >>>
UGT(x, y).sexpr()
4277 _check_bv_args(a, b)
4278 a, b = _coerce_exprs(a, b)
4279 return BoolRef(Z3_mk_bvugt(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
4283 """Create the Z3 expression (unsigned) division `self / other`.
4285 Use the operator /
for signed division.
4291 >>>
UDiv(x, y).sort()
4295 >>>
UDiv(x, y).sexpr()
4298 _check_bv_args(a, b)
4299 a, b = _coerce_exprs(a, b)
4300 return BitVecRef(Z3_mk_bvudiv(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
4304 """Create the Z3 expression (unsigned) remainder `self % other`.
4306 Use the operator %
for signed modulus,
and SRem()
for signed remainder.
4312 >>>
URem(x, y).sort()
4316 >>>
URem(x, y).sexpr()
4319 _check_bv_args(a, b)
4320 a, b = _coerce_exprs(a, b)
4321 return BitVecRef(Z3_mk_bvurem(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
4325 """Create the Z3 expression signed remainder.
4327 Use the operator %
for signed modulus,
and URem()
for unsigned remainder.
4333 >>>
SRem(x, y).sort()
4337 >>>
SRem(x, y).sexpr()
4340 _check_bv_args(a, b)
4341 a, b = _coerce_exprs(a, b)
4342 return BitVecRef(Z3_mk_bvsrem(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
4346 """Create the Z3 expression logical right shift.
4348 Use the operator >>
for the arithmetical right shift.
4353 >>> (x >> y).sexpr()
4355 >>>
LShR(x, y).sexpr()
4372 _check_bv_args(a, b)
4373 a, b = _coerce_exprs(a, b)
4374 return BitVecRef(Z3_mk_bvlshr(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
4377 def RotateLeft(a, b):
4378 """Return an expression representing `a` rotated to the left `b` times.
4388 _check_bv_args(a, b)
4389 a, b = _coerce_exprs(a, b)
4390 return BitVecRef(Z3_mk_ext_rotate_left(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
4393 def RotateRight(a, b):
4394 """Return an expression representing `a` rotated to the right `b` times.
4404 _check_bv_args(a, b)
4405 a, b = _coerce_exprs(a, b)
4406 return BitVecRef(Z3_mk_ext_rotate_right(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
4410 """Return a bit-vector expression with `n` extra sign-bits.
4430 >>> print(
"%.x" % v.as_long())
4434 _z3_assert(_is_int(n), "First argument must be an integer")
4435 _z3_assert(is_bv(a), "Second argument must be a Z3 bit-vector expression")
4436 return BitVecRef(Z3_mk_sign_ext(a.ctx_ref(), n, a.as_ast()), a.ctx)
4440 """Return a bit-vector expression with `n` extra zero-bits.
4462 _z3_assert(_is_int(n), "First argument must be an integer")
4463 _z3_assert(is_bv(a), "Second argument must be a Z3 bit-vector expression")
4464 return BitVecRef(Z3_mk_zero_ext(a.ctx_ref(), n, a.as_ast()), a.ctx)
4467 def RepeatBitVec(n, a):
4468 """Return an expression representing `n` copies of `a`.
4477 >>> print(
"%.x" % v0.as_long())
4482 >>> print(
"%.x" % v.as_long())
4486 _z3_assert(_is_int(n), "First argument must be an integer")
4487 _z3_assert(is_bv(a), "Second argument must be a Z3 bit-vector expression")
4488 return BitVecRef(Z3_mk_repeat(a.ctx_ref(), n, a.as_ast()), a.ctx)
4492 """Return the reduction-
and expression of `a`.
"""
4494 _z3_assert(is_bv(a), "First argument must be a Z3 bit-vector expression")
4495 return BitVecRef(Z3_mk_bvredand(a.ctx_ref(), a.as_ast()), a.ctx)
4499 """Return the reduction-
or expression of `a`.
"""
4501 _z3_assert(is_bv(a), "First argument must be a Z3 bit-vector expression")
4502 return BitVecRef(Z3_mk_bvredor(a.ctx_ref(), a.as_ast()), a.ctx)
4505 def BVAddNoOverflow(a, b, signed):
4506 """A predicate the determines that bit-vector addition does
not overflow
"""
4507 _check_bv_args(a, b)
4508 a, b = _coerce_exprs(a, b)
4509 return BoolRef(Z3_mk_bvadd_no_overflow(a.ctx_ref(), a.as_ast(), b.as_ast(), signed), a.ctx)
4512 def BVAddNoUnderflow(a, b):
4513 """A predicate the determines that signed bit-vector addition does
not underflow
"""
4514 _check_bv_args(a, b)
4515 a, b = _coerce_exprs(a, b)
4516 return BoolRef(Z3_mk_bvadd_no_underflow(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
4519 def BVSubNoOverflow(a, b):
4520 """A predicate the determines that bit-vector subtraction does
not overflow
"""
4521 _check_bv_args(a, b)
4522 a, b = _coerce_exprs(a, b)
4523 return BoolRef(Z3_mk_bvsub_no_overflow(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
4526 def BVSubNoUnderflow(a, b, signed):
4527 """A predicate the determines that bit-vector subtraction does
not underflow
"""
4528 _check_bv_args(a, b)
4529 a, b = _coerce_exprs(a, b)
4530 return BoolRef(Z3_mk_bvsub_no_underflow(a.ctx_ref(), a.as_ast(), b.as_ast(), signed), a.ctx)
4533 def BVSDivNoOverflow(a, b):
4534 """A predicate the determines that bit-vector signed division does
not overflow
"""
4535 _check_bv_args(a, b)
4536 a, b = _coerce_exprs(a, b)
4537 return BoolRef(Z3_mk_bvsdiv_no_overflow(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
4540 def BVSNegNoOverflow(a):
4541 """A predicate the determines that bit-vector unary negation does
not overflow
"""
4543 _z3_assert(is_bv(a), "First argument must be a Z3 bit-vector expression")
4544 return BoolRef(Z3_mk_bvneg_no_overflow(a.ctx_ref(), a.as_ast()), a.ctx)
4547 def BVMulNoOverflow(a, b, signed):
4548 """A predicate the determines that bit-vector multiplication does
not overflow
"""
4549 _check_bv_args(a, b)
4550 a, b = _coerce_exprs(a, b)
4551 return BoolRef(Z3_mk_bvmul_no_overflow(a.ctx_ref(), a.as_ast(), b.as_ast(), signed), a.ctx)
4554 def BVMulNoUnderflow(a, b):
4555 """A predicate the determines that bit-vector signed multiplication does
not underflow
"""
4556 _check_bv_args(a, b)
4557 a, b = _coerce_exprs(a, b)
4558 return BoolRef(Z3_mk_bvmul_no_underflow(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
4561 #########################################
4565 #########################################
4567 class ArraySortRef(SortRef):
4571 """Return the domain of the array sort `self`.
4577 return _to_sort_ref(Z3_get_array_sort_domain(self.ctx_ref(), self.ast), self.ctx)
4579 def domain_n(self, i):
4580 """Return the domain of the array sort `self`.
4582 return _to_sort_ref(Z3_get_array_sort_domain_n(self.ctx_ref(), self.ast, i), self.ctx)
4585 """Return the range of the array sort `self`.
4591 return _to_sort_ref(Z3_get_array_sort_range(self.ctx_ref(), self.ast), self.ctx)
4594 class ArrayRef(ExprRef):
4595 """Array expressions.
"""
4598 """Return the array sort of the array expression `self`.
4604 return ArraySortRef(Z3_get_sort(self.ctx_ref(), self.as_ast()), self.ctx)
4613 return self.sort().domain()
4615 def domain_n(self, i):
4617 return self.sort().domain_n(i)
4626 return self.sort().range()
4628 def __getitem__(self, arg):
4629 """Return the Z3 expression `self[arg]`.
4638 return _array_select(self, arg)
4641 return _to_expr_ref(Z3_mk_array_default(self.ctx_ref(), self.as_ast()), self.ctx)
4644 def _array_select(ar, arg):
4645 if isinstance(arg, tuple):
4646 args = [ar.sort().domain_n(i).cast(arg[i]) for i in range(len(arg))]
4647 _args, sz = _to_ast_array(args)
4648 return _to_expr_ref(Z3_mk_select_n(ar.ctx_ref(), ar.as_ast(), sz, _args), ar.ctx)
4649 arg = ar.sort().domain().cast(arg)
4650 return _to_expr_ref(Z3_mk_select(ar.ctx_ref(), ar.as_ast(), arg.as_ast()), ar.ctx)
4653 def is_array_sort(a):
4654 return Z3_get_sort_kind(a.ctx.ref(), Z3_get_sort(a.ctx.ref(), a.ast)) == Z3_ARRAY_SORT
4658 """Return `
True`
if `a`
is a Z3 array expression.
4668 return isinstance(a, ArrayRef)
4671 def is_const_array(a):
4672 """Return `
True`
if `a`
is a Z3 constant array.
4681 return is_app_of(a, Z3_OP_CONST_ARRAY)
4685 """Return `
True`
if `a`
is a Z3 constant array.
4694 return is_app_of(a, Z3_OP_CONST_ARRAY)
4698 """Return `
True`
if `a`
is a Z3 map array expression.
4710 return is_app_of(a, Z3_OP_ARRAY_MAP)
4714 """Return `
True`
if `a`
is a Z3 default array expression.
4719 return is_app_of(a, Z3_OP_ARRAY_DEFAULT)
4722 def get_map_func(a):
4723 """Return the function declaration associated with a Z3 map array expression.
4736 _z3_assert(is_map(a), "Z3 array map expression expected.")
4740 Z3_get_decl_ast_parameter(a.ctx_ref(), a.decl().ast, 0),
4746 def ArraySort(*sig):
4747 """Return the Z3 array sort with the given domain
and range sorts.
4760 sig = _get_args(sig)
4762 _z3_assert(len(sig) > 1, "At least two arguments expected")
4763 arity = len(sig) - 1
4768 _z3_assert(is_sort(s), "Z3 sort expected")
4769 _z3_assert(s.ctx == r.ctx, "Context mismatch")
4772 return ArraySortRef(Z3_mk_array_sort(ctx.ref(), d.ast, r.ast), ctx)
4773 dom = (Sort * arity)()
4774 for i in range(arity):
4776 return ArraySortRef(Z3_mk_array_sort_n(ctx.ref(), arity, dom, r.ast), ctx)
4779 def Array(name, *sorts):
4780 """Return an array constant named `name` with the given domain
and range sorts.
4788 s = ArraySort(sorts)
4790 return ArrayRef(Z3_mk_const(ctx.ref(), to_symbol(name, ctx), s.ast), ctx)
4793 def Update(a, *args):
4794 """Return a Z3 store array expression.
4797 >>> i, v =
Ints(
'i v')
4801 >>>
prove(s[i] == v)
4808 _z3_assert(is_array_sort(a), "First argument must be a Z3 array expression")
4809 args = _get_args(args)
4812 raise Z3Exception("array update requires index and value arguments")
4816 i = a.sort().domain().cast(i)
4817 v = a.sort().range().cast(v)
4818 return _to_expr_ref(Z3_mk_store(ctx.ref(), a.as_ast(), i.as_ast(), v.as_ast()), ctx)
4819 v = a.sort().range().cast(args[-1])
4820 idxs = [a.sort().domain_n(i).cast(args[i]) for i in range(len(args)-1)]
4821 _args, sz = _to_ast_array(idxs)
4822 return _to_expr_ref(Z3_mk_store_n(ctx.ref(), a.as_ast(), sz, _args, v.as_ast()), ctx)
4826 """ Return a default value
for array expression.
4832 _z3_assert(is_array_sort(a), "First argument must be a Z3 array expression")
4836 def Store(a, *args):
4837 """Return a Z3 store array expression.
4840 >>> i, v =
Ints(
'i v')
4841 >>> s =
Store(a, i, v)
4844 >>>
prove(s[i] == v)
4850 return Update(a, args)
4853 def Select(a, *args):
4854 """Return a Z3 select array expression.
4863 args = _get_args(args)
4865 _z3_assert(is_array_sort(a), "First argument must be a Z3 array expression")
4870 """Return a Z3 map array expression.
4875 >>> b =
Map(f, a1, a2)
4878 >>>
prove(b[0] == f(a1[0], a2[0]))
4881 args = _get_args(args)
4883 _z3_assert(len(args) > 0, "At least one Z3 array expression expected")
4884 _z3_assert(is_func_decl(f), "First argument must be a Z3 function declaration")
4885 _z3_assert(all([is_array(a) for a in args]), "Z3 array expected expected")
4886 _z3_assert(len(args) == f.arity(), "Number of arguments mismatch")
4887 _args, sz = _to_ast_array(args)
4889 return ArrayRef(Z3_mk_map(ctx.ref(), f.ast, sz, _args), ctx)
4893 """Return a Z3 constant array expression.
4907 _z3_assert(is_sort(dom), "Z3 sort expected")
4910 v = _py2expr(v, ctx)
4911 return ArrayRef(Z3_mk_const_array(ctx.ref(), dom.ast, v.as_ast()), ctx)
4915 """Return extensionality index
for one-dimensional arrays.
4922 _z3_assert(is_array_sort(a) and (is_array(b) or b.is_lambda()), "arguments must be arrays")
4923 return _to_expr_ref(Z3_mk_array_ext(ctx.ref(), a.as_ast(), b.as_ast()), ctx)
4926 def SetHasSize(a, k):
4928 k = _py2expr(k, ctx)
4929 return _to_expr_ref(Z3_mk_set_has_size(ctx.ref(), a.as_ast(), k.as_ast()), ctx)
4933 """Return `
True`
if `a`
is a Z3 array select application.
4942 return is_app_of(a, Z3_OP_SELECT)
4946 """Return `
True`
if `a`
is a Z3 array store application.
4954 return is_app_of(a, Z3_OP_STORE)
4956 #########################################
4960 #########################################
4964 """ Create a set sort over element sort s
"""
4965 return ArraySort(s, BoolSort())
4969 """Create the empty set
4974 return ArrayRef(Z3_mk_empty_set(ctx.ref(), s.ast), ctx)
4978 """Create the full set
4983 return ArrayRef(Z3_mk_full_set(ctx.ref(), s.ast), ctx)
4986 def SetUnion(*args):
4987 """ Take the union of sets
4993 args = _get_args(args)
4994 ctx = _ctx_from_ast_arg_list(args)
4995 _args, sz = _to_ast_array(args)
4996 return ArrayRef(Z3_mk_set_union(ctx.ref(), sz, _args), ctx)
4999 def SetIntersect(*args):
5000 """ Take the union of sets
5006 args = _get_args(args)
5007 ctx = _ctx_from_ast_arg_list(args)
5008 _args, sz = _to_ast_array(args)
5009 return ArrayRef(Z3_mk_set_intersect(ctx.ref(), sz, _args), ctx)
5013 """ Add element e to set s
5018 ctx = _ctx_from_ast_arg_list([s, e])
5019 e = _py2expr(e, ctx)
5020 return ArrayRef(Z3_mk_set_add(ctx.ref(), s.as_ast(), e.as_ast()), ctx)
5024 """ Remove element e to set s
5029 ctx = _ctx_from_ast_arg_list([s, e])
5030 e = _py2expr(e, ctx)
5031 return ArrayRef(Z3_mk_set_del(ctx.ref(), s.as_ast(), e.as_ast()), ctx)
5034 def SetComplement(s):
5035 """ The complement of set s
5041 return ArrayRef(Z3_mk_set_complement(ctx.ref(), s.as_ast()), ctx)
5044 def SetDifference(a, b):
5045 """ The set difference of a
and b
5051 ctx = _ctx_from_ast_arg_list([a, b])
5052 return ArrayRef(Z3_mk_set_difference(ctx.ref(), a.as_ast(), b.as_ast()), ctx)
5056 """ Check
if e
is a member of set s
5061 ctx = _ctx_from_ast_arg_list([s, e])
5062 e = _py2expr(e, ctx)
5063 return BoolRef(Z3_mk_set_member(ctx.ref(), e.as_ast(), s.as_ast()), ctx)
5067 """ Check
if a
is a subset of b
5073 ctx = _ctx_from_ast_arg_list([a, b])
5074 return BoolRef(Z3_mk_set_subset(ctx.ref(), a.as_ast(), b.as_ast()), ctx)
5077 #########################################
5081 #########################################
5083 def _valid_accessor(acc):
5084 """Return `
True`
if acc
is pair of the form (String, Datatype
or Sort).
"""
5085 if not isinstance(acc, tuple):
5089 return isinstance(acc[0], str) and (isinstance(acc[1], Datatype) or is_sort(acc[1]))
5093 """Helper
class for declaring Z3 datatypes.
5096 >>> List.declare(
'cons', (
'car',
IntSort()), (
'cdr', List))
5097 >>> List.declare(
'nil')
5098 >>> List = List.create()
5102 >>> List.cons(10, List.nil)
5104 >>> List.cons(10, List.nil).sort()
5106 >>> cons = List.cons
5110 >>> n = cons(1, cons(0, nil))
5112 cons(1, cons(0, nil))
5119 def __init__(self, name, ctx=None):
5120 self.ctx = _get_ctx(ctx)
5122 self.constructors = []
5124 def __deepcopy__(self, memo={}):
5125 r = Datatype(self.name, self.ctx)
5126 r.constructors = copy.deepcopy(self.constructors)
5129 def declare_core(self, name, rec_name, *args):
5131 _z3_assert(isinstance(name, str), "String expected")
5132 _z3_assert(isinstance(rec_name, str), "String expected")
5134 all([_valid_accessor(a) for a in args]),
5135 "Valid list of accessors expected. An accessor is a pair of the form (String, Datatype|Sort)",
5137 self.constructors.append((name, rec_name, args))
5139 def declare(self, name, *args):
5140 """Declare constructor named `name` with the given accessors `args`.
5141 Each accessor
is a pair `(name, sort)`, where `name`
is a string
and `sort` a Z3 sort
5142 or a reference to the datatypes being declared.
5144 In the following example `List.declare(
'cons', (
'car',
IntSort()), (
'cdr', List))`
5145 declares the constructor named `cons` that builds a new List using an integer
and a List.
5146 It also declares the accessors `car`
and `cdr`. The accessor `car` extracts the integer
5147 of a `cons` cell,
and `cdr` the list of a `cons` cell. After all constructors were declared,
5148 we use the method
create() to create the actual datatype
in Z3.
5151 >>> List.declare(
'cons', (
'car',
IntSort()), (
'cdr', List))
5152 >>> List.declare(
'nil')
5153 >>> List = List.create()
5156 _z3_assert(isinstance(name, str), "String expected")
5157 _z3_assert(name != "", "Constructor name cannot be empty")
5158 return self.declare_core(name, "is-" + name, *args)
5161 return "Datatype(%s, %s)" % (self.name, self.constructors)
5164 """Create a Z3 datatype based on the constructors declared using the method `
declare()`.
5166 The function `
CreateDatatypes()` must be used to define mutually recursive datatypes.
5169 >>> List.declare(
'cons', (
'car',
IntSort()), (
'cdr', List))
5170 >>> List.declare(
'nil')
5171 >>> List = List.create()
5174 >>> List.cons(10, List.nil)
5177 return CreateDatatypes([self])[0]
5180 class ScopedConstructor:
5181 """Auxiliary object used to create Z3 datatypes.
"""
5183 def __init__(self, c, ctx):
5188 if self.ctx.ref() is not None and Z3_del_constructor is not None:
5189 Z3_del_constructor(self.ctx.ref(), self.c)
5192 class ScopedConstructorList:
5193 """Auxiliary object used to create Z3 datatypes.
"""
5195 def __init__(self, c, ctx):
5200 if self.ctx.ref() is not None and Z3_del_constructor_list is not None:
5201 Z3_del_constructor_list(self.ctx.ref(), self.c)
5204 def CreateDatatypes(*ds):
5205 """Create mutually recursive Z3 datatypes using 1
or more Datatype helper objects.
5207 In the following example we define a Tree-List using two mutually recursive datatypes.
5209 >>> TreeList =
Datatype(
'TreeList')
5212 >>> Tree.declare(
'leaf', (
'val',
IntSort()))
5214 >>> Tree.declare(
'node', (
'children', TreeList))
5215 >>> TreeList.declare(
'nil')
5216 >>> TreeList.declare(
'cons', (
'car', Tree), (
'cdr', TreeList))
5218 >>> Tree.val(Tree.leaf(10))
5220 >>>
simplify(Tree.val(Tree.leaf(10)))
5222 >>> n1 = Tree.node(TreeList.cons(Tree.leaf(10), TreeList.cons(Tree.leaf(20), TreeList.nil)))
5224 node(cons(leaf(10), cons(leaf(20), nil)))
5225 >>> n2 = Tree.node(TreeList.cons(n1, TreeList.nil))
5228 >>>
simplify(TreeList.car(Tree.children(n2)) == n1)
5233 _z3_assert(len(ds) > 0, "At least one Datatype must be specified")
5234 _z3_assert(all([isinstance(d, Datatype) for d in ds]), "Arguments must be Datatypes")
5235 _z3_assert(all([d.ctx == ds[0].ctx for d in ds]), "Context mismatch")
5236 _z3_assert(all([d.constructors != [] for d in ds]), "Non-empty Datatypes expected")
5239 names = (Symbol * num)()
5240 out = (Sort * num)()
5241 clists = (ConstructorList * num)()
5243 for i in range(num):
5245 names[i] = to_symbol(d.name, ctx)
5246 num_cs = len(d.constructors)
5247 cs = (Constructor * num_cs)()
5248 for j in range(num_cs):
5249 c = d.constructors[j]
5250 cname = to_symbol(c[0], ctx)
5251 rname = to_symbol(c[1], ctx)
5254 fnames = (Symbol * num_fs)()
5255 sorts = (Sort * num_fs)()
5256 refs = (ctypes.c_uint * num_fs)()
5257 for k in range(num_fs):
5260 fnames[k] = to_symbol(fname, ctx)
5261 if isinstance(ftype, Datatype):
5264 ds.count(ftype) == 1,
5265 "One and only one occurrence of each datatype is expected",
5268 refs[k] = ds.index(ftype)
5271 _z3_assert(is_sort(ftype), "Z3 sort expected")
5272 sorts[k] = ftype.ast
5274 cs[j] = Z3_mk_constructor(ctx.ref(), cname, rname, num_fs, fnames, sorts, refs)
5275 to_delete.append(ScopedConstructor(cs[j], ctx))
5276 clists[i] = Z3_mk_constructor_list(ctx.ref(), num_cs, cs)
5277 to_delete.append(ScopedConstructorList(clists[i], ctx))
5278 Z3_mk_datatypes(ctx.ref(), num, names, out, clists)
5280 # Create a field for every constructor, recognizer and accessor
5281 for i in range(num):
5282 dref = DatatypeSortRef(out[i], ctx)
5283 num_cs = dref.num_constructors()
5284 for j in range(num_cs):
5285 cref = dref.constructor(j)
5286 cref_name = cref.name()
5287 cref_arity = cref.arity()
5288 if cref.arity() == 0:
5290 setattr(dref, cref_name, cref)
5291 rref = dref.recognizer(j)
5292 setattr(dref, "is_" + cref_name, rref)
5293 for k in range(cref_arity):
5294 aref = dref.accessor(j, k)
5295 setattr(dref, aref.name(), aref)
5297 return tuple(result)
5300 class DatatypeSortRef(SortRef):
5301 """Datatype sorts.
"""
5303 def num_constructors(self):
5304 """Return the number of constructors
in the given Z3 datatype.
5307 >>> List.declare(
'cons', (
'car',
IntSort()), (
'cdr', List))
5308 >>> List.declare(
'nil')
5309 >>> List = List.create()
5311 >>> List.num_constructors()
5314 return int(Z3_get_datatype_sort_num_constructors(self.ctx_ref(), self.ast))
5316 def constructor(self, idx):
5317 """Return a constructor of the datatype `self`.
5320 >>> List.declare(
'cons', (
'car',
IntSort()), (
'cdr', List))
5321 >>> List.declare(
'nil')
5322 >>> List = List.create()
5324 >>> List.num_constructors()
5326 >>> List.constructor(0)
5328 >>> List.constructor(1)
5332 _z3_assert(idx < self.num_constructors(), "Invalid constructor index")
5333 return FuncDeclRef(Z3_get_datatype_sort_constructor(self.ctx_ref(), self.ast, idx), self.ctx)
5335 def recognizer(self, idx):
5336 """In Z3, each constructor has an associated recognizer predicate.
5338 If the constructor
is named `name`, then the recognizer `is_name`.
5341 >>> List.declare(
'cons', (
'car',
IntSort()), (
'cdr', List))
5342 >>> List.declare(
'nil')
5343 >>> List = List.create()
5345 >>> List.num_constructors()
5347 >>> List.recognizer(0)
5349 >>> List.recognizer(1)
5351 >>>
simplify(List.is_nil(List.cons(10, List.nil)))
5353 >>>
simplify(List.is_cons(List.cons(10, List.nil)))
5355 >>> l =
Const(
'l', List)
5360 _z3_assert(idx < self.num_constructors(), "Invalid recognizer index")
5361 return FuncDeclRef(Z3_get_datatype_sort_recognizer(self.ctx_ref(), self.ast, idx), self.ctx)
5363 def accessor(self, i, j):
5364 """In Z3, each constructor has 0
or more accessor.
5365 The number of accessors
is equal to the arity of the constructor.
5368 >>> List.declare(
'cons', (
'car',
IntSort()), (
'cdr', List))
5369 >>> List.declare(
'nil')
5370 >>> List = List.create()
5371 >>> List.num_constructors()
5373 >>> List.constructor(0)
5375 >>> num_accs = List.constructor(0).arity()
5378 >>> List.accessor(0, 0)
5380 >>> List.accessor(0, 1)
5382 >>> List.constructor(1)
5384 >>> num_accs = List.constructor(1).arity()
5389 _z3_assert(i < self.num_constructors(), "Invalid constructor index")
5390 _z3_assert(j < self.constructor(i).arity(), "Invalid accessor index")
5392 Z3_get_datatype_sort_constructor_accessor(self.ctx_ref(), self.ast, i, j),
5397 class DatatypeRef(ExprRef):
5398 """Datatype expressions.
"""
5401 """Return the datatype sort of the datatype expression `self`.
"""
5402 return DatatypeSortRef(Z3_get_sort(self.ctx_ref(), self.as_ast()), self.ctx)
5404 def DatatypeSort(name, ctx = None):
5405 """Create a reference to a sort that was declared,
or will be declared,
as a recursive datatype
"""
5407 return DatatypeSortRef(Z3_mk_datatype_sort(ctx.ref(), to_symbol(name, ctx)), ctx)
5409 def TupleSort(name, sorts, ctx=None):
5410 """Create a named tuple sort base on a set of underlying sorts
5414 tuple = Datatype(name, ctx)
5415 projects = [("project%d" % i, sorts[i]) for i in range(len(sorts))]
5416 tuple.declare(name, *projects)
5417 tuple = tuple.create()
5418 return tuple, tuple.constructor(0), [tuple.accessor(0, i) for i in range(len(sorts))]
5421 def DisjointSum(name, sorts, ctx=None):
5422 """Create a named tagged union sort base on a set of underlying sorts
5426 sum = Datatype(name, ctx)
5427 for i in range(len(sorts)):
5428 sum.declare("inject%d" % i, ("project%d" % i, sorts[i]))
5430 return sum, [(sum.constructor(i), sum.accessor(i, 0)) for i in range(len(sorts))]
5433 def EnumSort(name, values, ctx=None):
5434 """Return a new enumeration sort named `name` containing the given values.
5436 The result
is a pair (sort, list of constants).
5438 >>> Color, (red, green, blue) =
EnumSort(
'Color', [
'red',
'green',
'blue'])
5441 _z3_assert(isinstance(name, str), "Name must be a string")
5442 _z3_assert(all([isinstance(v, str) for v in values]), "Enumeration sort values must be strings")
5443 _z3_assert(len(values) > 0, "At least one value expected")
5446 _val_names = (Symbol * num)()
5447 for i in range(num):
5448 _val_names[i] = to_symbol(values[i])
5449 _values = (FuncDecl * num)()
5450 _testers = (FuncDecl * num)()
5451 name = to_symbol(name)
5452 S = DatatypeSortRef(Z3_mk_enumeration_sort(ctx.ref(), name, num, _val_names, _values, _testers), ctx)
5454 for i in range(num):
5455 V.append(FuncDeclRef(_values[i], ctx))
5456 V = [a() for a in V]
5459 #########################################
5463 #########################################
5467 """Set of parameters used to configure Solvers, Tactics
and Simplifiers
in Z3.
5469 Consider using the function `args2params` to create instances of this object.
5472 def __init__(self, ctx=None, params=None):
5473 self.ctx = _get_ctx(ctx)
5475 self.params = Z3_mk_params(self.ctx.ref())
5477 self.params = params
5478 Z3_params_inc_ref(self.ctx.ref(), self.params)
5480 def __deepcopy__(self, memo={}):
5481 return ParamsRef(self.ctx, self.params)
5484 if self.ctx.ref() is not None and Z3_params_dec_ref is not None:
5485 Z3_params_dec_ref(self.ctx.ref(), self.params)
5487 def set(self, name, val):
5488 """Set parameter name with value val.
"""
5490 _z3_assert(isinstance(name, str), "parameter name must be a string")
5491 name_sym = to_symbol(name, self.ctx)
5492 if isinstance(val, bool):
5493 Z3_params_set_bool(self.ctx.ref(), self.params, name_sym, val)
5495 Z3_params_set_uint(self.ctx.ref(), self.params, name_sym, val)
5496 elif isinstance(val, float):
5497 Z3_params_set_double(self.ctx.ref(), self.params, name_sym, val)
5498 elif isinstance(val, str):
5499 Z3_params_set_symbol(self.ctx.ref(), self.params, name_sym, to_symbol(val, self.ctx))
5502 _z3_assert(False, "invalid parameter value")
5505 return Z3_params_to_string(self.ctx.ref(), self.params)
5507 def validate(self, ds):
5508 _z3_assert(isinstance(ds, ParamDescrsRef), "parameter description set expected")
5509 Z3_params_validate(self.ctx.ref(), self.params, ds.descr)
5512 def args2params(arguments, keywords, ctx=None):
5513 """Convert python arguments into a Z3_params object.
5514 A
':' is added to the keywords,
and '_' is replaced with
'-'
5516 >>>
args2params([
'model',
True,
'relevancy', 2], {
'elim_and' :
True})
5517 (params model true relevancy 2 elim_and true)
5520 _z3_assert(len(arguments) % 2 == 0, "Argument list must have an even number of elements.")
5535 class ParamDescrsRef:
5536 """Set of parameter descriptions
for Solvers, Tactics
and Simplifiers
in Z3.
5539 def __init__(self, descr, ctx=None):
5540 _z3_assert(isinstance(descr, ParamDescrs), "parameter description object expected")
5541 self.ctx = _get_ctx(ctx)
5543 Z3_param_descrs_inc_ref(self.ctx.ref(), self.descr)
5545 def __deepcopy__(self, memo={}):
5546 return ParamsDescrsRef(self.descr, self.ctx)
5549 if self.ctx.ref() is not None and Z3_param_descrs_dec_ref is not None:
5550 Z3_param_descrs_dec_ref(self.ctx.ref(), self.descr)
5553 """Return the size of
in the parameter description `self`.
5555 return int(Z3_param_descrs_size(self.ctx.ref(), self.descr))
5558 """Return the size of
in the parameter description `self`.
5562 def get_name(self, i):
5563 """Return the i-th parameter name
in the parameter description `self`.
5565 return _symbol2py(self.ctx, Z3_param_descrs_get_name(self.ctx.ref(), self.descr, i))
5567 def get_kind(self, n):
5568 """Return the kind of the parameter named `n`.
5570 return Z3_param_descrs_get_kind(self.ctx.ref(), self.descr, to_symbol(n, self.ctx))
5572 def get_documentation(self, n):
5573 """Return the documentation string of the parameter named `n`.
5575 return Z3_param_descrs_get_documentation(self.ctx.ref(), self.descr, to_symbol(n, self.ctx))
5577 def __getitem__(self, arg):
5579 return self.get_name(arg)
5581 return self.get_kind(arg)
5584 return Z3_param_descrs_to_string(self.ctx.ref(), self.descr)
5586 #########################################
5590 #########################################
5593 class Goal(Z3PPObject):
5594 """Goal
is a collection of constraints we want to find a solution
or show to be unsatisfiable (infeasible).
5596 Goals are processed using Tactics. A Tactic transforms a goal into a set of subgoals.
5597 A goal has a solution
if one of its subgoals has a solution.
5598 A goal
is unsatisfiable
if all subgoals are unsatisfiable.
5601 def __init__(self, models=True, unsat_cores=False, proofs=False, ctx=None, goal=None):
5603 _z3_assert(goal is None or ctx is not None,
5604 "If goal is different from None, then ctx must be also different from None")
5605 self.ctx = _get_ctx(ctx)
5607 if self.goal is None:
5608 self.goal = Z3_mk_goal(self.ctx.ref(), models, unsat_cores, proofs)
5609 Z3_goal_inc_ref(self.ctx.ref(), self.goal)
5612 if self.goal is not None and self.ctx.ref() is not None and Z3_goal_dec_ref is not None:
5613 Z3_goal_dec_ref(self.ctx.ref(), self.goal)
5616 """Return the depth of the goal `self`.
5617 The depth corresponds to the number of tactics applied to `self`.
5619 >>> x, y =
Ints(
'x y')
5621 >>> g.add(x == 0, y >= x + 1)
5624 >>> r =
Then(
'simplify',
'solve-eqs')(g)
5631 return int(Z3_goal_depth(self.ctx.ref(), self.goal))
5633 def inconsistent(self):
5634 """Return `
True`
if `self` contains the `
False` constraints.
5636 >>> x, y =
Ints(
'x y')
5638 >>> g.inconsistent()
5640 >>> g.add(x == 0, x == 1)
5643 >>> g.inconsistent()
5645 >>> g2 =
Tactic(
'propagate-values')(g)[0]
5646 >>> g2.inconsistent()
5649 return Z3_goal_inconsistent(self.ctx.ref(), self.goal)
5652 """Return the precision (under-approximation, over-approximation,
or precise) of the goal `self`.
5655 >>> g.prec() == Z3_GOAL_PRECISE
5657 >>> x, y =
Ints(
'x y')
5658 >>> g.add(x == y + 1)
5659 >>> g.prec() == Z3_GOAL_PRECISE
5661 >>> t =
With(
Tactic(
'add-bounds'), add_bound_lower=0, add_bound_upper=10)
5664 [x == y + 1, x <= 10, x >= 0, y <= 10, y >= 0]
5665 >>> g2.prec() == Z3_GOAL_PRECISE
5667 >>> g2.prec() == Z3_GOAL_UNDER
5670 return Z3_goal_precision(self.ctx.ref(), self.goal)
5672 def precision(self):
5673 """Alias
for `
prec()`.
5676 >>> g.precision() == Z3_GOAL_PRECISE
5682 """Return the number of constraints
in the goal `self`.
5687 >>> x, y =
Ints(
'x y')
5688 >>> g.add(x == 0, y > x)
5692 return int(Z3_goal_size(self.ctx.ref(), self.goal))
5695 """Return the number of constraints
in the goal `self`.
5700 >>> x, y =
Ints(
'x y')
5701 >>> g.add(x == 0, y > x)
5708 """Return a constraint
in the goal `self`.
5711 >>> x, y =
Ints(
'x y')
5712 >>> g.add(x == 0, y > x)
5718 return _to_expr_ref(Z3_goal_formula(self.ctx.ref(), self.goal, i), self.ctx)
5720 def __getitem__(self, arg):
5721 """Return a constraint
in the goal `self`.
5724 >>> x, y =
Ints(
'x y')
5725 >>> g.add(x == 0, y > x)
5731 if arg >= len(self):
5733 return self.get(arg)
5735 def assert_exprs(self, *args):
5736 """Assert constraints into the goal.
5740 >>> g.assert_exprs(x > 0, x < 2)
5744 args = _get_args(args)
5745 s = BoolSort(self.ctx)
5748 Z3_goal_assert(self.ctx.ref(), self.goal, arg.as_ast())
5750 def append(self, *args):
5755 >>> g.append(x > 0, x < 2)
5759 self.assert_exprs(*args)
5761 def insert(self, *args):
5766 >>> g.insert(x > 0, x < 2)
5770 self.assert_exprs(*args)
5772 def add(self, *args):
5777 >>> g.add(x > 0, x < 2)
5781 self.assert_exprs(*args)
5783 def convert_model(self, model):
5784 """Retrieve model
from a satisfiable goal
5785 >>> a, b =
Ints(
'a b')
5787 >>> g.add(
Or(a == 0, a == 1),
Or(b == 0, b == 1), a > b)
5791 [
Or(b == 0, b == 1),
Not(0 <= b)]
5793 [
Or(b == 0, b == 1),
Not(1 <= b)]
5809 _z3_assert(isinstance(model, ModelRef), "Z3 Model expected")
5810 return ModelRef(Z3_goal_convert_model(self.ctx.ref(), self.goal, model.model), self.ctx)
5813 return obj_to_string(self)
5816 """Return a textual representation of the s-expression representing the goal.
"""
5817 return Z3_goal_to_string(self.ctx.ref(), self.goal)
5819 def dimacs(self, include_names=True):
5820 """Return a textual representation of the goal
in DIMACS format.
"""
5821 return Z3_goal_to_dimacs_string(self.ctx.ref(), self.goal, include_names)
5823 def translate(self, target):
5824 """Copy goal `self` to context `target`.
5832 >>> g2 = g.translate(c2)
5843 _z3_assert(isinstance(target, Context), "target must be a context")
5844 return Goal(goal=Z3_goal_translate(self.ctx.ref(), self.goal, target.ref()), ctx=target)
5847 return self.translate(self.ctx)
5849 def __deepcopy__(self, memo={}):
5850 return self.translate(self.ctx)
5852 def simplify(self, *arguments, **keywords):
5853 """Return a new simplified goal.
5855 This method
is essentially invoking the simplify tactic.
5859 >>> g.add(x + 1 >= 2)
5862 >>> g2 = g.simplify()
5869 t = Tactic("simplify")
5870 return t.apply(self, *arguments, **keywords)[0]
5873 """Return goal `self`
as a single Z3 expression.
5888 return BoolVal(True, self.ctx)
5892 return And([self.get(i) for i in range(len(self))], self.ctx)
5894 #########################################
5898 #########################################
5901 class AstVector(Z3PPObject):
5902 """A collection (vector) of ASTs.
"""
5904 def __init__(self, v=None, ctx=None):
5907 self.ctx = _get_ctx(ctx)
5908 self.vector = Z3_mk_ast_vector(self.ctx.ref())
5911 assert ctx is not None
5913 Z3_ast_vector_inc_ref(self.ctx.ref(), self.vector)
5916 if self.vector is not None and self.ctx.ref() is not None and Z3_ast_vector_dec_ref is not None:
5917 Z3_ast_vector_dec_ref(self.ctx.ref(), self.vector)
5920 """Return the size of the vector `self`.
5925 >>> A.push(
Int(
'x'))
5926 >>> A.push(
Int(
'x'))
5930 return int(Z3_ast_vector_size(self.ctx.ref(), self.vector))
5932 def __getitem__(self, i):
5933 """Return the AST at position `i`.
5936 >>> A.push(
Int(
'x') + 1)
5937 >>> A.push(
Int(
'y'))
5944 if isinstance(i, int):
5948 if i >= self.__len__():
5950 return _to_ast_ref(Z3_ast_vector_get(self.ctx.ref(), self.vector, i), self.ctx)
5952 elif isinstance(i, slice):
5954 for ii in range(*i.indices(self.__len__())):
5955 result.append(_to_ast_ref(
5956 Z3_ast_vector_get(self.ctx.ref(), self.vector, ii),
5961 def __setitem__(self, i, v):
5962 """Update AST at position `i`.
5965 >>> A.push(
Int(
'x') + 1)
5966 >>> A.push(
Int(
'y'))
5973 if i >= self.__len__():
5975 Z3_ast_vector_set(self.ctx.ref(), self.vector, i, v.as_ast())
5978 """Add `v`
in the end of the vector.
5983 >>> A.push(
Int(
'x'))
5987 Z3_ast_vector_push(self.ctx.ref(), self.vector, v.as_ast())
5989 def resize(self, sz):
5990 """Resize the vector to `sz` elements.
5996 >>>
for i
in range(10): A[i] =
Int(
'x')
6000 Z3_ast_vector_resize(self.ctx.ref(), self.vector, sz)
6002 def __contains__(self, item):
6003 """Return `
True`
if the vector contains `item`.
6025 def translate(self, other_ctx):
6026 """Copy vector `self` to context `other_ctx`.
6032 >>> B = A.translate(c2)
6037 Z3_ast_vector_translate(self.ctx.ref(), self.vector, other_ctx.ref()),
6042 return self.translate(self.ctx)
6044 def __deepcopy__(self, memo={}):
6045 return self.translate(self.ctx)
6048 return obj_to_string(self)
6051 """Return a textual representation of the s-expression representing the vector.
"""
6052 return Z3_ast_vector_to_string(self.ctx.ref(), self.vector)
6054 #########################################
6058 #########################################
6062 """A mapping
from ASTs to ASTs.
"""
6064 def __init__(self, m=None, ctx=None):
6067 self.ctx = _get_ctx(ctx)
6068 self.map = Z3_mk_ast_map(self.ctx.ref())
6071 assert ctx is not None
6073 Z3_ast_map_inc_ref(self.ctx.ref(), self.map)
6075 def __deepcopy__(self, memo={}):
6076 return AstMap(self.map, self.ctx)
6079 if self.map is not None and self.ctx.ref() is not None and Z3_ast_map_dec_ref is not None:
6080 Z3_ast_map_dec_ref(self.ctx.ref(), self.map)
6083 """Return the size of the map.
6093 return int(Z3_ast_map_size(self.ctx.ref(), self.map))
6095 def __contains__(self, key):
6096 """Return `
True`
if the map contains key `key`.
6106 return Z3_ast_map_contains(self.ctx.ref(), self.map, key.as_ast())
6108 def __getitem__(self, key):
6109 """Retrieve the value associated with key `key`.
6117 return _to_ast_ref(Z3_ast_map_find(self.ctx.ref(), self.map, key.as_ast()), self.ctx)
6119 def __setitem__(self, k, v):
6120 """Add/Update key `k` with value `v`.
6133 Z3_ast_map_insert(self.ctx.ref(), self.map, k.as_ast(), v.as_ast())
6136 return Z3_ast_map_to_string(self.ctx.ref(), self.map)
6139 """Remove the entry associated with key `k`.
6150 Z3_ast_map_erase(self.ctx.ref(), self.map, k.as_ast())
6153 """Remove all entries
from the map.
6165 Z3_ast_map_reset(self.ctx.ref(), self.map)
6168 """Return an AstVector containing all keys
in the map.
6177 return AstVector(Z3_ast_map_keys(self.ctx.ref(), self.map), self.ctx)
6179 #########################################
6183 #########################################
6187 """Store the value of the interpretation of a function
in a particular point.
"""
6189 def __init__(self, entry, ctx):
6192 Z3_func_entry_inc_ref(self.ctx.ref(), self.entry)
6194 def __deepcopy__(self, memo={}):
6195 return FuncEntry(self.entry, self.ctx)
6198 if self.ctx.ref() is not None and Z3_func_entry_dec_ref is not None:
6199 Z3_func_entry_dec_ref(self.ctx.ref(), self.entry)
6202 """Return the number of arguments
in the given entry.
6206 >>> s.add(f(0, 1) == 10, f(1, 2) == 20, f(1, 0) == 10)
6211 >>> f_i.num_entries()
6213 >>> e = f_i.entry(0)
6217 return int(Z3_func_entry_get_num_args(self.ctx.ref(), self.entry))
6219 def arg_value(self, idx):
6220 """Return the value of argument `idx`.
6224 >>> s.add(f(0, 1) == 10, f(1, 2) == 20, f(1, 0) == 10)
6229 >>> f_i.num_entries()
6231 >>> e = f_i.entry(0)
6242 ...
except IndexError:
6243 ... print(
"index error")
6246 if idx >= self.num_args():
6248 return _to_expr_ref(Z3_func_entry_get_arg(self.ctx.ref(), self.entry, idx), self.ctx)
6251 """Return the value of the function at point `self`.
6255 >>> s.add(f(0, 1) == 10, f(1, 2) == 20, f(1, 0) == 10)
6260 >>> f_i.num_entries()
6262 >>> e = f_i.entry(0)
6270 return _to_expr_ref(Z3_func_entry_get_value(self.ctx.ref(), self.entry), self.ctx)
6273 """Return entry `self`
as a Python list.
6276 >>> s.add(f(0, 1) == 10, f(1, 2) == 20, f(1, 0) == 10)
6281 >>> f_i.num_entries()
6283 >>> e = f_i.entry(0)
6287 args = [self.arg_value(i) for i in range(self.num_args())]
6288 args.append(self.value())
6292 return repr(self.as_list())
6295 class FuncInterp(Z3PPObject):
6296 """Stores the interpretation of a function
in a Z3 model.
"""
6298 def __init__(self, f, ctx):
6301 if self.f is not None:
6302 Z3_func_interp_inc_ref(self.ctx.ref(), self.f)
6305 if self.f is not None and self.ctx.ref() is not None and Z3_func_interp_dec_ref is not None:
6306 Z3_func_interp_dec_ref(self.ctx.ref(), self.f)
6308 def else_value(self):
6310 Return the `
else` value
for a function interpretation.
6311 Return
None if Z3 did
not specify the `
else` value
for
6316 >>> s.add(
f(0) == 1,
f(1) == 1,
f(2) == 0)
6325 r = Z3_func_interp_get_else(self.ctx.ref(), self.f)
6327 return _to_expr_ref(r, self.ctx)
6331 def num_entries(self):
6332 """Return the number of entries/points
in the function interpretation `self`.
6336 >>> s.add(
f(0) == 1,
f(1) == 1,
f(2) == 0)
6345 return int(Z3_func_interp_get_num_entries(self.ctx.ref(), self.f))
6348 """Return the number of arguments
for each entry
in the function interpretation `self`.
6352 >>> s.add(
f(0) == 1,
f(1) == 1,
f(2) == 0)
6359 return int(Z3_func_interp_get_arity(self.ctx.ref(), self.f))
6361 def entry(self, idx):
6362 """Return an entry at position `idx < self.
num_entries()`
in the function interpretation `self`.
6366 >>> s.add(
f(0) == 1,
f(1) == 1,
f(2) == 0)
6377 if idx >= self.num_entries():
6379 return FuncEntry(Z3_func_interp_get_entry(self.ctx.ref(), self.f, idx), self.ctx)
6381 def translate(self, other_ctx):
6382 """Copy model
'self' to context
'other_ctx'.
6384 return ModelRef(Z3_model_translate(self.ctx.ref(), self.model, other_ctx.ref()), other_ctx)
6387 return self.translate(self.ctx)
6389 def __deepcopy__(self, memo={}):
6390 return self.translate(self.ctx)
6393 """Return the function interpretation
as a Python list.
6396 >>> s.add(
f(0) == 1,
f(1) == 1,
f(2) == 0)
6405 r = [self.entry(i).as_list() for i in range(self.num_entries())]
6406 r.append(self.else_value())
6410 return obj_to_string(self)
6413 class ModelRef(Z3PPObject):
6414 """Model/Solution of a satisfiability problem (aka system of constraints).
"""
6416 def __init__(self, m, ctx):
6417 assert ctx is not None
6420 Z3_model_inc_ref(self.ctx.ref(), self.model)
6423 if self.ctx.ref() is not None and Z3_model_dec_ref is not None:
6424 Z3_model_dec_ref(self.ctx.ref(), self.model)
6427 return obj_to_string(self)
6430 """Return a textual representation of the s-expression representing the model.
"""
6431 return Z3_model_to_string(self.ctx.ref(), self.model)
6433 def eval(self, t, model_completion=False):
6434 """Evaluate the expression `t`
in the model `self`.
6435 If `model_completion`
is enabled, then a default interpretation
is automatically added
6436 for symbols that do
not have an interpretation
in the model `self`.
6440 >>> s.add(x > 0, x < 2)
6453 >>> m.eval(y, model_completion=
True)
6460 if Z3_model_eval(self.ctx.ref(), self.model, t.as_ast(), model_completion, r):
6461 return _to_expr_ref(r[0], self.ctx)
6462 raise Z3Exception("failed to evaluate expression in the model")
6464 def evaluate(self, t, model_completion=False):
6465 """Alias
for `eval`.
6469 >>> s.add(x > 0, x < 2)
6473 >>> m.evaluate(x + 1)
6475 >>> m.evaluate(x == 1)
6478 >>> m.evaluate(y + x)
6482 >>> m.evaluate(y, model_completion=
True)
6485 >>> m.evaluate(y + x)
6488 return self.eval(t, model_completion)
6491 """Return the number of constant
and function declarations
in the model `self`.
6496 >>> s.add(x > 0, f(x) != x)
6503 num_consts = int(Z3_model_get_num_consts(self.ctx.ref(), self.model))
6504 num_funcs = int(Z3_model_get_num_funcs(self.ctx.ref(), self.model))
6505 return num_consts + num_funcs
6507 def get_interp(self, decl):
6508 """Return the interpretation
for a given declaration
or constant.
6513 >>> s.add(x > 0, x < 2, f(x) == 0)
6523 _z3_assert(isinstance(decl, FuncDeclRef) or is_const(decl), "Z3 declaration expected")
6527 if decl.arity() == 0:
6528 _r = Z3_model_get_const_interp(self.ctx.ref(), self.model, decl.ast)
6529 if _r.value is None:
6531 r = _to_expr_ref(_r, self.ctx)
6533 fi = self.get_interp(get_as_array_func(r))
6545 sz = fi.num_entries()
6549 e = Store(e, fe.arg_value(0), fe.value())
6555 return FuncInterp(Z3_model_get_func_interp(self.ctx.ref(), self.model, decl.ast), self.ctx)
6559 def num_sorts(self):
6560 """Return the number of uninterpreted sorts that contain an interpretation
in the model `self`.
6563 >>> a, b =
Consts(
'a b', A)
6572 return int(Z3_model_get_num_sorts(self.ctx.ref(), self.model))
6574 def get_sort(self, idx):
6575 """Return the uninterpreted sort at position `idx` < self.
num_sorts().
6579 >>> a1, a2 =
Consts(
'a1 a2', A)
6580 >>> b1, b2 =
Consts(
'b1 b2', B)
6582 >>> s.add(a1 != a2, b1 != b2)
6593 if idx >= self.num_sorts():
6595 return _to_sort_ref(Z3_model_get_sort(self.ctx.ref(), self.model, idx), self.ctx)
6598 """Return all uninterpreted sorts that have an interpretation
in the model `self`.
6602 >>> a1, a2 =
Consts(
'a1 a2', A)
6603 >>> b1, b2 =
Consts(
'b1 b2', B)
6605 >>> s.add(a1 != a2, b1 != b2)
6612 return [self.get_sort(i) for i in range(self.num_sorts())]
6614 def get_universe(self, s):
6615 """Return the interpretation
for the uninterpreted sort `s`
in the model `self`.
6618 >>> a, b =
Consts(
'a b', A)
6624 >>> m.get_universe(A)
6628 _z3_assert(isinstance(s, SortRef), "Z3 sort expected")
6630 return AstVector(Z3_model_get_sort_universe(self.ctx.ref(), self.model, s.ast), self.ctx)
6634 def __getitem__(self, idx):
6635 """If `idx`
is an integer, then the declaration at position `idx`
in the model `self`
is returned.
6636 If `idx`
is a declaration, then the actual interpretation
is returned.
6638 The elements can be retrieved using position
or the actual declaration.
6643 >>> s.add(x > 0, x < 2, f(x) == 0)
6657 >>>
for d
in m: print(
"%s -> %s" % (d, m[d]))
6662 if idx >= len(self):
6664 num_consts = Z3_model_get_num_consts(self.ctx.ref(), self.model)
6665 if (idx < num_consts):
6666 return FuncDeclRef(Z3_model_get_const_decl(self.ctx.ref(), self.model, idx), self.ctx)
6668 return FuncDeclRef(Z3_model_get_func_decl(self.ctx.ref(), self.model, idx - num_consts), self.ctx)
6669 if isinstance(idx, FuncDeclRef):
6670 return self.get_interp(idx)
6672 return self.get_interp(idx.decl())
6673 if isinstance(idx, SortRef):
6674 return self.get_universe(idx)
6676 _z3_assert(False, "Integer, Z3 declaration, or Z3 constant expected")
6680 """Return a list with all symbols that have an interpretation
in the model `self`.
6684 >>> s.add(x > 0, x < 2, f(x) == 0)
6692 for i in range(Z3_model_get_num_consts(self.ctx.ref(), self.model)):
6693 r.append(FuncDeclRef(Z3_model_get_const_decl(self.ctx.ref(), self.model, i), self.ctx))
6694 for i in range(Z3_model_get_num_funcs(self.ctx.ref(), self.model)):
6695 r.append(FuncDeclRef(Z3_model_get_func_decl(self.ctx.ref(), self.model, i), self.ctx))
6698 def update_value(self, x, value):
6699 """Update the interpretation of a constant
"""
6702 if is_func_decl(x) and x.arity() != 0 and isinstance(value, FuncInterp):
6704 fi2 = Z3_add_func_interp(x.ctx_ref(), self.model, x.ast, value.else_value().ast);
6705 fi2 = FuncInterp(fi2, x.ctx)
6706 for i in range(value.num_entries()):
6708 n = Z3_func_entry_get_num_args(x.ctx_ref(), e.entry)
6711 v.push(e.arg_value(j))
6712 val = Z3_func_entry_get_value(x.ctx_ref(), e.entry)
6713 Z3_func_interp_add_entry(x.ctx_ref(), fi2.f, v.vector, val)
6715 if not is_func_decl(x) or x.arity() != 0:
6716 raise Z3Exception("Expecting 0-ary function or constant expression")
6717 value = _py2expr(value)
6718 Z3_add_const_interp(x.ctx_ref(), self.model, x.ast, value.ast)
6720 def translate(self, target):
6721 """Translate `self` to the context `target`. That
is,
return a copy of `self`
in the context `target`.
6724 _z3_assert(isinstance(target, Context), "argument must be a Z3 context")
6725 model = Z3_model_translate(self.ctx.ref(), self.model, target.ref())
6726 return ModelRef(model, target)
6729 return self.translate(self.ctx)
6731 def __deepcopy__(self, memo={}):
6732 return self.translate(self.ctx)
6735 def Model(ctx=None):
6737 return ModelRef(Z3_mk_model(ctx.ref()), ctx)
6741 """Return true
if n
is a Z3 expression of the form (_
as-array f).
"""
6742 return isinstance(n, ExprRef) and Z3_is_as_array(n.ctx.ref(), n.as_ast())
6745 def get_as_array_func(n):
6746 """Return the function declaration f associated with a Z3 expression of the form (_
as-array f).
"""
6748 _z3_assert(is_as_array(n), "as-array Z3 expression expected.")
6749 return FuncDeclRef(Z3_get_as_array_func_decl(n.ctx.ref(), n.as_ast()), n.ctx)
6751 #########################################
6755 #########################################
6759 """Statistics
for `Solver.check()`.
"""
6761 def __init__(self, stats, ctx):
6764 Z3_stats_inc_ref(self.ctx.ref(), self.stats)
6766 def __deepcopy__(self, memo={}):
6767 return Statistics(self.stats, self.ctx)
6770 if self.ctx.ref() is not None and Z3_stats_dec_ref is not None:
6771 Z3_stats_dec_ref(self.ctx.ref(), self.stats)
6777 out.write(u('<table border="1" cellpadding="2" cellspacing="0">'))
6780 out.write(u('<tr style="background-color:#CFCFCF">'))
6783 out.write(u("<tr>"))
6785 out.write(u("<td>%s</td><td>%s</td></tr>" % (k, v)))
6786 out.write(u("</table>"))
6787 return out.getvalue()
6789 return Z3_stats_to_string(self.ctx.ref(), self.stats)
6792 """Return the number of statistical counters.
6795 >>> s =
Then(
'simplify',
'nlsat').solver()
6799 >>> st = s.statistics()
6803 return int(Z3_stats_size(self.ctx.ref(), self.stats))
6805 def __getitem__(self, idx):
6806 """Return the value of statistical counter at position `idx`. The result
is a pair (key, value).
6809 >>> s =
Then(
'simplify',
'nlsat').solver()
6813 >>> st = s.statistics()
6817 (
'nlsat propagations', 2)
6821 if idx >= len(self):
6823 if Z3_stats_is_uint(self.ctx.ref(), self.stats, idx):
6824 val = int(Z3_stats_get_uint_value(self.ctx.ref(), self.stats, idx))
6826 val = Z3_stats_get_double_value(self.ctx.ref(), self.stats, idx)
6827 return (Z3_stats_get_key(self.ctx.ref(), self.stats, idx), val)
6830 """Return the list of statistical counters.
6833 >>> s =
Then(
'simplify',
'nlsat').solver()
6837 >>> st = s.statistics()
6839 return [Z3_stats_get_key(self.ctx.ref(), self.stats, idx) for idx in range(len(self))]
6841 def get_key_value(self, key):
6842 """Return the value of a particular statistical counter.
6845 >>> s =
Then(
'simplify',
'nlsat').solver()
6849 >>> st = s.statistics()
6850 >>> st.get_key_value(
'nlsat propagations')
6853 for idx in range(len(self)):
6854 if key == Z3_stats_get_key(self.ctx.ref(), self.stats, idx):
6855 if Z3_stats_is_uint(self.ctx.ref(), self.stats, idx):
6856 return int(Z3_stats_get_uint_value(self.ctx.ref(), self.stats, idx))
6858 return Z3_stats_get_double_value(self.ctx.ref(), self.stats, idx)
6859 raise Z3Exception("unknown key")
6861 def __getattr__(self, name):
6862 """Access the value of statistical using attributes.
6864 Remark: to access a counter containing blank spaces (e.g.,
'nlsat propagations'),
6865 we should use
'_' (e.g.,
'nlsat_propagations').
6868 >>> s =
Then(
'simplify',
'nlsat').solver()
6872 >>> st = s.statistics()
6873 >>> st.nlsat_propagations
6878 key = name.replace("_", " ")
6880 return self.get_key_value(key)
6882 raise AttributeError
6884 #########################################
6888 #########################################
6891 class CheckSatResult:
6892 """Represents the result of a satisfiability check: sat, unsat, unknown.
6898 >>> isinstance(r, CheckSatResult)
6902 def __init__(self, r):
6905 def __deepcopy__(self, memo={}):
6906 return CheckSatResult(self.r)
6908 def __eq__(self, other):
6909 return isinstance(other, CheckSatResult) and self.r == other.r
6911 def __ne__(self, other):
6912 return not self.__eq__(other)
6916 if self.r == Z3_L_TRUE:
6918 elif self.r == Z3_L_FALSE:
6919 return "<b>unsat</b>"
6921 return "<b>unknown</b>"
6923 if self.r == Z3_L_TRUE:
6925 elif self.r == Z3_L_FALSE:
6930 def _repr_html_(self):
6931 in_html = in_html_mode()
6934 set_html_mode(in_html)
6938 sat = CheckSatResult(Z3_L_TRUE)
6939 unsat = CheckSatResult(Z3_L_FALSE)
6940 unknown = CheckSatResult(Z3_L_UNDEF)
6943 class Solver(Z3PPObject):
6945 Solver API provides methods
for implementing the main SMT 2.0 commands:
6946 push, pop, check, get-model, etc.
6949 def __init__(self, solver=None, ctx=None, logFile=None):
6950 assert solver is None or ctx is not None
6951 self.ctx = _get_ctx(ctx)
6952 self.backtrack_level = 4000000000
6955 self.solver = Z3_mk_solver(self.ctx.ref())
6957 self.solver = solver
6958 Z3_solver_inc_ref(self.ctx.ref(), self.solver)
6959 if logFile is not None:
6960 self.set("smtlib2_log", logFile)
6963 if self.solver is not None and self.ctx.ref() is not None and Z3_solver_dec_ref is not None:
6964 Z3_solver_dec_ref(self.ctx.ref(), self.solver)
6966 def __enter__(self):
6970 def __exit__(self, *exc_info):
6973 def set(self, *args, **keys):
6974 """Set a configuration option.
6975 The method `
help()`
return a string containing all available options.
6979 >>> s.set(mbqi=
True)
6980 >>> s.set(
'MBQI',
True)
6981 >>> s.set(
':mbqi',
True)
6983 p = args2params(args, keys, self.ctx)
6984 Z3_solver_set_params(self.ctx.ref(), self.solver, p.params)
6987 """Create a backtracking point.
7006 Z3_solver_push(self.ctx.ref(), self.solver)
7008 def pop(self, num=1):
7009 """Backtrack \\c num backtracking points.
7028 Z3_solver_pop(self.ctx.ref(), self.solver, num)
7030 def num_scopes(self):
7031 """Return the current number of backtracking points.
7046 return Z3_solver_get_num_scopes(self.ctx.ref(), self.solver)
7049 """Remove all asserted constraints
and backtracking points created using `
push()`.
7060 Z3_solver_reset(self.ctx.ref(), self.solver)
7062 def assert_exprs(self, *args):
7063 """Assert constraints into the solver.
7067 >>> s.assert_exprs(x > 0, x < 2)
7071 args = _get_args(args)
7072 s = BoolSort(self.ctx)
7074 if isinstance(arg, Goal) or isinstance(arg, AstVector):
7076 Z3_solver_assert(self.ctx.ref(), self.solver, f.as_ast())
7079 Z3_solver_assert(self.ctx.ref(), self.solver, arg.as_ast())
7081 def add(self, *args):
7082 """Assert constraints into the solver.
7086 >>> s.add(x > 0, x < 2)
7090 self.assert_exprs(*args)
7092 def __iadd__(self, fml):
7096 def append(self, *args):
7097 """Assert constraints into the solver.
7101 >>> s.append(x > 0, x < 2)
7105 self.assert_exprs(*args)
7107 def insert(self, *args):
7108 """Assert constraints into the solver.
7112 >>> s.insert(x > 0, x < 2)
7116 self.assert_exprs(*args)
7118 def assert_and_track(self, a, p):
7119 """Assert constraint `a`
and track it
in the unsat core using the Boolean constant `p`.
7121 If `p`
is a string, it will be automatically converted into a Boolean constant.
7126 >>> s.set(unsat_core=
True)
7127 >>> s.assert_and_track(x > 0,
'p1')
7128 >>> s.assert_and_track(x != 1,
'p2')
7129 >>> s.assert_and_track(x < 0, p3)
7130 >>> print(s.check())
7132 >>> c = s.unsat_core()
7142 if isinstance(p, str):
7143 p = Bool(p, self.ctx)
7144 _z3_assert(isinstance(a, BoolRef), "Boolean expression expected")
7145 _z3_assert(isinstance(p, BoolRef) and is_const(p), "Boolean expression expected")
7146 Z3_solver_assert_and_track(self.ctx.ref(), self.solver, a.as_ast(), p.as_ast())
7148 def check(self, *assumptions):
7149 """Check whether the assertions
in the given solver plus the optional assumptions are consistent
or not.
7155 >>> s.add(x > 0, x < 2)
7158 >>> s.model().eval(x)
7164 >>> s.add(2**x == 4)
7168 s = BoolSort(self.ctx)
7169 assumptions = _get_args(assumptions)
7170 num = len(assumptions)
7171 _assumptions = (Ast * num)()
7172 for i in range(num):
7173 _assumptions[i] = s.cast(assumptions[i]).as_ast()
7174 r = Z3_solver_check_assumptions(self.ctx.ref(), self.solver, num, _assumptions)
7175 return CheckSatResult(r)
7178 """Return a model
for the last `
check()`.
7180 This function raises an exception
if
7181 a model
is not available (e.g., last `
check()` returned unsat).
7185 >>> s.add(a + 2 == 0)
7192 return ModelRef(Z3_solver_get_model(self.ctx.ref(), self.solver), self.ctx)
7194 raise Z3Exception("model is not available")
7196 def import_model_converter(self, other):
7197 """Import model converter
from other into the current solver
"""
7198 Z3_solver_import_model_converter(self.ctx.ref(), other.solver, self.solver)
7200 def interrupt(self):
7201 """Interrupt the execution of the solver object.
7202 Remarks: This ensures that the interrupt applies only
7203 to the given solver object
and it applies only
if it
is running.
7205 Z3_solver_interrupt(self.ctx.ref(), self.solver)
7207 def unsat_core(self):
7208 """Return a subset (
as an AST vector) of the assumptions provided to the last
check().
7210 These are the assumptions Z3 used
in the unsatisfiability proof.
7211 Assumptions are available
in Z3. They are used to extract unsatisfiable cores.
7212 They may be also used to
"retract" assumptions. Note that, assumptions are
not really
7213 "soft constraints", but they can be used to implement them.
7215 >>> p1, p2, p3 =
Bools(
'p1 p2 p3')
7216 >>> x, y =
Ints(
'x y')
7221 >>> s.add(
Implies(p3, y > -3))
7222 >>> s.check(p1, p2, p3)
7224 >>> core = s.unsat_core()
7237 return AstVector(Z3_solver_get_unsat_core(self.ctx.ref(), self.solver), self.ctx)
7239 def consequences(self, assumptions, variables):
7240 """Determine fixed values
for the variables based on the solver state
and assumptions.
7242 >>> a, b, c, d =
Bools(
'a b c d')
7244 >>> s.consequences([a],[b,c,d])
7246 >>> s.consequences([
Not(c),d],[a,b,c,d])
7249 if isinstance(assumptions, list):
7250 _asms = AstVector(None, self.ctx)
7251 for a in assumptions:
7254 if isinstance(variables, list):
7255 _vars = AstVector(None, self.ctx)
7259 _z3_assert(isinstance(assumptions, AstVector), "ast vector expected")
7260 _z3_assert(isinstance(variables, AstVector), "ast vector expected")
7261 consequences = AstVector(None, self.ctx)
7262 r = Z3_solver_get_consequences(self.ctx.ref(), self.solver, assumptions.vector,
7263 variables.vector, consequences.vector)
7264 sz = len(consequences)
7265 consequences = [consequences[i] for i in range(sz)]
7266 return CheckSatResult(r), consequences
7268 def from_file(self, filename):
7269 """Parse assertions
from a file
"""
7270 Z3_solver_from_file(self.ctx.ref(), self.solver, filename)
7272 def from_string(self, s):
7273 """Parse assertions
from a string
"""
7274 Z3_solver_from_string(self.ctx.ref(), self.solver, s)
7276 def cube(self, vars=None):
7278 The method takes an optional set of variables that restrict which
7279 variables may be used
as a starting point
for cubing.
7280 If vars
is not None, then the first case split
is based on a variable
in
7283 self.cube_vs = AstVector(None, self.ctx)
7284 if vars is not None:
7286 self.cube_vs.push(v)
7288 lvl = self.backtrack_level
7289 self.backtrack_level = 4000000000
7290 r = AstVector(Z3_solver_cube(self.ctx.ref(), self.solver, self.cube_vs.vector, lvl), self.ctx)
7291 if (len(r) == 1 and is_false(r[0])):
7297 def cube_vars(self):
7298 """Access the set of variables that were touched by the most recently generated cube.
7299 This set of variables can be used
as a starting point
for additional cubes.
7300 The idea
is that variables that appear
in clauses that are reduced by the most recent
7301 cube are likely more useful to cube on.
"""
7305 t = _py2expr(t, self.ctx)
7306 """Retrieve congruence closure root of the term t relative to the current search state
7307 The function primarily works
for SimpleSolver. Terms
and variables that are
7308 eliminated during pre-processing are
not visible to the congruence closure.
7310 return _to_expr_ref(Z3_solver_congruence_root(self.ctx.ref(), self.solver, t.ast), self.ctx)
7313 t = _py2expr(t, self.ctx)
7314 """Retrieve congruence closure sibling of the term t relative to the current search state
7315 The function primarily works
for SimpleSolver. Terms
and variables that are
7316 eliminated during pre-processing are
not visible to the congruence closure.
7318 return _to_expr_ref(Z3_solver_congruence_next(self.ctx.ref(), self.solver, t.ast), self.ctx)
7321 """Return a proof
for the last `
check()`. Proof construction must be enabled.
"""
7322 return _to_expr_ref(Z3_solver_get_proof(self.ctx.ref(), self.solver), self.ctx)
7324 def assertions(self):
7325 """Return an AST vector containing all added constraints.
7336 return AstVector(Z3_solver_get_assertions(self.ctx.ref(), self.solver), self.ctx)
7339 """Return an AST vector containing all currently inferred units.
7341 return AstVector(Z3_solver_get_units(self.ctx.ref(), self.solver), self.ctx)
7343 def non_units(self):
7344 """Return an AST vector containing all atomic formulas
in solver state that are
not units.
7346 return AstVector(Z3_solver_get_non_units(self.ctx.ref(), self.solver), self.ctx)
7348 def trail_levels(self):
7349 """Return trail
and decision levels of the solver state after a
check() call.
7351 trail = self.trail()
7352 levels = (ctypes.c_uint * len(trail))()
7353 Z3_solver_get_levels(self.ctx.ref(), self.solver, trail.vector, len(trail), levels)
7354 return trail, levels
7357 """Return trail of the solver state after a
check() call.
7359 return AstVector(Z3_solver_get_trail(self.ctx.ref(), self.solver), self.ctx)
7361 def statistics(self):
7362 """Return statistics
for the last `
check()`.
7369 >>> st = s.statistics()
7370 >>> st.get_key_value(
'final checks')
7377 return Statistics(Z3_solver_get_statistics(self.ctx.ref(), self.solver), self.ctx)
7379 def reason_unknown(self):
7380 """Return a string describing why the last `
check()` returned `unknown`.
7384 >>> s.add(2**x == 4)
7387 >>> s.reason_unknown()
7388 '(incomplete (theory arithmetic))'
7390 return Z3_solver_get_reason_unknown(self.ctx.ref(), self.solver)
7393 """Display a string describing all available options.
"""
7394 print(Z3_solver_get_help(self.ctx.ref(), self.solver))
7396 def param_descrs(self):
7397 """Return the parameter description set.
"""
7398 return ParamDescrsRef(Z3_solver_get_param_descrs(self.ctx.ref(), self.solver), self.ctx)
7401 """Return a formatted string with all added constraints.
"""
7402 return obj_to_string(self)
7404 def translate(self, target):
7405 """Translate `self` to the context `target`. That
is,
return a copy of `self`
in the context `target`.
7410 >>> s2 = s1.translate(c2)
7413 _z3_assert(isinstance(target, Context), "argument must be a Z3 context")
7414 solver = Z3_solver_translate(self.ctx.ref(), self.solver, target.ref())
7415 return Solver(solver, target)
7418 return self.translate(self.ctx)
7420 def __deepcopy__(self, memo={}):
7421 return self.translate(self.ctx)
7424 """Return a formatted string (
in Lisp-like format) with all added constraints.
7425 We say the string
is in s-expression format.
7433 return Z3_solver_to_string(self.ctx.ref(), self.solver)
7435 def dimacs(self, include_names=True):
7436 """Return a textual representation of the solver
in DIMACS format.
"""
7437 return Z3_solver_to_dimacs_string(self.ctx.ref(), self.solver, include_names)
7440 """return SMTLIB2 formatted benchmark
for solver
's assertions"""
7447 for i
in range(sz1):
7448 v[i] = es[i].as_ast()
7450 e = es[sz1].as_ast()
7454 self.ctx.ref(),
"benchmark generated from python API",
"",
"unknown",
"", sz1, v, e,
7459 """Create a solver customized for the given logic.
7461 The parameter `logic` is a string. It should be contains
7462 the name of a SMT-LIB logic.
7463 See http://www.smtlib.org/ for the name of all available logics.
7465 >>> s = SolverFor("QF_LIA")
7480 """Return a simple general purpose solver with limited amount of preprocessing.
7482 >>> s = SimpleSolver()
7499 """Fixedpoint API provides methods for solving with recursive predicates"""
7502 assert fixedpoint
is None or ctx
is not None
7505 if fixedpoint
is None:
7516 if self.
fixedpoint is not None and self.ctx.ref()
is not None and Z3_fixedpoint_dec_ref
is not None:
7520 """Set a configuration option. The method `help()` return a string containing all available options.
7526 """Display a string describing all available options."""
7530 """Return the parameter description set."""
7534 """Assert constraints as background axioms for the fixedpoint solver."""
7535 args = _get_args(args)
7538 if isinstance(arg, Goal)
or isinstance(arg, AstVector):
7548 """Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr."""
7556 """Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr."""
7560 """Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr."""
7564 """Assert rules defining recursive predicates to the fixedpoint solver.
7567 >>> s = Fixedpoint()
7568 >>> s.register_relation(a.decl())
7569 >>> s.register_relation(b.decl())
7582 body = _get_args(body)
7586 def rule(self, head, body=None, name=None):
7587 """Assert rules defining recursive predicates to the fixedpoint solver. Alias for add_rule."""
7591 """Assert facts defining recursive predicates to the fixedpoint solver. Alias for add_rule."""
7595 """Query the fixedpoint engine whether formula is derivable.
7596 You can also pass an tuple or list of recursive predicates.
7598 query = _get_args(query)
7600 if sz >= 1
and isinstance(query[0], FuncDeclRef):
7601 _decls = (FuncDecl * sz)()
7611 query =
And(query, self.
ctx)
7612 query = self.
abstract(query,
False)
7617 """Query the fixedpoint engine whether formula is derivable starting at the given query level.
7619 query = _get_args(query)
7621 if sz >= 1
and isinstance(query[0], FuncDecl):
7622 _z3_assert(
False,
"unsupported")
7628 query = self.
abstract(query,
False)
7629 r = Z3_fixedpoint_query_from_lvl(self.ctx.ref(), self.
fixedpoint, query.as_ast(), lvl)
7637 body = _get_args(body)
7642 """Retrieve answer from last query call."""
7644 return _to_expr_ref(r, self.
ctx)
7647 """Retrieve a ground cex from last query call."""
7648 r = Z3_fixedpoint_get_ground_sat_answer(self.ctx.ref(), self.
fixedpoint)
7649 return _to_expr_ref(r, self.
ctx)
7652 """retrieve rules along the counterexample trace"""
7656 """retrieve rule names along the counterexample trace"""
7659 names = _symbol2py(self.
ctx, Z3_fixedpoint_get_rule_names_along_trace(self.ctx.ref(), self.
fixedpoint))
7661 return names.split(
";")
7664 """Retrieve number of levels used for predicate in PDR engine"""
7668 """Retrieve properties known about predicate for the level'th unfolding.
7669 -1 is treated as the limit (infinity)
7672 return _to_expr_ref(r, self.
ctx)
7675 """Add property to predicate for the level'th unfolding.
7676 -1 is treated as infinity (infinity)
7681 """Register relation as recursive"""
7682 relations = _get_args(relations)
7687 """Control how relation is represented"""
7688 representations = _get_args(representations)
7689 representations = [
to_symbol(s)
for s
in representations]
7690 sz = len(representations)
7691 args = (Symbol * sz)()
7693 args[i] = representations[i]
7697 """Parse rules and queries from a string"""
7701 """Parse rules and queries from a file"""
7705 """retrieve rules that have been added to fixedpoint context"""
7709 """retrieve assertions that have been added to fixedpoint context"""
7713 """Return a formatted string with all added rules and constraints."""
7717 """Return a formatted string (in Lisp-like format) with all added constraints.
7718 We say the string is in s-expression format.
7723 """Return a formatted string (in Lisp-like format) with all added constraints.
7724 We say the string is in s-expression format.
7725 Include also queries.
7727 args, len = _to_ast_array(queries)
7731 """Return statistics for the last `query()`.
7736 """Return a string describing why the last `query()` returned `unknown`.
7741 """Add variable or several variables.
7742 The added variable or variables will be bound in the rules
7745 vars = _get_args(vars)
7765 """Finite domain sort."""
7768 """Return the size of the finite domain sort"""
7769 r = (ctypes.c_ulonglong * 1)()
7773 raise Z3Exception(
"Failed to retrieve finite domain sort size")
7777 """Create a named finite domain sort of a given size sz"""
7778 if not isinstance(name, Symbol):
7785 """Return True if `s` is a Z3 finite-domain sort.
7787 >>> is_finite_domain_sort(FiniteDomainSort('S', 100))
7789 >>> is_finite_domain_sort(IntSort())
7792 return isinstance(s, FiniteDomainSortRef)
7796 """Finite-domain expressions."""
7799 """Return the sort of the finite-domain expression `self`."""
7803 """Return a Z3 floating point expression as a Python string."""
7808 """Return `True` if `a` is a Z3 finite-domain expression.
7810 >>> s = FiniteDomainSort('S', 100)
7811 >>> b = Const('b', s)
7812 >>> is_finite_domain(b)
7814 >>> is_finite_domain(Int('x'))
7817 return isinstance(a, FiniteDomainRef)
7821 """Integer values."""
7824 """Return a Z3 finite-domain numeral as a Python long (bignum) numeral.
7826 >>> s = FiniteDomainSort('S', 100)
7827 >>> v = FiniteDomainVal(3, s)
7836 """Return a Z3 finite-domain numeral as a Python string.
7838 >>> s = FiniteDomainSort('S', 100)
7839 >>> v = FiniteDomainVal(42, s)
7847 """Return a Z3 finite-domain value. If `ctx=None`, then the global context is used.
7849 >>> s = FiniteDomainSort('S', 256)
7850 >>> FiniteDomainVal(255, s)
7852 >>> FiniteDomainVal('100', s)
7862 """Return `True` if `a` is a Z3 finite-domain value.
7864 >>> s = FiniteDomainSort('S', 100)
7865 >>> b = Const('b', s)
7866 >>> is_finite_domain_value(b)
7868 >>> b = FiniteDomainVal(10, s)
7871 >>> is_finite_domain_value(b)
7918 def _global_on_model(ctx):
7919 (fn, mdl) = _on_models[ctx]
7923 _on_model_eh = on_model_eh_type(_global_on_model)
7927 """Optimize API provides methods for solving using objective functions and weighted soft constraints"""
7939 if self.
optimize is not None and self.ctx.ref()
is not None and Z3_optimize_dec_ref
is not None:
7945 """Set a configuration option.
7946 The method `help()` return a string containing all available options.
7952 """Display a string describing all available options."""
7956 """Return the parameter description set."""
7960 """Assert constraints as background axioms for the optimize solver."""
7961 args = _get_args(args)
7964 if isinstance(arg, Goal)
or isinstance(arg, AstVector):
7972 """Assert constraints as background axioms for the optimize solver. Alias for assert_expr."""
7980 """Assert constraint `a` and track it in the unsat core using the Boolean constant `p`.
7982 If `p` is a string, it will be automatically converted into a Boolean constant.
7987 >>> s.assert_and_track(x > 0, 'p1')
7988 >>> s.assert_and_track(x != 1, 'p2')
7989 >>> s.assert_and_track(x < 0, p3)
7990 >>> print(s.check())
7992 >>> c = s.unsat_core()
8002 if isinstance(p, str):
8004 _z3_assert(isinstance(a, BoolRef),
"Boolean expression expected")
8005 _z3_assert(isinstance(p, BoolRef)
and is_const(p),
"Boolean expression expected")
8009 """Add soft constraint with optional weight and optional identifier.
8010 If no weight is supplied, then the penalty for violating the soft constraint
8012 Soft constraints are grouped by identifiers. Soft constraints that are
8013 added without identifiers are grouped by default.
8016 weight =
"%d" % weight
8017 elif isinstance(weight, float):
8018 weight =
"%f" % weight
8019 if not isinstance(weight, str):
8020 raise Z3Exception(
"weight should be a string or an integer")
8028 if sys.version_info.major >= 3
and isinstance(arg, Iterable):
8029 return [asoft(a)
for a
in arg]
8033 """Add objective function to maximize."""
8041 """Add objective function to minimize."""
8049 """create a backtracking point for added rules, facts and assertions"""
8053 """restore to previously created backtracking point"""
8057 """Check consistency and produce optimal values."""
8058 assumptions = _get_args(assumptions)
8059 num = len(assumptions)
8060 _assumptions = (Ast * num)()
8061 for i
in range(num):
8062 _assumptions[i] = assumptions[i].as_ast()
8066 """Return a string that describes why the last `check()` returned `unknown`."""
8070 """Return a model for the last check()."""
8074 raise Z3Exception(
"model is not available")
8080 if not isinstance(obj, OptimizeObjective):
8081 raise Z3Exception(
"Expecting objective handle returned by maximize/minimize")
8085 if not isinstance(obj, OptimizeObjective):
8086 raise Z3Exception(
"Expecting objective handle returned by maximize/minimize")
8090 if not isinstance(obj, OptimizeObjective):
8091 raise Z3Exception(
"Expecting objective handle returned by maximize/minimize")
8092 return obj.lower_values()
8095 if not isinstance(obj, OptimizeObjective):
8096 raise Z3Exception(
"Expecting objective handle returned by maximize/minimize")
8097 return obj.upper_values()
8100 """Parse assertions and objectives from a file"""
8104 """Parse assertions and objectives from a string"""
8108 """Return an AST vector containing all added constraints."""
8112 """returns set of objective functions"""
8116 """Return a formatted string with all added rules and constraints."""
8120 """Return a formatted string (in Lisp-like format) with all added constraints.
8121 We say the string is in s-expression format.
8126 """Return statistics for the last check`.
8131 """Register a callback that is invoked with every incremental improvement to
8132 objective values. The callback takes a model as argument.
8133 The life-time of the model is limited to the callback so the
8134 model has to be (deep) copied if it is to be used after the callback
8136 id = len(_on_models) + 41
8138 _on_models[id] = (on_model, mdl)
8141 self.ctx.ref(), self.
optimize, mdl.model, ctypes.c_void_p(id), _on_model_eh,
8151 """An ApplyResult object contains the subgoals produced by a tactic when applied to a goal.
8152 It also contains model and proof converters.
8164 if self.ctx.ref()
is not None and Z3_apply_result_dec_ref
is not None:
8168 """Return the number of subgoals in `self`.
8170 >>> a, b = Ints('a b')
8172 >>> g.add(Or(a == 0, a == 1), Or(b == 0, b == 1), a > b)
8173 >>> t = Tactic('split-clause')
8177 >>> t = Then(Tactic('split-clause'), Tactic('split-clause'))
8180 >>> t = Then(Tactic('split-clause'), Tactic('split-clause'), Tactic('propagate-values'))
8187 """Return one of the subgoals stored in ApplyResult object `self`.
8189 >>> a, b = Ints('a b')
8191 >>> g.add(Or(a == 0, a == 1), Or(b == 0, b == 1), a > b)
8192 >>> t = Tactic('split-clause')
8195 [a == 0, Or(b == 0, b == 1), a > b]
8197 [a == 1, Or(b == 0, b == 1), a > b]
8199 if idx >= len(self):
8204 return obj_to_string(self)
8207 """Return a textual representation of the s-expression representing the set of subgoals in `self`."""
8211 """Return a Z3 expression consisting of all subgoals.
8216 >>> g.add(Or(x == 2, x == 3))
8217 >>> r = Tactic('simplify')(g)
8219 [[Not(x <= 1), Or(x == 2, x == 3)]]
8221 And(Not(x <= 1), Or(x == 2, x == 3))
8222 >>> r = Tactic('split-clause')(g)
8224 [[x > 1, x == 2], [x > 1, x == 3]]
8226 Or(And(x > 1, x == 2), And(x > 1, x == 3))
8243 """Simplifiers act as pre-processing utilities for solvers.
8244 Build a custom simplifier and add it to a solver"""
8249 if isinstance(simplifier, SimplifierObj):
8251 elif isinstance(simplifier, list):
8252 simps = [
Simplifier(s, ctx)
for s
in simplifier]
8254 for i
in range(1, len(simps)):
8260 _z3_assert(isinstance(simplifier, str),
"simplifier name expected")
8264 raise Z3Exception(
"unknown simplifier '%s'" % simplifier)
8271 if self.
simplifier is not None and self.ctx.ref()
is not None and Z3_simplifier_dec_ref
is not None:
8275 """Return a simplifier that uses the given configuration options"""
8280 """Return a solver that applies the simplification pre-processing specified by the simplifier"""
8284 """Display a string containing a description of the available options for the `self` simplifier."""
8288 """Return the parameter description set."""
8300 """Tactics transform, solver and/or simplify sets of constraints (Goal).
8301 A Tactic can be converted into a Solver using the method solver().
8303 Several combinators are available for creating new tactics using the built-in ones:
8304 Then(), OrElse(), FailIf(), Repeat(), When(), Cond().
8310 if isinstance(tactic, TacticObj):
8314 _z3_assert(isinstance(tactic, str),
"tactic name expected")
8318 raise Z3Exception(
"unknown tactic '%s'" % tactic)
8325 if self.
tactic is not None and self.ctx.ref()
is not None and Z3_tactic_dec_ref
is not None:
8329 """Create a solver using the tactic `self`.
8331 The solver supports the methods `push()` and `pop()`, but it
8332 will always solve each `check()` from scratch.
8334 >>> t = Then('simplify', 'nlsat')
8337 >>> s.add(x**2 == 2, x > 0)
8345 def apply(self, goal, *arguments, **keywords):
8346 """Apply tactic `self` to the given goal or Z3 Boolean expression using the given options.
8348 >>> x, y = Ints('x y')
8349 >>> t = Tactic('solve-eqs')
8350 >>> t.apply(And(x == 0, y >= x + 1))
8354 _z3_assert(isinstance(goal, (Goal, BoolRef)),
"Z3 Goal or Boolean expressions expected")
8355 goal = _to_goal(goal)
8356 if len(arguments) > 0
or len(keywords) > 0:
8363 """Apply tactic `self` to the given goal or Z3 Boolean expression using the given options.
8365 >>> x, y = Ints('x y')
8366 >>> t = Tactic('solve-eqs')
8367 >>> t(And(x == 0, y >= x + 1))
8370 return self.
apply(goal, *arguments, **keywords)
8373 """Display a string containing a description of the available options for the `self` tactic."""
8377 """Return the parameter description set."""
8382 if isinstance(a, BoolRef):
8383 goal =
Goal(ctx=a.ctx)
8390 def _to_tactic(t, ctx=None):
8391 if isinstance(t, Tactic):
8397 def _and_then(t1, t2, ctx=None):
8398 t1 = _to_tactic(t1, ctx)
8399 t2 = _to_tactic(t2, ctx)
8401 _z3_assert(t1.ctx == t2.ctx,
"Context mismatch")
8405 def _or_else(t1, t2, ctx=None):
8406 t1 = _to_tactic(t1, ctx)
8407 t2 = _to_tactic(t2, ctx)
8409 _z3_assert(t1.ctx == t2.ctx,
"Context mismatch")
8414 """Return a tactic that applies the tactics in `*ts` in sequence.
8416 >>> x, y = Ints('x y')
8417 >>> t = AndThen(Tactic('simplify'), Tactic('solve-eqs'))
8418 >>> t(And(x == 0, y > x + 1))
8420 >>> t(And(x == 0, y > x + 1)).as_expr()
8424 _z3_assert(len(ts) >= 2,
"At least two arguments expected")
8425 ctx = ks.get(
"ctx",
None)
8428 for i
in range(num - 1):
8429 r = _and_then(r, ts[i + 1], ctx)
8434 """Return a tactic that applies the tactics in `*ts` in sequence. Shorthand for AndThen(*ts, **ks).
8436 >>> x, y = Ints('x y')
8437 >>> t = Then(Tactic('simplify'), Tactic('solve-eqs'))
8438 >>> t(And(x == 0, y > x + 1))
8440 >>> t(And(x == 0, y > x + 1)).as_expr()
8447 """Return a tactic that applies the tactics in `*ts` until one of them succeeds (it doesn't fail).
8450 >>> t = OrElse(Tactic('split-clause'), Tactic('skip'))
8451 >>> # Tactic split-clause fails if there is no clause in the given goal.
8454 >>> t(Or(x == 0, x == 1))
8455 [[x == 0], [x == 1]]
8458 _z3_assert(len(ts) >= 2,
"At least two arguments expected")
8459 ctx = ks.get(
"ctx",
None)
8462 for i
in range(num - 1):
8463 r = _or_else(r, ts[i + 1], ctx)
8468 """Return a tactic that applies the tactics in `*ts` in parallel until one of them succeeds (it doesn't fail).
8471 >>> t = ParOr(Tactic('simplify'), Tactic('fail'))
8476 _z3_assert(len(ts) >= 2,
"At least two arguments expected")
8477 ctx = _get_ctx(ks.get(
"ctx",
None))
8478 ts = [_to_tactic(t, ctx)
for t
in ts]
8480 _args = (TacticObj * sz)()
8482 _args[i] = ts[i].tactic
8487 """Return a tactic that applies t1 and then t2 to every subgoal produced by t1.
8488 The subgoals are processed in parallel.
8490 >>> x, y = Ints('x y')
8491 >>> t = ParThen(Tactic('split-clause'), Tactic('propagate-values'))
8492 >>> t(And(Or(x == 1, x == 2), y == x + 1))
8493 [[x == 1, y == 2], [x == 2, y == 3]]
8495 t1 = _to_tactic(t1, ctx)
8496 t2 = _to_tactic(t2, ctx)
8498 _z3_assert(t1.ctx == t2.ctx,
"Context mismatch")
8503 """Alias for ParThen(t1, t2, ctx)."""
8508 """Return a tactic that applies tactic `t` using the given configuration options.
8510 >>> x, y = Ints('x y')
8511 >>> t = With(Tactic('simplify'), som=True)
8512 >>> t((x + 1)*(y + 2) == 0)
8513 [[2*x + y + x*y == -2]]
8515 ctx = keys.pop(
"ctx",
None)
8516 t = _to_tactic(t, ctx)
8522 """Return a tactic that applies tactic `t` using the given configuration options.
8524 >>> x, y = Ints('x y')
8526 >>> p.set("som", True)
8527 >>> t = WithParams(Tactic('simplify'), p)
8528 >>> t((x + 1)*(y + 2) == 0)
8529 [[2*x + y + x*y == -2]]
8531 t = _to_tactic(t,
None)
8536 """Return a tactic that keeps applying `t` until the goal is not modified anymore
8537 or the maximum number of iterations `max` is reached.
8539 >>> x, y = Ints('x y')
8540 >>> c = And(Or(x == 0, x == 1), Or(y == 0, y == 1), x > y)
8541 >>> t = Repeat(OrElse(Tactic('split-clause'), Tactic('skip')))
8543 >>> for subgoal in r: print(subgoal)
8544 [x == 0, y == 0, x > y]
8545 [x == 0, y == 1, x > y]
8546 [x == 1, y == 0, x > y]
8547 [x == 1, y == 1, x > y]
8548 >>> t = Then(t, Tactic('propagate-values'))
8552 t = _to_tactic(t, ctx)
8557 """Return a tactic that applies `t` to a given goal for `ms` milliseconds.
8559 If `t` does not terminate in `ms` milliseconds, then it fails.
8561 t = _to_tactic(t, ctx)
8566 """Return a list of all available tactics in Z3.
8569 >>> l.count('simplify') == 1
8577 """Return a short description for the tactic named `name`.
8579 >>> d = tactic_description('simplify')
8586 """Display a (tabular) description of all available tactics in Z3."""
8589 print(
'<table border="1" cellpadding="2" cellspacing="0">')
8592 print(
'<tr style="background-color:#CFCFCF">')
8597 print(
"<td>%s</td><td>%s</td></tr>" % (t, insert_line_breaks(
tactic_description(t), 40)))
8605 """Probes are used to inspect a goal (aka problem) and collect information that may be used
8606 to decide which solver and/or preprocessing step will be used.
8612 if isinstance(probe, ProbeObj):
8614 elif isinstance(probe, float):
8616 elif _is_int(probe):
8618 elif isinstance(probe, bool):
8625 _z3_assert(isinstance(probe, str),
"probe name expected")
8629 raise Z3Exception(
"unknown probe '%s'" % probe)
8636 if self.
probe is not None and self.ctx.ref()
is not None and Z3_probe_dec_ref
is not None:
8640 """Return a probe that evaluates to "true" when the value returned by `self`
8641 is less than the value returned by `other`.
8643 >>> p = Probe('size') < 10
8654 """Return a probe that evaluates to "true" when the value returned by `self`
8655 is greater than the value returned by `other`.
8657 >>> p = Probe('size') > 10
8668 """Return a probe that evaluates to "true" when the value returned by `self`
8669 is less than or equal to the value returned by `other`.
8671 >>> p = Probe('size') <= 2
8682 """Return a probe that evaluates to "true" when the value returned by `self`
8683 is greater than or equal to the value returned by `other`.
8685 >>> p = Probe('size') >= 2
8696 """Return a probe that evaluates to "true" when the value returned by `self`
8697 is equal to the value returned by `other`.
8699 >>> p = Probe('size') == 2
8710 """Return a probe that evaluates to "true" when the value returned by `self`
8711 is not equal to the value returned by `other`.
8713 >>> p = Probe('size') != 2
8725 """Evaluate the probe `self` in the given goal.
8727 >>> p = Probe('size')
8737 >>> p = Probe('num-consts')
8740 >>> p = Probe('is-propositional')
8743 >>> p = Probe('is-qflia')
8748 _z3_assert(isinstance(goal, (Goal, BoolRef)),
"Z3 Goal or Boolean expression expected")
8749 goal = _to_goal(goal)
8754 """Return `True` if `p` is a Z3 probe.
8756 >>> is_probe(Int('x'))
8758 >>> is_probe(Probe('memory'))
8761 return isinstance(p, Probe)
8764 def _to_probe(p, ctx=None):
8768 return Probe(p, ctx)
8772 """Return a list of all available probes in Z3.
8775 >>> l.count('memory') == 1
8783 """Return a short description for the probe named `name`.
8785 >>> d = probe_description('memory')
8792 """Display a (tabular) description of all available probes in Z3."""
8795 print(
'<table border="1" cellpadding="2" cellspacing="0">')
8798 print(
'<tr style="background-color:#CFCFCF">')
8803 print(
"<td>%s</td><td>%s</td></tr>" % (p, insert_line_breaks(
probe_description(p), 40)))
8810 def _probe_nary(f, args, ctx):
8812 _z3_assert(len(args) > 0,
"At least one argument expected")
8814 r = _to_probe(args[0], ctx)
8815 for i
in range(num - 1):
8816 r =
Probe(f(ctx.ref(), r.probe, _to_probe(args[i + 1], ctx).probe), ctx)
8820 def _probe_and(args, ctx):
8821 return _probe_nary(Z3_probe_and, args, ctx)
8824 def _probe_or(args, ctx):
8825 return _probe_nary(Z3_probe_or, args, ctx)
8829 """Return a tactic that fails if the probe `p` evaluates to true.
8830 Otherwise, it returns the input goal unmodified.
8832 In the following example, the tactic applies 'simplify' if and only if there are
8833 more than 2 constraints in the goal.
8835 >>> t = OrElse(FailIf(Probe('size') > 2), Tactic('simplify'))
8836 >>> x, y = Ints('x y')
8842 >>> g.add(x == y + 1)
8844 [[Not(x <= 0), Not(y <= 0), x == 1 + y]]
8846 p = _to_probe(p, ctx)
8851 """Return a tactic that applies tactic `t` only if probe `p` evaluates to true.
8852 Otherwise, it returns the input goal unmodified.
8854 >>> t = When(Probe('size') > 2, Tactic('simplify'))
8855 >>> x, y = Ints('x y')
8861 >>> g.add(x == y + 1)
8863 [[Not(x <= 0), Not(y <= 0), x == 1 + y]]
8865 p = _to_probe(p, ctx)
8866 t = _to_tactic(t, ctx)
8871 """Return a tactic that applies tactic `t1` to a goal if probe `p` evaluates to true, and `t2` otherwise.
8873 >>> t = Cond(Probe('is-qfnra'), Tactic('qfnra'), Tactic('smt'))
8875 p = _to_probe(p, ctx)
8876 t1 = _to_tactic(t1, ctx)
8877 t2 = _to_tactic(t2, ctx)
8888 """Simplify the expression `a` using the given options.
8890 This function has many options. Use `help_simplify` to obtain the complete list.
8894 >>> simplify(x + 1 + y + x + 1)
8896 >>> simplify((x + 1)*(y + 1), som=True)
8898 >>> simplify(Distinct(x, y, 1), blast_distinct=True)
8899 And(Not(x == y), Not(x == 1), Not(y == 1))
8900 >>> simplify(And(x == 0, y == 1), elim_and=True)
8901 Not(Or(Not(x == 0), Not(y == 1)))
8904 _z3_assert(
is_expr(a),
"Z3 expression expected")
8905 if len(arguments) > 0
or len(keywords) > 0:
8907 return _to_expr_ref(
Z3_simplify_ex(a.ctx_ref(), a.as_ast(), p.params), a.ctx)
8909 return _to_expr_ref(
Z3_simplify(a.ctx_ref(), a.as_ast()), a.ctx)
8913 """Return a string describing all options available for Z3 `simplify` procedure."""
8918 """Return the set of parameter descriptions for Z3 `simplify` procedure."""
8923 """Apply substitution m on t, m is a list of pairs of the form (from, to).
8924 Every occurrence in t of from is replaced with to.
8928 >>> substitute(x + 1, (x, y + 1))
8930 >>> f = Function('f', IntSort(), IntSort())
8931 >>> substitute(f(x) + f(y), (f(x), IntVal(1)), (f(y), IntVal(1)))
8934 if isinstance(m, tuple):
8936 if isinstance(m1, list)
and all(isinstance(p, tuple)
for p
in m1):
8939 _z3_assert(
is_expr(t),
"Z3 expression expected")
8941 all([isinstance(p, tuple)
and is_expr(p[0])
and is_expr(p[1])
for p
in m]),
8942 "Z3 invalid substitution, expression pairs expected.")
8944 all([p[0].sort().
eq(p[1].sort())
for p
in m]),
8945 'Z3 invalid substitution, mismatching "from" and "to" sorts.')
8947 _from = (Ast * num)()
8949 for i
in range(num):
8950 _from[i] = m[i][0].as_ast()
8951 _to[i] = m[i][1].as_ast()
8952 return _to_expr_ref(
Z3_substitute(t.ctx.ref(), t.as_ast(), num, _from, _to), t.ctx)
8956 """Substitute the free variables in t with the expression in m.
8958 >>> v0 = Var(0, IntSort())
8959 >>> v1 = Var(1, IntSort())
8961 >>> f = Function('f', IntSort(), IntSort(), IntSort())
8962 >>> # replace v0 with x+1 and v1 with x
8963 >>> substitute_vars(f(v0, v1), x + 1, x)
8967 _z3_assert(
is_expr(t),
"Z3 expression expected")
8968 _z3_assert(all([
is_expr(n)
for n
in m]),
"Z3 invalid substitution, list of expressions expected.")
8971 for i
in range(num):
8972 _to[i] = m[i].as_ast()
8976 """Apply substitution m on t, m is a list of pairs of a function and expression (from, to)
8977 Every occurrence in to of the function from is replaced with the expression to.
8978 The expression to can have free variables, that refer to the arguments of from.
8981 if isinstance(m, tuple):
8983 if isinstance(m1, list)
and all(isinstance(p, tuple)
for p
in m1):
8986 _z3_assert(
is_expr(t),
"Z3 expression expected")
8987 _z3_assert(all([isinstance(p, tuple)
and is_func_decl(p[0])
and is_expr(p[1])
for p
in m]),
"Z3 invalid substitution, function pairs expected.")
8989 _from = (FuncDecl * num)()
8991 for i
in range(num):
8992 _from[i] = m[i][0].as_func_decl()
8993 _to[i] = m[i][1].as_ast()
8994 return _to_expr_ref(
Z3_substitute_funs(t.ctx.ref(), t.as_ast(), num, _from, _to), t.ctx)
8998 """Create the sum of the Z3 expressions.
9000 >>> a, b, c = Ints('a b c')
9005 >>> A = IntVector('a', 5)
9007 a__0 + a__1 + a__2 + a__3 + a__4
9009 args = _get_args(args)
9012 ctx = _ctx_from_ast_arg_list(args)
9014 return _reduce(
lambda a, b: a + b, args, 0)
9015 args = _coerce_expr_list(args, ctx)
9017 return _reduce(
lambda a, b: a + b, args, 0)
9019 _args, sz = _to_ast_array(args)
9024 """Create the product of the Z3 expressions.
9026 >>> a, b, c = Ints('a b c')
9027 >>> Product(a, b, c)
9029 >>> Product([a, b, c])
9031 >>> A = IntVector('a', 5)
9033 a__0*a__1*a__2*a__3*a__4
9035 args = _get_args(args)
9038 ctx = _ctx_from_ast_arg_list(args)
9040 return _reduce(
lambda a, b: a * b, args, 1)
9041 args = _coerce_expr_list(args, ctx)
9043 return _reduce(
lambda a, b: a * b, args, 1)
9045 _args, sz = _to_ast_array(args)
9049 """Create the absolute value of an arithmetic expression"""
9050 return If(arg > 0, arg, -arg)
9054 """Create an at-most Pseudo-Boolean k constraint.
9056 >>> a, b, c = Bools('a b c')
9057 >>> f = AtMost(a, b, c, 2)
9059 args = _get_args(args)
9061 _z3_assert(len(args) > 1,
"Non empty list of arguments expected")
9062 ctx = _ctx_from_ast_arg_list(args)
9064 _z3_assert(ctx
is not None,
"At least one of the arguments must be a Z3 expression")
9065 args1 = _coerce_expr_list(args[:-1], ctx)
9067 _args, sz = _to_ast_array(args1)
9072 """Create an at-least Pseudo-Boolean k constraint.
9074 >>> a, b, c = Bools('a b c')
9075 >>> f = AtLeast(a, b, c, 2)
9077 args = _get_args(args)
9079 _z3_assert(len(args) > 1,
"Non empty list of arguments expected")
9080 ctx = _ctx_from_ast_arg_list(args)
9082 _z3_assert(ctx
is not None,
"At least one of the arguments must be a Z3 expression")
9083 args1 = _coerce_expr_list(args[:-1], ctx)
9085 _args, sz = _to_ast_array(args1)
9089 def _reorder_pb_arg(arg):
9091 if not _is_int(b)
and _is_int(a):
9096 def _pb_args_coeffs(args, default_ctx=None):
9097 args = _get_args_ast_list(args)
9099 return _get_ctx(default_ctx), 0, (Ast * 0)(), (ctypes.c_int * 0)()
9100 args = [_reorder_pb_arg(arg)
for arg
in args]
9101 args, coeffs = zip(*args)
9103 _z3_assert(len(args) > 0,
"Non empty list of arguments expected")
9104 ctx = _ctx_from_ast_arg_list(args)
9106 _z3_assert(ctx
is not None,
"At least one of the arguments must be a Z3 expression")
9107 args = _coerce_expr_list(args, ctx)
9108 _args, sz = _to_ast_array(args)
9109 _coeffs = (ctypes.c_int * len(coeffs))()
9110 for i
in range(len(coeffs)):
9111 _z3_check_cint_overflow(coeffs[i],
"coefficient")
9112 _coeffs[i] = coeffs[i]
9113 return ctx, sz, _args, _coeffs, args
9117 """Create a Pseudo-Boolean inequality k constraint.
9119 >>> a, b, c = Bools('a b c')
9120 >>> f = PbLe(((a,1),(b,3),(c,2)), 3)
9122 _z3_check_cint_overflow(k,
"k")
9123 ctx, sz, _args, _coeffs, args = _pb_args_coeffs(args)
9128 """Create a Pseudo-Boolean inequality k constraint.
9130 >>> a, b, c = Bools('a b c')
9131 >>> f = PbGe(((a,1),(b,3),(c,2)), 3)
9133 _z3_check_cint_overflow(k,
"k")
9134 ctx, sz, _args, _coeffs, args = _pb_args_coeffs(args)
9139 """Create a Pseudo-Boolean equality k constraint.
9141 >>> a, b, c = Bools('a b c')
9142 >>> f = PbEq(((a,1),(b,3),(c,2)), 3)
9144 _z3_check_cint_overflow(k,
"k")
9145 ctx, sz, _args, _coeffs, args = _pb_args_coeffs(args)
9150 """Solve the constraints `*args`.
9152 This is a simple function for creating demonstrations. It creates a solver,
9153 configure it using the options in `keywords`, adds the constraints
9154 in `args`, and invokes check.
9157 >>> solve(a > 0, a < 2)
9160 show = keywords.pop(
"show",
False)
9168 print(
"no solution")
9170 print(
"failed to solve")
9180 """Solve the constraints `*args` using solver `s`.
9182 This is a simple function for creating demonstrations. It is similar to `solve`,
9183 but it uses the given solver `s`.
9184 It configures solver `s` using the options in `keywords`, adds the constraints
9185 in `args`, and invokes check.
9187 show = keywords.pop(
"show",
False)
9189 _z3_assert(isinstance(s, Solver),
"Solver object expected")
9197 print(
"no solution")
9199 print(
"failed to solve")
9210 def prove(claim, show=False, **keywords):
9211 """Try to prove the given claim.
9213 This is a simple function for creating demonstrations. It tries to prove
9214 `claim` by showing the negation is unsatisfiable.
9216 >>> p, q = Bools('p q')
9217 >>> prove(Not(And(p, q)) == Or(Not(p), Not(q)))
9221 _z3_assert(
is_bool(claim),
"Z3 Boolean expression expected")
9231 print(
"failed to prove")
9234 print(
"counterexample")
9238 def _solve_html(*args, **keywords):
9239 """Version of function `solve` that renders HTML output."""
9240 show = keywords.pop(
"show",
False)
9245 print(
"<b>Problem:</b>")
9249 print(
"<b>no solution</b>")
9251 print(
"<b>failed to solve</b>")
9258 print(
"<b>Solution:</b>")
9262 def _solve_using_html(s, *args, **keywords):
9263 """Version of function `solve_using` that renders HTML."""
9264 show = keywords.pop(
"show",
False)
9266 _z3_assert(isinstance(s, Solver),
"Solver object expected")
9270 print(
"<b>Problem:</b>")
9274 print(
"<b>no solution</b>")
9276 print(
"<b>failed to solve</b>")
9283 print(
"<b>Solution:</b>")
9287 def _prove_html(claim, show=False, **keywords):
9288 """Version of function `prove` that renders HTML."""
9290 _z3_assert(
is_bool(claim),
"Z3 Boolean expression expected")
9298 print(
"<b>proved</b>")
9300 print(
"<b>failed to prove</b>")
9303 print(
"<b>counterexample</b>")
9307 def _dict2sarray(sorts, ctx):
9309 _names = (Symbol * sz)()
9310 _sorts = (Sort * sz)()
9315 _z3_assert(isinstance(k, str),
"String expected")
9316 _z3_assert(
is_sort(v),
"Z3 sort expected")
9320 return sz, _names, _sorts
9323 def _dict2darray(decls, ctx):
9325 _names = (Symbol * sz)()
9326 _decls = (FuncDecl * sz)()
9331 _z3_assert(isinstance(k, str),
"String expected")
9335 _decls[i] = v.decl().ast
9339 return sz, _names, _decls
9348 if self.ctx.ref()
is not None and self.
pctx is not None and Z3_parser_context_dec_ref
is not None:
9362 """Parse a string in SMT 2.0 format using the given sorts and decls.
9364 The arguments sorts and decls are Python dictionaries used to initialize
9365 the symbol table used for the SMT 2.0 parser.
9367 >>> parse_smt2_string('(declare-const x Int) (assert (> x 0)) (assert (< x 10))')
9369 >>> x, y = Ints('x y')
9370 >>> f = Function('f', IntSort(), IntSort())
9371 >>> parse_smt2_string('(assert (> (+ foo (g bar)) 0))', decls={ 'foo' : x, 'bar' : y, 'g' : f})
9373 >>> parse_smt2_string('(declare-const a U) (assert (> a 0))', sorts={ 'U' : IntSort() })
9377 ssz, snames, ssorts = _dict2sarray(sorts, ctx)
9378 dsz, dnames, ddecls = _dict2darray(decls, ctx)
9379 return AstVector(Z3_parse_smtlib2_string(ctx.ref(), s, ssz, snames, ssorts, dsz, dnames, ddecls), ctx)
9382 def parse_smt2_file(f, sorts={}, decls={}, ctx=None):
9383 """Parse a file
in SMT 2.0 format using the given sorts
and decls.
9388 ssz, snames, ssorts = _dict2sarray(sorts, ctx)
9389 dsz, dnames, ddecls = _dict2darray(decls, ctx)
9390 return AstVector(Z3_parse_smtlib2_file(ctx.ref(), f, ssz, snames, ssorts, dsz, dnames, ddecls), ctx)
9393 #########################################
9395 # Floating-Point Arithmetic
9397 #########################################
9400 # Global default rounding mode
9401 _dflt_rounding_mode = Z3_OP_FPA_RM_NEAREST_TIES_TO_EVEN
9402 _dflt_fpsort_ebits = 11
9403 _dflt_fpsort_sbits = 53
9406 def get_default_rounding_mode(ctx=None):
9407 """Retrieves the
global default rounding mode.
"""
9408 global _dflt_rounding_mode
9409 if _dflt_rounding_mode == Z3_OP_FPA_RM_TOWARD_ZERO:
9411 elif _dflt_rounding_mode == Z3_OP_FPA_RM_TOWARD_NEGATIVE:
9413 elif _dflt_rounding_mode == Z3_OP_FPA_RM_TOWARD_POSITIVE:
9415 elif _dflt_rounding_mode == Z3_OP_FPA_RM_NEAREST_TIES_TO_EVEN:
9417 elif _dflt_rounding_mode == Z3_OP_FPA_RM_NEAREST_TIES_TO_AWAY:
9421 _ROUNDING_MODES = frozenset({
9422 Z3_OP_FPA_RM_TOWARD_ZERO,
9423 Z3_OP_FPA_RM_TOWARD_NEGATIVE,
9424 Z3_OP_FPA_RM_TOWARD_POSITIVE,
9425 Z3_OP_FPA_RM_NEAREST_TIES_TO_EVEN,
9426 Z3_OP_FPA_RM_NEAREST_TIES_TO_AWAY
9430 def set_default_rounding_mode(rm, ctx=None):
9431 global _dflt_rounding_mode
9432 if is_fprm_value(rm):
9433 _dflt_rounding_mode = rm.decl().kind()
9435 _z3_assert(_dflt_rounding_mode in _ROUNDING_MODES, "illegal rounding mode")
9436 _dflt_rounding_mode = rm
9439 def get_default_fp_sort(ctx=None):
9440 return FPSort(_dflt_fpsort_ebits, _dflt_fpsort_sbits, ctx)
9443 def set_default_fp_sort(ebits, sbits, ctx=None):
9444 global _dflt_fpsort_ebits
9445 global _dflt_fpsort_sbits
9446 _dflt_fpsort_ebits = ebits
9447 _dflt_fpsort_sbits = sbits
9450 def _dflt_rm(ctx=None):
9451 return get_default_rounding_mode(ctx)
9454 def _dflt_fps(ctx=None):
9455 return get_default_fp_sort(ctx)
9458 def _coerce_fp_expr_list(alist, ctx):
9459 first_fp_sort = None
9462 if first_fp_sort is None:
9463 first_fp_sort = a.sort()
9464 elif first_fp_sort == a.sort():
9465 pass # OK, same as before
9467 # we saw at least 2 different float sorts; something will
9468 # throw a sort mismatch later, for now assume None.
9469 first_fp_sort = None
9473 for i in range(len(alist)):
9475 is_repr = isinstance(a, str) and a.contains("2**(") and a.endswith(")")
9476 if is_repr or _is_int(a) or isinstance(a, (float, bool)):
9477 r.append(FPVal(a, None, first_fp_sort, ctx))
9480 return _coerce_expr_list(r, ctx)
9485 class FPSortRef(SortRef):
9486 """Floating-point sort.
"""
9489 """Retrieves the number of bits reserved
for the exponent
in the FloatingPoint sort `self`.
9494 return int(Z3_fpa_get_ebits(self.ctx_ref(), self.ast))
9497 """Retrieves the number of bits reserved
for the significand
in the FloatingPoint sort `self`.
9502 return int(Z3_fpa_get_sbits(self.ctx_ref(), self.ast))
9504 def cast(self, val):
9505 """Try to cast `val`
as a floating-point expression.
9509 >>> b.cast(1.0).
sexpr()
9510 '(fp #b0 #x7f #b00000000000000000000000)'
9514 _z3_assert(self.ctx == val.ctx, "Context mismatch")
9517 return FPVal(val, None, self, self.ctx)
9520 def Float16(ctx=None):
9521 """Floating-point 16-bit (half) sort.
"""
9523 return FPSortRef(Z3_mk_fpa_sort_16(ctx.ref()), ctx)
9526 def FloatHalf(ctx=None):
9527 """Floating-point 16-bit (half) sort.
"""
9529 return FPSortRef(Z3_mk_fpa_sort_half(ctx.ref()), ctx)
9532 def Float32(ctx=None):
9533 """Floating-point 32-bit (single) sort.
"""
9535 return FPSortRef(Z3_mk_fpa_sort_32(ctx.ref()), ctx)
9538 def FloatSingle(ctx=None):
9539 """Floating-point 32-bit (single) sort.
"""
9541 return FPSortRef(Z3_mk_fpa_sort_single(ctx.ref()), ctx)
9544 def Float64(ctx=None):
9545 """Floating-point 64-bit (double) sort.
"""
9547 return FPSortRef(Z3_mk_fpa_sort_64(ctx.ref()), ctx)
9550 def FloatDouble(ctx=None):
9551 """Floating-point 64-bit (double) sort.
"""
9553 return FPSortRef(Z3_mk_fpa_sort_double(ctx.ref()), ctx)
9556 def Float128(ctx=None):
9557 """Floating-point 128-bit (quadruple) sort.
"""
9559 return FPSortRef(Z3_mk_fpa_sort_128(ctx.ref()), ctx)
9562 def FloatQuadruple(ctx=None):
9563 """Floating-point 128-bit (quadruple) sort.
"""
9565 return FPSortRef(Z3_mk_fpa_sort_quadruple(ctx.ref()), ctx)
9568 class FPRMSortRef(SortRef):
9569 """"Floating-point rounding mode sort."""
9573 """Return True if `s` is a Z3 floating-point sort.
9580 return isinstance(s, FPSortRef)
9583 def is_fprm_sort(s):
9584 """Return
True if `s`
is a Z3 floating-point rounding mode sort.
9591 return isinstance(s, FPRMSortRef)
9596 class FPRef(ExprRef):
9597 """Floating-point expressions.
"""
9600 """Return the sort of the floating-point expression `self`.
9605 >>> x.sort() ==
FPSort(8, 24)
9608 return FPSortRef(Z3_get_sort(self.ctx_ref(), self.as_ast()), self.ctx)
9611 """Retrieves the number of bits reserved
for the exponent
in the FloatingPoint expression `self`.
9616 return self.sort().ebits()
9619 """Retrieves the number of bits reserved
for the exponent
in the FloatingPoint expression `self`.
9624 return self.sort().sbits()
9626 def as_string(self):
9627 """Return a Z3 floating point expression
as a Python string.
"""
9628 return Z3_ast_to_string(self.ctx_ref(), self.as_ast())
9630 def __le__(self, other):
9631 return fpLEQ(self, other, self.ctx)
9633 def __lt__(self, other):
9634 return fpLT(self, other, self.ctx)
9636 def __ge__(self, other):
9637 return fpGEQ(self, other, self.ctx)
9639 def __gt__(self, other):
9640 return fpGT(self, other, self.ctx)
9642 def __add__(self, other):
9643 """Create the Z3 expression `self + other`.
9652 [a, b] = _coerce_fp_expr_list([self, other], self.ctx)
9653 return fpAdd(_dflt_rm(), a, b, self.ctx)
9655 def __radd__(self, other):
9656 """Create the Z3 expression `other + self`.
9662 [a, b] = _coerce_fp_expr_list([other, self], self.ctx)
9663 return fpAdd(_dflt_rm(), a, b, self.ctx)
9665 def __sub__(self, other):
9666 """Create the Z3 expression `self - other`.
9675 [a, b] = _coerce_fp_expr_list([self, other], self.ctx)
9676 return fpSub(_dflt_rm(), a, b, self.ctx)
9678 def __rsub__(self, other):
9679 """Create the Z3 expression `other - self`.
9685 [a, b] = _coerce_fp_expr_list([other, self], self.ctx)
9686 return fpSub(_dflt_rm(), a, b, self.ctx)
9688 def __mul__(self, other):
9689 """Create the Z3 expression `self * other`.
9700 [a, b] = _coerce_fp_expr_list([self, other], self.ctx)
9701 return fpMul(_dflt_rm(), a, b, self.ctx)
9703 def __rmul__(self, other):
9704 """Create the Z3 expression `other * self`.
9713 [a, b] = _coerce_fp_expr_list([other, self], self.ctx)
9714 return fpMul(_dflt_rm(), a, b, self.ctx)
9717 """Create the Z3 expression `+self`.
"""
9721 """Create the Z3 expression `-self`.
9729 def __div__(self, other):
9730 """Create the Z3 expression `self / other`.
9741 [a, b] = _coerce_fp_expr_list([self, other], self.ctx)
9742 return fpDiv(_dflt_rm(), a, b, self.ctx)
9744 def __rdiv__(self, other):
9745 """Create the Z3 expression `other / self`.
9754 [a, b] = _coerce_fp_expr_list([other, self], self.ctx)
9755 return fpDiv(_dflt_rm(), a, b, self.ctx)
9757 def __truediv__(self, other):
9758 """Create the Z3 expression division `self / other`.
"""
9759 return self.__div__(other)
9761 def __rtruediv__(self, other):
9762 """Create the Z3 expression division `other / self`.
"""
9763 return self.__rdiv__(other)
9765 def __mod__(self, other):
9766 """Create the Z3 expression mod `self % other`.
"""
9767 return fpRem(self, other)
9769 def __rmod__(self, other):
9770 """Create the Z3 expression mod `other % self`.
"""
9771 return fpRem(other, self)
9774 class FPRMRef(ExprRef):
9775 """Floating-point rounding mode expressions
"""
9777 def as_string(self):
9778 """Return a Z3 floating point expression
as a Python string.
"""
9779 return Z3_ast_to_string(self.ctx_ref(), self.as_ast())
9782 def RoundNearestTiesToEven(ctx=None):
9784 return FPRMRef(Z3_mk_fpa_round_nearest_ties_to_even(ctx.ref()), ctx)
9789 return FPRMRef(Z3_mk_fpa_round_nearest_ties_to_even(ctx.ref()), ctx)
9792 def RoundNearestTiesToAway(ctx=None):
9794 return FPRMRef(Z3_mk_fpa_round_nearest_ties_to_away(ctx.ref()), ctx)
9799 return FPRMRef(Z3_mk_fpa_round_nearest_ties_to_away(ctx.ref()), ctx)
9802 def RoundTowardPositive(ctx=None):
9804 return FPRMRef(Z3_mk_fpa_round_toward_positive(ctx.ref()), ctx)
9809 return FPRMRef(Z3_mk_fpa_round_toward_positive(ctx.ref()), ctx)
9812 def RoundTowardNegative(ctx=None):
9814 return FPRMRef(Z3_mk_fpa_round_toward_negative(ctx.ref()), ctx)
9819 return FPRMRef(Z3_mk_fpa_round_toward_negative(ctx.ref()), ctx)
9822 def RoundTowardZero(ctx=None):
9824 return FPRMRef(Z3_mk_fpa_round_toward_zero(ctx.ref()), ctx)
9829 return FPRMRef(Z3_mk_fpa_round_toward_zero(ctx.ref()), ctx)
9833 """Return `
True`
if `a`
is a Z3 floating-point rounding mode expression.
9842 return isinstance(a, FPRMRef)
9845 def is_fprm_value(a):
9846 """Return `
True`
if `a`
is a Z3 floating-point rounding mode numeral value.
"""
9847 return is_fprm(a) and _is_numeral(a.ctx, a.ast)
9852 class FPNumRef(FPRef):
9853 """The sign of the numeral.
9864 num = (ctypes.c_int)()
9865 nsign = Z3_fpa_get_numeral_sign(self.ctx.ref(), self.as_ast(), byref(num))
9867 raise Z3Exception("error retrieving the sign of a numeral.")
9868 return num.value != 0
9870 """The sign of a floating-point numeral
as a bit-vector expression.
9872 Remark: NaN
's are invalid arguments.
9875 def sign_as_bv(self):
9876 return BitVecNumRef(Z3_fpa_get_numeral_sign_bv(self.ctx.ref(), self.as_ast()), self.ctx)
9878 """The significand of the numeral.
9885 def significand(self):
9886 return Z3_fpa_get_numeral_significand_string(self.ctx.ref(), self.as_ast())
9888 """The significand of the numeral
as a long.
9891 >>> x.significand_as_long()
9895 def significand_as_long(self):
9896 ptr = (ctypes.c_ulonglong * 1)()
9897 if not Z3_fpa_get_numeral_significand_uint64(self.ctx.ref(), self.as_ast(), ptr):
9898 raise Z3Exception("error retrieving the significand of a numeral.")
9901 """The significand of the numeral
as a bit-vector expression.
9903 Remark: NaN are invalid arguments.
9906 def significand_as_bv(self):
9907 return BitVecNumRef(Z3_fpa_get_numeral_significand_bv(self.ctx.ref(), self.as_ast()), self.ctx)
9909 """The exponent of the numeral.
9916 def exponent(self, biased=True):
9917 return Z3_fpa_get_numeral_exponent_string(self.ctx.ref(), self.as_ast(), biased)
9919 """The exponent of the numeral
as a long.
9922 >>> x.exponent_as_long()
9926 def exponent_as_long(self, biased=True):
9927 ptr = (ctypes.c_longlong * 1)()
9928 if not Z3_fpa_get_numeral_exponent_int64(self.ctx.ref(), self.as_ast(), ptr, biased):
9929 raise Z3Exception("error retrieving the exponent of a numeral.")
9932 """The exponent of the numeral
as a bit-vector expression.
9934 Remark: NaNs are invalid arguments.
9937 def exponent_as_bv(self, biased=True):
9938 return BitVecNumRef(Z3_fpa_get_numeral_exponent_bv(self.ctx.ref(), self.as_ast(), biased), self.ctx)
9940 """Indicates whether the numeral
is a NaN.
"""
9943 return Z3_fpa_is_numeral_nan(self.ctx.ref(), self.as_ast())
9945 """Indicates whether the numeral
is +oo
or -oo.
"""
9948 return Z3_fpa_is_numeral_inf(self.ctx.ref(), self.as_ast())
9950 """Indicates whether the numeral
is +zero
or -zero.
"""
9953 return Z3_fpa_is_numeral_zero(self.ctx.ref(), self.as_ast())
9955 """Indicates whether the numeral
is normal.
"""
9958 return Z3_fpa_is_numeral_normal(self.ctx.ref(), self.as_ast())
9960 """Indicates whether the numeral
is subnormal.
"""
9962 def isSubnormal(self):
9963 return Z3_fpa_is_numeral_subnormal(self.ctx.ref(), self.as_ast())
9965 """Indicates whether the numeral
is positive.
"""
9967 def isPositive(self):
9968 return Z3_fpa_is_numeral_positive(self.ctx.ref(), self.as_ast())
9970 """Indicates whether the numeral
is negative.
"""
9972 def isNegative(self):
9973 return Z3_fpa_is_numeral_negative(self.ctx.ref(), self.as_ast())
9976 The string representation of the numeral.
9983 def as_string(self):
9984 s = Z3_get_numeral_string(self.ctx.ref(), self.as_ast())
9985 return ("FPVal(%s, %s)" % (s, self.sort()))
9989 """Return `
True`
if `a`
is a Z3 floating-point expression.
9999 return isinstance(a, FPRef)
10002 def is_fp_value(a):
10003 """Return `
True`
if `a`
is a Z3 floating-point numeral value.
10014 return is_fp(a) and _is_numeral(a.ctx, a.ast)
10017 def FPSort(ebits, sbits, ctx=None):
10018 """Return a Z3 floating-point sort of the given sizes. If `ctx=
None`, then the
global context
is used.
10020 >>> Single =
FPSort(8, 24)
10021 >>> Double =
FPSort(11, 53)
10024 >>> x =
Const(
'x', Single)
10028 ctx = _get_ctx(ctx)
10029 return FPSortRef(Z3_mk_fpa_sort(ctx.ref(), ebits, sbits), ctx)
10032 def _to_float_str(val, exp=0):
10033 if isinstance(val, float):
10034 if math.isnan(val):
10037 sone = math.copysign(1.0, val)
10042 elif val == float("+inf"):
10044 elif val == float("-inf"):
10047 v = val.as_integer_ratio()
10050 rvs = str(num) + "/" + str(den)
10051 res = rvs + "p" + _to_int_str(exp)
10052 elif isinstance(val, bool):
10059 elif isinstance(val, str):
10060 inx = val.find("*(2**")
10063 elif val[-1] == ")":
10065 exp = str(int(val[inx + 5:-1]) + int(exp))
10067 _z3_assert(False, "String does not have floating-point numeral form.")
10069 _z3_assert(False, "Python value cannot be used to create floating-point numerals.")
10073 return res + "p" + exp
10077 """Create a Z3 floating-point NaN term.
10080 >>> set_fpa_pretty(
True)
10083 >>> pb = get_fpa_pretty()
10084 >>> set_fpa_pretty(
False)
10087 >>> set_fpa_pretty(pb)
10089 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10090 return FPNumRef(Z3_mk_fpa_nan(s.ctx_ref(), s.ast), s.ctx)
10093 def fpPlusInfinity(s):
10094 """Create a Z3 floating-point +oo term.
10097 >>> pb = get_fpa_pretty()
10098 >>> set_fpa_pretty(
True)
10101 >>> set_fpa_pretty(
False)
10104 >>> set_fpa_pretty(pb)
10106 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10107 return FPNumRef(Z3_mk_fpa_inf(s.ctx_ref(), s.ast, False), s.ctx)
10110 def fpMinusInfinity(s):
10111 """Create a Z3 floating-point -oo term.
"""
10112 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10113 return FPNumRef(Z3_mk_fpa_inf(s.ctx_ref(), s.ast, True), s.ctx)
10116 def fpInfinity(s, negative):
10117 """Create a Z3 floating-point +oo
or -oo term.
"""
10118 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10119 _z3_assert(isinstance(negative, bool), "expected Boolean flag")
10120 return FPNumRef(Z3_mk_fpa_inf(s.ctx_ref(), s.ast, negative), s.ctx)
10124 """Create a Z3 floating-point +0.0 term.
"""
10125 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10126 return FPNumRef(Z3_mk_fpa_zero(s.ctx_ref(), s.ast, False), s.ctx)
10129 def fpMinusZero(s):
10130 """Create a Z3 floating-point -0.0 term.
"""
10131 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10132 return FPNumRef(Z3_mk_fpa_zero(s.ctx_ref(), s.ast, True), s.ctx)
10135 def fpZero(s, negative):
10136 """Create a Z3 floating-point +0.0
or -0.0 term.
"""
10137 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10138 _z3_assert(isinstance(negative, bool), "expected Boolean flag")
10139 return FPNumRef(Z3_mk_fpa_zero(s.ctx_ref(), s.ast, negative), s.ctx)
10142 def FPVal(sig, exp=None, fps=None, ctx=None):
10143 """Return a floating-point value of value `val`
and sort `fps`.
10144 If `ctx=
None`, then the
global context
is used.
10149 >>> print(
"0x%.8x" % v.exponent_as_long(
False))
10164 ctx = _get_ctx(ctx)
10165 if is_fp_sort(exp):
10169 fps = _dflt_fps(ctx)
10170 _z3_assert(is_fp_sort(fps), "sort mismatch")
10173 val = _to_float_str(sig)
10174 if val == "NaN" or val == "nan":
10176 elif val == "-0.0":
10177 return fpMinusZero(fps)
10178 elif val == "0.0" or val == "+0.0":
10179 return fpPlusZero(fps)
10180 elif val == "+oo" or val == "+inf" or val == "+Inf":
10181 return fpPlusInfinity(fps)
10182 elif val == "-oo" or val == "-inf" or val == "-Inf":
10183 return fpMinusInfinity(fps)
10185 return FPNumRef(Z3_mk_numeral(ctx.ref(), val, fps.ast), ctx)
10188 def FP(name, fpsort, ctx=None):
10189 """Return a floating-point constant named `name`.
10190 `fpsort`
is the floating-point sort.
10191 If `ctx=
None`, then the
global context
is used.
10200 >>> word =
FPSort(8, 24)
10201 >>> x2 =
FP(
'x', word)
10205 if isinstance(fpsort, FPSortRef) and ctx is None:
10208 ctx = _get_ctx(ctx)
10209 return FPRef(Z3_mk_const(ctx.ref(), to_symbol(name, ctx), fpsort.ast), ctx)
10212 def FPs(names, fpsort, ctx=None):
10213 """Return an array of floating-point constants.
10215 >>> x, y, z =
FPs(
'x y z',
FPSort(8, 24))
10225 ctx = _get_ctx(ctx)
10226 if isinstance(names, str):
10227 names = names.split(" ")
10228 return [FP(name, fpsort, ctx) for name in names]
10231 def fpAbs(a, ctx=None):
10232 """Create a Z3 floating-point absolute value expression.
10236 >>> x =
FPVal(1.0, s)
10239 >>> y =
FPVal(-20.0, s)
10243 fpAbs(-1.25*(2**4))
10244 >>>
fpAbs(-1.25*(2**4))
10245 fpAbs(-1.25*(2**4))
10246 >>>
fpAbs(x).sort()
10249 ctx = _get_ctx(ctx)
10250 [a] = _coerce_fp_expr_list([a], ctx)
10251 return FPRef(Z3_mk_fpa_abs(ctx.ref(), a.as_ast()), ctx)
10254 def fpNeg(a, ctx=None):
10255 """Create a Z3 floating-point addition expression.
10262 >>>
fpNeg(x).sort()
10265 ctx = _get_ctx(ctx)
10266 [a] = _coerce_fp_expr_list([a], ctx)
10267 return FPRef(Z3_mk_fpa_neg(ctx.ref(), a.as_ast()), ctx)
10270 def _mk_fp_unary(f, rm, a, ctx):
10271 ctx = _get_ctx(ctx)
10272 [a] = _coerce_fp_expr_list([a], ctx)
10274 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10275 _z3_assert(is_fp(a), "Second argument must be a Z3 floating-point expression")
10276 return FPRef(f(ctx.ref(), rm.as_ast(), a.as_ast()), ctx)
10279 def _mk_fp_unary_pred(f, a, ctx):
10280 ctx = _get_ctx(ctx)
10281 [a] = _coerce_fp_expr_list([a], ctx)
10283 _z3_assert(is_fp(a), "First argument must be a Z3 floating-point expression")
10284 return BoolRef(f(ctx.ref(), a.as_ast()), ctx)
10287 def _mk_fp_bin(f, rm, a, b, ctx):
10288 ctx = _get_ctx(ctx)
10289 [a, b] = _coerce_fp_expr_list([a, b], ctx)
10291 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10292 _z3_assert(is_fp(a) or is_fp(b), "Second or third argument must be a Z3 floating-point expression")
10293 return FPRef(f(ctx.ref(), rm.as_ast(), a.as_ast(), b.as_ast()), ctx)
10296 def _mk_fp_bin_norm(f, a, b, ctx):
10297 ctx = _get_ctx(ctx)
10298 [a, b] = _coerce_fp_expr_list([a, b], ctx)
10300 _z3_assert(is_fp(a) or is_fp(b), "First or second argument must be a Z3 floating-point expression")
10301 return FPRef(f(ctx.ref(), a.as_ast(), b.as_ast()), ctx)
10304 def _mk_fp_bin_pred(f, a, b, ctx):
10305 ctx = _get_ctx(ctx)
10306 [a, b] = _coerce_fp_expr_list([a, b], ctx)
10308 _z3_assert(is_fp(a) or is_fp(b), "First or second argument must be a Z3 floating-point expression")
10309 return BoolRef(f(ctx.ref(), a.as_ast(), b.as_ast()), ctx)
10312 def _mk_fp_tern(f, rm, a, b, c, ctx):
10313 ctx = _get_ctx(ctx)
10314 [a, b, c] = _coerce_fp_expr_list([a, b, c], ctx)
10316 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10317 _z3_assert(is_fp(a) or is_fp(b) or is_fp(
10318 c), "Second, third or fourth argument must be a Z3 floating-point expression")
10319 return FPRef(f(ctx.ref(), rm.as_ast(), a.as_ast(), b.as_ast(), c.as_ast()), ctx)
10322 def fpAdd(rm, a, b, ctx=None):
10323 """Create a Z3 floating-point addition expression.
10329 >>>
fpAdd(rm, x, y)
10333 >>>
fpAdd(rm, x, y).sort()
10336 return _mk_fp_bin(Z3_mk_fpa_add, rm, a, b, ctx)
10339 def fpSub(rm, a, b, ctx=None):
10340 """Create a Z3 floating-point subtraction expression.
10346 >>>
fpSub(rm, x, y)
10348 >>>
fpSub(rm, x, y).sort()
10351 return _mk_fp_bin(Z3_mk_fpa_sub, rm, a, b, ctx)
10354 def fpMul(rm, a, b, ctx=None):
10355 """Create a Z3 floating-point multiplication expression.
10361 >>>
fpMul(rm, x, y)
10363 >>>
fpMul(rm, x, y).sort()
10366 return _mk_fp_bin(Z3_mk_fpa_mul, rm, a, b, ctx)
10369 def fpDiv(rm, a, b, ctx=None):
10370 """Create a Z3 floating-point division expression.
10376 >>>
fpDiv(rm, x, y)
10378 >>>
fpDiv(rm, x, y).sort()
10381 return _mk_fp_bin(Z3_mk_fpa_div, rm, a, b, ctx)
10384 def fpRem(a, b, ctx=None):
10385 """Create a Z3 floating-point remainder expression.
10392 >>>
fpRem(x, y).sort()
10395 return _mk_fp_bin_norm(Z3_mk_fpa_rem, a, b, ctx)
10398 def fpMin(a, b, ctx=None):
10399 """Create a Z3 floating-point minimum expression.
10407 >>>
fpMin(x, y).sort()
10410 return _mk_fp_bin_norm(Z3_mk_fpa_min, a, b, ctx)
10413 def fpMax(a, b, ctx=None):
10414 """Create a Z3 floating-point maximum expression.
10422 >>>
fpMax(x, y).sort()
10425 return _mk_fp_bin_norm(Z3_mk_fpa_max, a, b, ctx)
10428 def fpFMA(rm, a, b, c, ctx=None):
10429 """Create a Z3 floating-point fused multiply-add expression.
10431 return _mk_fp_tern(Z3_mk_fpa_fma, rm, a, b, c, ctx)
10434 def fpSqrt(rm, a, ctx=None):
10435 """Create a Z3 floating-point square root expression.
10437 return _mk_fp_unary(Z3_mk_fpa_sqrt, rm, a, ctx)
10440 def fpRoundToIntegral(rm, a, ctx=None):
10441 """Create a Z3 floating-point roundToIntegral expression.
10443 return _mk_fp_unary(Z3_mk_fpa_round_to_integral, rm, a, ctx)
10446 def fpIsNaN(a, ctx=None):
10447 """Create a Z3 floating-point isNaN expression.
10455 return _mk_fp_unary_pred(Z3_mk_fpa_is_nan, a, ctx)
10458 def fpIsInf(a, ctx=None):
10459 """Create a Z3 floating-point isInfinite expression.
10466 return _mk_fp_unary_pred(Z3_mk_fpa_is_infinite, a, ctx)
10469 def fpIsZero(a, ctx=None):
10470 """Create a Z3 floating-point isZero expression.
10472 return _mk_fp_unary_pred(Z3_mk_fpa_is_zero, a, ctx)
10475 def fpIsNormal(a, ctx=None):
10476 """Create a Z3 floating-point isNormal expression.
10478 return _mk_fp_unary_pred(Z3_mk_fpa_is_normal, a, ctx)
10481 def fpIsSubnormal(a, ctx=None):
10482 """Create a Z3 floating-point isSubnormal expression.
10484 return _mk_fp_unary_pred(Z3_mk_fpa_is_subnormal, a, ctx)
10487 def fpIsNegative(a, ctx=None):
10488 """Create a Z3 floating-point isNegative expression.
10490 return _mk_fp_unary_pred(Z3_mk_fpa_is_negative, a, ctx)
10493 def fpIsPositive(a, ctx=None):
10494 """Create a Z3 floating-point isPositive expression.
10496 return _mk_fp_unary_pred(Z3_mk_fpa_is_positive, a, ctx)
10499 def _check_fp_args(a, b):
10501 _z3_assert(is_fp(a) or is_fp(b), "First or second argument must be a Z3 floating-point expression")
10504 def fpLT(a, b, ctx=None):
10505 """Create the Z3 floating-point expression `other < self`.
10510 >>> (x < y).sexpr()
10513 return _mk_fp_bin_pred(Z3_mk_fpa_lt, a, b, ctx)
10516 def fpLEQ(a, b, ctx=None):
10517 """Create the Z3 floating-point expression `other <= self`.
10522 >>> (x <= y).sexpr()
10525 return _mk_fp_bin_pred(Z3_mk_fpa_leq, a, b, ctx)
10528 def fpGT(a, b, ctx=None):
10529 """Create the Z3 floating-point expression `other > self`.
10534 >>> (x > y).sexpr()
10537 return _mk_fp_bin_pred(Z3_mk_fpa_gt, a, b, ctx)
10540 def fpGEQ(a, b, ctx=None):
10541 """Create the Z3 floating-point expression `other >= self`.
10546 >>> (x >= y).sexpr()
10549 return _mk_fp_bin_pred(Z3_mk_fpa_geq, a, b, ctx)
10552 def fpEQ(a, b, ctx=None):
10553 """Create the Z3 floating-point expression `
fpEQ(other, self)`.
10558 >>>
fpEQ(x, y).sexpr()
10561 return _mk_fp_bin_pred(Z3_mk_fpa_eq, a, b, ctx)
10564 def fpNEQ(a, b, ctx=None):
10565 """Create the Z3 floating-point expression `
Not(
fpEQ(other, self))`.
10570 >>> (x != y).sexpr()
10573 return Not(fpEQ(a, b, ctx))
10576 def fpFP(sgn, exp, sig, ctx=None):
10577 """Create the Z3 floating-point value `
fpFP(sgn, sig, exp)`
from the three bit-vectors sgn, sig,
and exp.
10582 fpFP(1, 127, 4194304)
10583 >>> xv =
FPVal(-1.5, s)
10587 >>> slvr.add(
fpEQ(x, xv))
10590 >>> xv =
FPVal(+1.5, s)
10594 >>> slvr.add(
fpEQ(x, xv))
10598 _z3_assert(is_bv(sgn) and is_bv(exp) and is_bv(sig), "sort mismatch")
10599 _z3_assert(sgn.sort().size() == 1, "sort mismatch")
10600 ctx = _get_ctx(ctx)
10601 _z3_assert(ctx == sgn.ctx == exp.ctx == sig.ctx, "context mismatch")
10602 return FPRef(Z3_mk_fpa_fp(ctx.ref(), sgn.ast, exp.ast, sig.ast), ctx)
10605 def fpToFP(a1, a2=None, a3=None, ctx=None):
10606 """Create a Z3 floating-point conversion expression
from other term sorts
10609 From a bit-vector term
in IEEE 754-2008 format:
10615 From a floating-point term with different precision:
10626 From a signed bit-vector term:
10631 ctx = _get_ctx(ctx)
10632 if is_bv(a1) and is_fp_sort(a2):
10633 return FPRef(Z3_mk_fpa_to_fp_bv(ctx.ref(), a1.ast, a2.ast), ctx)
10634 elif is_fprm(a1) and is_fp(a2) and is_fp_sort(a3):
10635 return FPRef(Z3_mk_fpa_to_fp_float(ctx.ref(), a1.ast, a2.ast, a3.ast), ctx)
10636 elif is_fprm(a1) and is_real(a2) and is_fp_sort(a3):
10637 return FPRef(Z3_mk_fpa_to_fp_real(ctx.ref(), a1.ast, a2.ast, a3.ast), ctx)
10638 elif is_fprm(a1) and is_bv(a2) and is_fp_sort(a3):
10639 return FPRef(Z3_mk_fpa_to_fp_signed(ctx.ref(), a1.ast, a2.ast, a3.ast), ctx)
10641 raise Z3Exception("Unsupported combination of arguments for conversion to floating-point term.")
10644 def fpBVToFP(v, sort, ctx=None):
10645 """Create a Z3 floating-point conversion expression that represents the
10646 conversion
from a bit-vector term to a floating-point term.
10655 _z3_assert(is_bv(v), "First argument must be a Z3 bit-vector expression")
10656 _z3_assert(is_fp_sort(sort), "Second argument must be a Z3 floating-point sort.")
10657 ctx = _get_ctx(ctx)
10658 return FPRef(Z3_mk_fpa_to_fp_bv(ctx.ref(), v.ast, sort.ast), ctx)
10661 def fpFPToFP(rm, v, sort, ctx=None):
10662 """Create a Z3 floating-point conversion expression that represents the
10663 conversion
from a floating-point term to a floating-point term of different precision.
10674 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
10675 _z3_assert(is_fp(v), "Second argument must be a Z3 floating-point expression.")
10676 _z3_assert(is_fp_sort(sort), "Third argument must be a Z3 floating-point sort.")
10677 ctx = _get_ctx(ctx)
10678 return FPRef(Z3_mk_fpa_to_fp_float(ctx.ref(), rm.ast, v.ast, sort.ast), ctx)
10681 def fpRealToFP(rm, v, sort, ctx=None):
10682 """Create a Z3 floating-point conversion expression that represents the
10683 conversion
from a real term to a floating-point term.
10692 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
10693 _z3_assert(is_real(v), "Second argument must be a Z3 expression or real sort.")
10694 _z3_assert(is_fp_sort(sort), "Third argument must be a Z3 floating-point sort.")
10695 ctx = _get_ctx(ctx)
10696 return FPRef(Z3_mk_fpa_to_fp_real(ctx.ref(), rm.ast, v.ast, sort.ast), ctx)
10699 def fpSignedToFP(rm, v, sort, ctx=None):
10700 """Create a Z3 floating-point conversion expression that represents the
10701 conversion
from a signed bit-vector term (encoding an integer) to a floating-point term.
10710 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
10711 _z3_assert(is_bv(v), "Second argument must be a Z3 bit-vector expression")
10712 _z3_assert(is_fp_sort(sort), "Third argument must be a Z3 floating-point sort.")
10713 ctx = _get_ctx(ctx)
10714 return FPRef(Z3_mk_fpa_to_fp_signed(ctx.ref(), rm.ast, v.ast, sort.ast), ctx)
10717 def fpUnsignedToFP(rm, v, sort, ctx=None):
10718 """Create a Z3 floating-point conversion expression that represents the
10719 conversion
from an unsigned bit-vector term (encoding an integer) to a floating-point term.
10728 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
10729 _z3_assert(is_bv(v), "Second argument must be a Z3 bit-vector expression")
10730 _z3_assert(is_fp_sort(sort), "Third argument must be a Z3 floating-point sort.")
10731 ctx = _get_ctx(ctx)
10732 return FPRef(Z3_mk_fpa_to_fp_unsigned(ctx.ref(), rm.ast, v.ast, sort.ast), ctx)
10735 def fpToFPUnsigned(rm, x, s, ctx=None):
10736 """Create a Z3 floating-point conversion expression,
from unsigned bit-vector to floating-point expression.
"""
10738 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10739 _z3_assert(is_bv(x), "Second argument must be a Z3 bit-vector expression")
10740 _z3_assert(is_fp_sort(s), "Third argument must be Z3 floating-point sort")
10741 ctx = _get_ctx(ctx)
10742 return FPRef(Z3_mk_fpa_to_fp_unsigned(ctx.ref(), rm.ast, x.ast, s.ast), ctx)
10745 def fpToSBV(rm, x, s, ctx=None):
10746 """Create a Z3 floating-point conversion expression,
from floating-point expression to signed bit-vector.
10750 >>> print(
is_fp(x))
10752 >>> print(
is_bv(y))
10754 >>> print(
is_fp(y))
10756 >>> print(
is_bv(x))
10760 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10761 _z3_assert(is_fp(x), "Second argument must be a Z3 floating-point expression")
10762 _z3_assert(is_bv_sort(s), "Third argument must be Z3 bit-vector sort")
10763 ctx = _get_ctx(ctx)
10764 return BitVecRef(Z3_mk_fpa_to_sbv(ctx.ref(), rm.ast, x.ast, s.size()), ctx)
10767 def fpToUBV(rm, x, s, ctx=None):
10768 """Create a Z3 floating-point conversion expression,
from floating-point expression to unsigned bit-vector.
10772 >>> print(
is_fp(x))
10774 >>> print(
is_bv(y))
10776 >>> print(
is_fp(y))
10778 >>> print(
is_bv(x))
10782 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10783 _z3_assert(is_fp(x), "Second argument must be a Z3 floating-point expression")
10784 _z3_assert(is_bv_sort(s), "Third argument must be Z3 bit-vector sort")
10785 ctx = _get_ctx(ctx)
10786 return BitVecRef(Z3_mk_fpa_to_ubv(ctx.ref(), rm.ast, x.ast, s.size()), ctx)
10789 def fpToReal(x, ctx=None):
10790 """Create a Z3 floating-point conversion expression,
from floating-point expression to real.
10794 >>> print(
is_fp(x))
10798 >>> print(
is_fp(y))
10804 _z3_assert(is_fp(x), "First argument must be a Z3 floating-point expression")
10805 ctx = _get_ctx(ctx)
10806 return ArithRef(Z3_mk_fpa_to_real(ctx.ref(), x.ast), ctx)
10809 def fpToIEEEBV(x, ctx=None):
10810 """\brief Conversion of a floating-point term into a bit-vector term
in IEEE 754-2008 format.
10812 The size of the resulting bit-vector
is automatically determined.
10814 Note that IEEE 754-2008 allows multiple different representations of NaN. This conversion
10815 knows only one NaN
and it will always produce the same bit-vector representation of
10820 >>> print(
is_fp(x))
10822 >>> print(
is_bv(y))
10824 >>> print(
is_fp(y))
10826 >>> print(
is_bv(x))
10830 _z3_assert(is_fp(x), "First argument must be a Z3 floating-point expression")
10831 ctx = _get_ctx(ctx)
10832 return BitVecRef(Z3_mk_fpa_to_ieee_bv(ctx.ref(), x.ast), ctx)
10835 #########################################
10837 # Strings, Sequences and Regular expressions
10839 #########################################
10841 class SeqSortRef(SortRef):
10842 """Sequence sort.
"""
10844 def is_string(self):
10845 """Determine
if sort
is a string
10853 return Z3_is_string_sort(self.ctx_ref(), self.ast)
10856 return _to_sort_ref(Z3_get_seq_sort_basis(self.ctx_ref(), self.ast), self.ctx)
10858 class CharSortRef(SortRef):
10859 """Character sort.
"""
10862 def StringSort(ctx=None):
10863 """Create a string sort
10868 ctx = _get_ctx(ctx)
10869 return SeqSortRef(Z3_mk_string_sort(ctx.ref()), ctx)
10871 def CharSort(ctx=None):
10872 """Create a character sort
10877 ctx = _get_ctx(ctx)
10878 return CharSortRef(Z3_mk_char_sort(ctx.ref()), ctx)
10882 """Create a sequence sort over elements provided
in the argument
10887 return SeqSortRef(Z3_mk_seq_sort(s.ctx_ref(), s.ast), s.ctx)
10890 class SeqRef(ExprRef):
10891 """Sequence expression.
"""
10894 return SeqSortRef(Z3_get_sort(self.ctx_ref(), self.as_ast()), self.ctx)
10896 def __add__(self, other):
10897 return Concat(self, other)
10899 def __radd__(self, other):
10900 return Concat(other, self)
10902 def __getitem__(self, i):
10904 i = IntVal(i, self.ctx)
10905 return _to_expr_ref(Z3_mk_seq_nth(self.ctx_ref(), self.as_ast(), i.as_ast()), self.ctx)
10909 i = IntVal(i, self.ctx)
10910 return SeqRef(Z3_mk_seq_at(self.ctx_ref(), self.as_ast(), i.as_ast()), self.ctx)
10912 def is_string(self):
10913 return Z3_is_string_sort(self.ctx_ref(), Z3_get_sort(self.ctx_ref(), self.as_ast()))
10915 def is_string_value(self):
10916 return Z3_is_string(self.ctx_ref(), self.as_ast())
10918 def as_string(self):
10919 """Return a string representation of sequence expression.
"""
10920 if self.is_string_value():
10921 string_length = ctypes.c_uint()
10922 chars = Z3_get_lstring(self.ctx_ref(), self.as_ast(), byref(string_length))
10923 return string_at(chars, size=string_length.value).decode("latin-1")
10924 return Z3_ast_to_string(self.ctx_ref(), self.as_ast())
10926 def __le__(self, other):
10927 return _to_expr_ref(Z3_mk_str_le(self.ctx_ref(), self.as_ast(), other.as_ast()), self.ctx)
10929 def __lt__(self, other):
10930 return _to_expr_ref(Z3_mk_str_lt(self.ctx_ref(), self.as_ast(), other.as_ast()), self.ctx)
10932 def __ge__(self, other):
10933 return _to_expr_ref(Z3_mk_str_le(self.ctx_ref(), other.as_ast(), self.as_ast()), self.ctx)
10935 def __gt__(self, other):
10936 return _to_expr_ref(Z3_mk_str_lt(self.ctx_ref(), other.as_ast(), self.as_ast()), self.ctx)
10939 def _coerce_char(ch, ctx=None):
10940 if isinstance(ch, str):
10941 ctx = _get_ctx(ctx)
10942 ch = CharVal(ch, ctx)
10943 if not is_expr(ch):
10944 raise Z3Exception("Character expression expected")
10947 class CharRef(ExprRef):
10948 """Character expression.
"""
10950 def __le__(self, other):
10951 other = _coerce_char(other, self.ctx)
10952 return _to_expr_ref(Z3_mk_char_le(self.ctx_ref(), self.as_ast(), other.as_ast()), self.ctx)
10955 return _to_expr_ref(Z3_mk_char_to_int(self.ctx_ref(), self.as_ast()), self.ctx)
10958 return _to_expr_ref(Z3_mk_char_to_bv(self.ctx_ref(), self.as_ast()), self.ctx)
10960 def is_digit(self):
10961 return _to_expr_ref(Z3_mk_char_is_digit(self.ctx_ref(), self.as_ast()), self.ctx)
10964 def CharVal(ch, ctx=None):
10965 ctx = _get_ctx(ctx)
10966 if isinstance(ch, str):
10968 if not isinstance(ch, int):
10969 raise Z3Exception("character value should be an ordinal")
10970 return _to_expr_ref(Z3_mk_char(ctx.ref(), ch), ctx)
10972 def CharFromBv(bv):
10973 if not is_expr(bv):
10974 raise Z3Exception("Bit-vector expression needed")
10975 return _to_expr_ref(Z3_mk_char_from_bv(bv.ctx_ref(), bv.as_ast()), bv.ctx)
10977 def CharToBv(ch, ctx=None):
10978 ch = _coerce_char(ch, ctx)
10981 def CharToInt(ch, ctx=None):
10982 ch = _coerce_char(ch, ctx)
10985 def CharIsDigit(ch, ctx=None):
10986 ch = _coerce_char(ch, ctx)
10987 return ch.is_digit()
10989 def _coerce_seq(s, ctx=None):
10990 if isinstance(s, str):
10991 ctx = _get_ctx(ctx)
10992 s = StringVal(s, ctx)
10994 raise Z3Exception("Non-expression passed as a sequence")
10996 raise Z3Exception("Non-sequence passed as a sequence")
11000 def _get_ctx2(a, b, ctx=None):
11011 """Return `
True`
if `a`
is a Z3 sequence expression.
11017 return isinstance(a, SeqRef)
11021 """Return `
True`
if `a`
is a Z3 string expression.
11025 return isinstance(a, SeqRef) and a.is_string()
11028 def is_string_value(a):
11029 """return 'True' if 'a' is a Z3 string constant expression.
11035 return isinstance(a, SeqRef) and a.is_string_value()
11037 def StringVal(s, ctx=None):
11038 """create a string expression
"""
11039 s = "".join(str(ch) if 32 <= ord(ch) and ord(ch) < 127 else "\\u{%x}" % (ord(ch)) for ch in s)
11040 ctx = _get_ctx(ctx)
11041 return SeqRef(Z3_mk_string(ctx.ref(), s), ctx)
11044 def String(name, ctx=None):
11045 """Return a string constant named `name`. If `ctx=
None`, then the
global context
is used.
11049 ctx = _get_ctx(ctx)
11050 return SeqRef(Z3_mk_const(ctx.ref(), to_symbol(name, ctx), StringSort(ctx).ast), ctx)
11053 def Strings(names, ctx=None):
11054 """Return a tuple of String constants.
"""
11055 ctx = _get_ctx(ctx)
11056 if isinstance(names, str):
11057 names = names.split(" ")
11058 return [String(name, ctx) for name in names]
11061 def SubString(s, offset, length):
11062 """Extract substring
or subsequence starting at offset
"""
11063 return Extract(s, offset, length)
11066 def SubSeq(s, offset, length):
11067 """Extract substring
or subsequence starting at offset
"""
11068 return Extract(s, offset, length)
11072 """Create the empty sequence of the given sort
11075 >>> print(e.eq(e2))
11084 if isinstance(s, SeqSortRef):
11085 return SeqRef(Z3_mk_seq_empty(s.ctx_ref(), s.ast), s.ctx)
11086 if isinstance(s, ReSortRef):
11087 return ReRef(Z3_mk_re_empty(s.ctx_ref(), s.ast), s.ctx)
11088 raise Z3Exception("Non-sequence, non-regular expression sort passed to Empty")
11092 """Create the regular expression that accepts the universal language
11100 if isinstance(s, ReSortRef):
11101 return ReRef(Z3_mk_re_full(s.ctx_ref(), s.ast), s.ctx)
11102 raise Z3Exception("Non-sequence, non-regular expression sort passed to Full")
11107 """Create a singleton sequence
"""
11108 return SeqRef(Z3_mk_seq_unit(a.ctx_ref(), a.as_ast()), a.ctx)
11111 def PrefixOf(a, b):
11112 """Check
if 'a' is a prefix of
'b'
11120 ctx = _get_ctx2(a, b)
11121 a = _coerce_seq(a, ctx)
11122 b = _coerce_seq(b, ctx)
11123 return BoolRef(Z3_mk_seq_prefix(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
11126 def SuffixOf(a, b):
11127 """Check
if 'a' is a suffix of
'b'
11135 ctx = _get_ctx2(a, b)
11136 a = _coerce_seq(a, ctx)
11137 b = _coerce_seq(b, ctx)
11138 return BoolRef(Z3_mk_seq_suffix(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
11141 def Contains(a, b):
11142 """Check
if 'a' contains
'b'
11149 >>> x, y, z =
Strings(
'x y z')
11154 ctx = _get_ctx2(a, b)
11155 a = _coerce_seq(a, ctx)
11156 b = _coerce_seq(b, ctx)
11157 return BoolRef(Z3_mk_seq_contains(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
11160 def Replace(s, src, dst):
11161 """Replace the first occurrence of
'src' by
'dst' in 's'
11162 >>> r =
Replace(
"aaa",
"a",
"b")
11166 ctx = _get_ctx2(dst, s)
11167 if ctx is None and is_expr(src):
11169 src = _coerce_seq(src, ctx)
11170 dst = _coerce_seq(dst, ctx)
11171 s = _coerce_seq(s, ctx)
11172 return SeqRef(Z3_mk_seq_replace(src.ctx_ref(), s.as_ast(), src.as_ast(), dst.as_ast()), s.ctx)
11175 def IndexOf(s, substr, offset=None):
11176 """Retrieve the index of substring within a string starting at a specified offset.
11185 if is_expr(offset):
11187 ctx = _get_ctx2(s, substr, ctx)
11188 s = _coerce_seq(s, ctx)
11189 substr = _coerce_seq(substr, ctx)
11190 if _is_int(offset):
11191 offset = IntVal(offset, ctx)
11192 return ArithRef(Z3_mk_seq_index(s.ctx_ref(), s.as_ast(), substr.as_ast(), offset.as_ast()), s.ctx)
11195 def LastIndexOf(s, substr):
11196 """Retrieve the last index of substring within a string
"""
11198 ctx = _get_ctx2(s, substr, ctx)
11199 s = _coerce_seq(s, ctx)
11200 substr = _coerce_seq(substr, ctx)
11201 return ArithRef(Z3_mk_seq_last_index(s.ctx_ref(), s.as_ast(), substr.as_ast()), s.ctx)
11205 """Obtain the length of a sequence
's'
11211 return ArithRef(Z3_mk_seq_length(s.ctx_ref(), s.as_ast()), s.ctx)
11215 """Convert string expression to integer
11227 return ArithRef(Z3_mk_str_to_int(s.ctx_ref(), s.as_ast()), s.ctx)
11231 """Convert integer expression to string
"""
11234 return SeqRef(Z3_mk_int_to_str(s.ctx_ref(), s.as_ast()), s.ctx)
11238 """Convert a unit length string to integer code
"""
11241 return ArithRef(Z3_mk_string_to_code(s.ctx_ref(), s.as_ast()), s.ctx)
11243 def StrFromCode(c):
11244 """Convert code to a string
"""
11247 return SeqRef(Z3_mk_string_from_code(c.ctx_ref(), c.as_ast()), c.ctx)
11249 def Re(s, ctx=None):
11250 """The regular expression that accepts sequence
's'
11255 s = _coerce_seq(s, ctx)
11256 return ReRef(Z3_mk_seq_to_re(s.ctx_ref(), s.as_ast()), s.ctx)
11259 # Regular expressions
11261 class ReSortRef(SortRef):
11262 """Regular expression sort.
"""
11265 return _to_sort_ref(Z3_get_re_sort_basis(self.ctx_ref(), self.ast), self.ctx)
11270 return ReSortRef(Z3_mk_re_sort(s.ctx.ref(), s.ast), s.ctx)
11271 if s is None or isinstance(s, Context):
11273 return ReSortRef(Z3_mk_re_sort(ctx.ref(), Z3_mk_string_sort(ctx.ref())), s.ctx)
11274 raise Z3Exception("Regular expression sort constructor expects either a string or a context or no argument")
11277 class ReRef(ExprRef):
11278 """Regular expressions.
"""
11280 def __add__(self, other):
11281 return Union(self, other)
11285 return isinstance(s, ReRef)
11289 """Create regular expression membership test
11298 s = _coerce_seq(s, re.ctx)
11299 return BoolRef(Z3_mk_seq_in_re(s.ctx_ref(), s.as_ast(), re.as_ast()), s.ctx)
11303 """Create union of regular expressions.
11308 args = _get_args(args)
11311 _z3_assert(sz > 0, "At least one argument expected.")
11312 _z3_assert(all([is_re(a) for a in args]), "All arguments must be regular expressions.")
11317 for i in range(sz):
11318 v[i] = args[i].as_ast()
11319 return ReRef(Z3_mk_re_union(ctx.ref(), sz, v), ctx)
11322 def Intersect(*args):
11323 """Create intersection of regular expressions.
11326 args = _get_args(args)
11329 _z3_assert(sz > 0, "At least one argument expected.")
11330 _z3_assert(all([is_re(a) for a in args]), "All arguments must be regular expressions.")
11335 for i in range(sz):
11336 v[i] = args[i].as_ast()
11337 return ReRef(Z3_mk_re_intersect(ctx.ref(), sz, v), ctx)
11341 """Create the regular expression accepting one
or more repetitions of argument.
11351 _z3_assert(is_expr(re), "expression expected")
11352 return ReRef(Z3_mk_re_plus(re.ctx_ref(), re.as_ast()), re.ctx)
11356 """Create the regular expression that optionally accepts the argument.
11366 _z3_assert(is_expr(re), "expression expected")
11367 return ReRef(Z3_mk_re_option(re.ctx_ref(), re.as_ast()), re.ctx)
11370 def Complement(re):
11371 """Create the complement regular expression.
"""
11372 return ReRef(Z3_mk_re_complement(re.ctx_ref(), re.as_ast()), re.ctx)
11376 """Create the regular expression accepting zero
or more repetitions of argument.
11386 _z3_assert(is_expr(re), "expression expected")
11387 return ReRef(Z3_mk_re_star(re.ctx_ref(), re.as_ast()), re.ctx)
11390 def Loop(re, lo, hi=0):
11391 """Create the regular expression accepting between a lower
and upper bound repetitions
11392 >>> re =
Loop(
Re(
"a"), 1, 3)
11401 _z3_assert(is_expr(re), "expression expected")
11402 return ReRef(Z3_mk_re_loop(re.ctx_ref(), re.as_ast(), lo, hi), re.ctx)
11405 def Range(lo, hi, ctx=None):
11406 """Create the range regular expression over two sequences of length 1
11407 >>> range =
Range(
"a",
"z")
11413 lo = _coerce_seq(lo, ctx)
11414 hi = _coerce_seq(hi, ctx)
11416 _z3_assert(is_expr(lo), "expression expected")
11417 _z3_assert(is_expr(hi), "expression expected")
11418 return ReRef(Z3_mk_re_range(lo.ctx_ref(), lo.ast, hi.ast), lo.ctx)
11420 def Diff(a, b, ctx=None):
11421 """Create the difference regular expression
11424 _z3_assert(is_expr(a), "expression expected")
11425 _z3_assert(is_expr(b), "expression expected")
11426 return ReRef(Z3_mk_re_diff(a.ctx_ref(), a.ast, b.ast), a.ctx)
11428 def AllChar(regex_sort, ctx=None):
11429 """Create a regular expression that accepts all single character strings
11431 return ReRef(Z3_mk_re_allchar(regex_sort.ctx_ref(), regex_sort.ast), regex_sort.ctx)
11433 # Special Relations
11436 def PartialOrder(a, index):
11437 return FuncDeclRef(Z3_mk_partial_order(a.ctx_ref(), a.ast, index), a.ctx)
11440 def LinearOrder(a, index):
11441 return FuncDeclRef(Z3_mk_linear_order(a.ctx_ref(), a.ast, index), a.ctx)
11444 def TreeOrder(a, index):
11445 return FuncDeclRef(Z3_mk_tree_order(a.ctx_ref(), a.ast, index), a.ctx)
11448 def PiecewiseLinearOrder(a, index):
11449 return FuncDeclRef(Z3_mk_piecewise_linear_order(a.ctx_ref(), a.ast, index), a.ctx)
11452 def TransitiveClosure(f):
11453 """Given a binary relation R, such that the two arguments have the same sort
11454 create the transitive closure relation R+.
11455 The transitive closure R+
is a new relation.
11457 return FuncDeclRef(Z3_mk_transitive_closure(f.ctx_ref(), f.ast), f.ctx)
11461 super(ctypes.c_void_p, ast).__init__(ptr)
11464 def to_ContextObj(ptr,):
11465 ctx = ContextObj(ptr)
11466 super(ctypes.c_void_p, ctx).__init__(ptr)
11469 def to_AstVectorObj(ptr,):
11470 v = AstVectorObj(ptr)
11471 super(ctypes.c_void_p, v).__init__(ptr)
11474 # NB. my-hacky-class only works for a single instance of OnClause
11475 # it should be replaced with a proper correlation between OnClause
11476 # and object references that can be passed over the FFI.
11477 # for UserPropagator we use a global dictionary, which isn't great code.
11479 _my_hacky_class = None
11480 def on_clause_eh(ctx, p, n, dep, clause):
11481 onc = _my_hacky_class
11482 p = _to_expr_ref(to_Ast(p), onc.ctx)
11483 clause = AstVector(to_AstVectorObj(clause), onc.ctx)
11484 deps = [dep[i] for i in range(n)]
11485 onc.on_clause(p, deps, clause)
11487 _on_clause_eh = Z3_on_clause_eh(on_clause_eh)
11490 def __init__(self, s, on_clause):
11493 self.on_clause = on_clause
11495 global _my_hacky_class
11496 _my_hacky_class = self
11497 Z3_solver_register_on_clause(self.ctx.ref(), self.s.solver, self.idx, _on_clause_eh)
11500 class PropClosures:
11501 def __init__(self):
11505 def set_threaded(self):
11506 if self.lock is None:
11508 self.lock = threading.Lock()
11510 def get(self, ctx):
11513 r = self.bases[ctx]
11515 r = self.bases[ctx]
11518 def set(self, ctx, r):
11521 self.bases[ctx] = r
11523 self.bases[ctx] = r
11525 def insert(self, r):
11528 id = len(self.bases) + 3
11531 id = len(self.bases) + 3
11536 _prop_closures = None
11539 def ensure_prop_closures():
11540 global _prop_closures
11541 if _prop_closures is None:
11542 _prop_closures = PropClosures()
11545 def user_prop_push(ctx, cb):
11546 prop = _prop_closures.get(ctx)
11551 def user_prop_pop(ctx, cb, num_scopes):
11552 prop = _prop_closures.get(ctx)
11554 prop.pop(num_scopes)
11557 def user_prop_fresh(ctx, _new_ctx):
11558 _prop_closures.set_threaded()
11559 prop = _prop_closures.get(ctx)
11561 Z3_del_context(nctx.ctx)
11562 new_ctx = to_ContextObj(_new_ctx)
11564 nctx.eh = Z3_set_error_handler(new_ctx, z3_error_handler)
11566 new_prop = prop.fresh(nctx)
11567 _prop_closures.set(new_prop.id, new_prop)
11571 def user_prop_fixed(ctx, cb, id, value):
11572 prop = _prop_closures.get(ctx)
11575 id = _to_expr_ref(to_Ast(id), prop.ctx())
11576 value = _to_expr_ref(to_Ast(value), prop.ctx())
11577 prop.fixed(id, value)
11580 def user_prop_created(ctx, cb, id):
11581 prop = _prop_closures.get(ctx)
11584 id = _to_expr_ref(to_Ast(id), prop.ctx())
11589 def user_prop_final(ctx, cb):
11590 prop = _prop_closures.get(ctx)
11596 def user_prop_eq(ctx, cb, x, y):
11597 prop = _prop_closures.get(ctx)
11600 x = _to_expr_ref(to_Ast(x), prop.ctx())
11601 y = _to_expr_ref(to_Ast(y), prop.ctx())
11605 def user_prop_diseq(ctx, cb, x, y):
11606 prop = _prop_closures.get(ctx)
11609 x = _to_expr_ref(to_Ast(x), prop.ctx())
11610 y = _to_expr_ref(to_Ast(y), prop.ctx())
11614 def user_prop_decide(ctx, cb, t, idx, phase):
11615 prop = _prop_closures.get(ctx)
11618 t = _to_expr_ref(to_Ast(t_ref), prop.ctx())
11619 prop.decide(t, idx, phase)
11623 _user_prop_push = Z3_push_eh(user_prop_push)
11624 _user_prop_pop = Z3_pop_eh(user_prop_pop)
11625 _user_prop_fresh = Z3_fresh_eh(user_prop_fresh)
11626 _user_prop_fixed = Z3_fixed_eh(user_prop_fixed)
11627 _user_prop_created = Z3_created_eh(user_prop_created)
11628 _user_prop_final = Z3_final_eh(user_prop_final)
11629 _user_prop_eq = Z3_eq_eh(user_prop_eq)
11630 _user_prop_diseq = Z3_eq_eh(user_prop_diseq)
11631 _user_prop_decide = Z3_decide_eh(user_prop_decide)
11634 def PropagateFunction(name, *sig):
11635 """Create a function that gets tracked by user propagator.
11636 Every term headed by this function symbol
is tracked.
11637 If a term
is fixed
and the fixed callback
is registered a
11638 callback
is invoked that the term headed by this function
is fixed.
11640 sig = _get_args(sig)
11642 _z3_assert(len(sig) > 0, "At least two arguments expected")
11643 arity = len(sig) - 1
11646 _z3_assert(is_sort(rng), "Z3 sort expected")
11647 dom = (Sort * arity)()
11648 for i in range(arity):
11650 _z3_assert(is_sort(sig[i]), "Z3 sort expected")
11651 dom[i] = sig[i].ast
11653 return FuncDeclRef(Z3_solver_propagate_declare(ctx.ref(), to_symbol(name, ctx), arity, dom, rng.ast), ctx)
11657 class UserPropagateBase:
11660 # Either solver is set or ctx is set.
11661 # Propagators that are created through callbacks
11662 # to "fresh" inherit the context of that is supplied
11663 # as argument to the callback.
11664 # This context should not be deleted. It is owned by the solver.
11666 def __init__(self, s, ctx=None):
11667 assert s is None or ctx is None
11668 ensure_prop_closures()
11671 self.fresh_ctx = None
11673 self.id = _prop_closures.insert(self)
11678 self.created = None
11680 self.fresh_ctx = ctx
11682 Z3_solver_propagate_init(self.ctx_ref(),
11684 ctypes.c_void_p(self.id),
11691 self._ctx.ctx = None
11695 return self.fresh_ctx
11697 return self.solver.ctx
11700 return self.ctx().ref()
11702 def add_fixed(self, fixed):
11703 assert not self.fixed
11704 assert not self._ctx
11706 Z3_solver_propagate_fixed(self.ctx_ref(), self.solver.solver, _user_prop_fixed)
11709 def add_created(self, created):
11710 assert not self.created
11711 assert not self._ctx
11713 Z3_solver_propagate_created(self.ctx_ref(), self.solver.solver, _user_prop_created)
11714 self.created = created
11716 def add_final(self, final):
11717 assert not self.final
11718 assert not self._ctx
11720 Z3_solver_propagate_final(self.ctx_ref(), self.solver.solver, _user_prop_final)
11723 def add_eq(self, eq):
11725 assert not self._ctx
11727 Z3_solver_propagate_eq(self.ctx_ref(), self.solver.solver, _user_prop_eq)
11730 def add_diseq(self, diseq):
11731 assert not self.diseq
11732 assert not self._ctx
11734 Z3_solver_propagate_diseq(self.ctx_ref(), self.solver.solver, _user_prop_diseq)
11737 def add_decide(self, decide):
11738 assert not self.decide
11739 assert not self._ctx
11741 Z3_solver_propagate_decide(self.ctx_ref(), self.solver.solver, _user_prop_decide)
11742 self.decide = decide
11745 raise Z3Exception("push needs to be overwritten")
11747 def pop(self, num_scopes):
11748 raise Z3Exception("pop needs to be overwritten")
11750 def fresh(self, new_ctx):
11751 raise Z3Exception("fresh needs to be overwritten")
11754 assert not self._ctx
11756 Z3_solver_propagate_register(self.ctx_ref(), self.solver.solver, e.ast)
11758 Z3_solver_propagate_register_cb(self.ctx_ref(), ctypes.c_void_p(self.cb), e.ast)
11761 # Tell the solver to perform the next split on a given term
11762 # If the term is a bit-vector the index idx specifies the index of the Boolean variable being
11763 # split on. A phase of true = 1/false = -1/undef = 0 = let solver decide is the last argument.
11765 def next_split(self, t, idx, phase):
11766 return Z3_solver_next_split(self.ctx_ref(), ctypes.c_void_p(self.cb), t.ast, idx, phase)
11769 # Propagation can only be invoked as during a fixed or final callback.
11771 def propagate(self, e, ids, eqs=[]):
11772 _ids, num_fixed = _to_ast_array(ids)
11774 _lhs, _num_lhs = _to_ast_array([x for x, y in eqs])
11775 _rhs, _num_rhs = _to_ast_array([y for x, y in eqs])
11776 return Z3_solver_propagate_consequence(e.ctx.ref(), ctypes.c_void_p(
11777 self.cb), num_fixed, _ids, num_eqs, _lhs, _rhs, e.ast)
11779 def conflict(self, deps = [], eqs = []):
11780 self.propagate(BoolVal(False, self.ctx()), deps, eqs)
Z3_param_descrs Z3_API Z3_optimize_get_param_descrs(Z3_context c, Z3_optimize o)
Return the parameter description set for the given optimize object.
Z3_string Z3_API Z3_get_probe_name(Z3_context c, unsigned i)
Return the name of the i probe.
Z3_ast_vector Z3_API Z3_optimize_get_objectives(Z3_context c, Z3_optimize o)
Return objectives on the optimization context. If the objective function is a max-sat objective it is...
Z3_ast Z3_API Z3_mk_distinct(Z3_context c, unsigned num_args, Z3_ast const args[])
Create an AST node representing distinct(args[0], ..., args[num_args-1]).
Z3_fixedpoint Z3_API Z3_mk_fixedpoint(Z3_context c)
Create a new fixedpoint context.
Z3_probe Z3_API Z3_probe_le(Z3_context x, Z3_probe p1, Z3_probe p2)
Return a probe that evaluates to "true" when the value returned by p1 is less than or equal to the va...
def simplify(a, arguments, keywords)
Utils.
Z3_func_decl Z3_API Z3_mk_fresh_func_decl(Z3_context c, Z3_string prefix, unsigned domain_size, Z3_sort const domain[], Z3_sort range)
Declare a fresh constant or function.
void Z3_API Z3_global_param_set(Z3_string param_id, Z3_string param_value)
Set a global (or module) parameter. This setting is shared by all Z3 contexts.
Z3_string Z3_API Z3_apply_result_to_string(Z3_context c, Z3_apply_result r)
Convert the Z3_apply_result object returned by Z3_tactic_apply into a string.
Z3_string Z3_API Z3_get_decl_rational_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the rational value, as a string, associated with a rational parameter.
void Z3_API Z3_fixedpoint_add_rule(Z3_context c, Z3_fixedpoint d, Z3_ast rule, Z3_symbol name)
Add a universal Horn clause as a named rule. The horn_rule should be of the form: ...
def update_rule(self, head, body, name)
Z3_probe Z3_API Z3_probe_ge(Z3_context x, Z3_probe p1, Z3_probe p2)
Return a probe that evaluates to "true" when the value returned by p1 is greater than or equal to the...
Z3_param_descrs Z3_API Z3_tactic_get_param_descrs(Z3_context c, Z3_tactic t)
Return the parameter description set for the given tactic object.
def get_cover_delta(self, level, predicate)
Z3_tactic Z3_API Z3_tactic_when(Z3_context c, Z3_probe p, Z3_tactic t)
Return a tactic that applies t to a given goal is the probe p evaluates to true. If p evaluates to fa...
Z3_ast Z3_API Z3_mk_bound(Z3_context c, unsigned index, Z3_sort ty)
Create a variable.
def upper_values(self, obj)
Z3_ast Z3_API Z3_mk_mul(Z3_context c, unsigned num_args, Z3_ast const args[])
Create an AST node representing args[0] * ... * args[num_args-1].
def __getitem__(self, idx)
void Z3_API Z3_tactic_inc_ref(Z3_context c, Z3_tactic t)
Increment the reference counter of the given tactic.
Z3_symbol Z3_API Z3_get_decl_name(Z3_context c, Z3_func_decl d)
Return the constant declaration name as a symbol.
void Z3_API Z3_disable_trace(Z3_string tag)
Disable tracing messages tagged as tag when Z3 is compiled in debug mode. It is a NOOP otherwise...
void Z3_API Z3_simplifier_dec_ref(Z3_context c, Z3_simplifier g)
Decrement the reference counter of the given simplifier.
Z3_tactic Z3_API Z3_tactic_and_then(Z3_context c, Z3_tactic t1, Z3_tactic t2)
Return a tactic that applies t1 to a given goal and t2 to every subgoal produced by t1...
Z3_symbol_kind Z3_API Z3_get_symbol_kind(Z3_context c, Z3_symbol s)
Return Z3_INT_SYMBOL if the symbol was constructed using Z3_mk_int_symbol, and Z3_STRING_SYMBOL if th...
Z3_string Z3_API Z3_ast_to_string(Z3_context c, Z3_ast a)
Convert the given AST node into a string.
Z3_symbol Z3_API Z3_mk_string_symbol(Z3_context c, Z3_string s)
Create a Z3 symbol using a C string.
expr range(expr const &lo, expr const &hi)
Z3_ast_vector Z3_API Z3_fixedpoint_from_string(Z3_context c, Z3_fixedpoint f, Z3_string s)
Parse an SMT-LIB2 string with fixedpoint rules. Add the rules to the current fixedpoint context...
Z3_probe Z3_API Z3_probe_gt(Z3_context x, Z3_probe p1, Z3_probe p2)
Return a probe that evaluates to "true" when the value returned by p1 is greater than the value retur...
def substitute_vars(t, m)
Z3_ast Z3_API Z3_mk_const(Z3_context c, Z3_symbol s, Z3_sort ty)
Declare and create a constant.
Z3_simplifier Z3_API Z3_simplifier_and_then(Z3_context c, Z3_simplifier t1, Z3_simplifier t2)
Return a simplifier that applies t1 to a given goal and t2 to every subgoal produced by t1...
Z3_tactic Z3_API Z3_mk_tactic(Z3_context c, Z3_string name)
Return a tactic associated with the given name. The complete list of tactics may be obtained using th...
Z3_probe Z3_API Z3_probe_const(Z3_context x, double val)
Return a probe that always evaluates to val.
Z3_probe Z3_API Z3_probe_eq(Z3_context x, Z3_probe p1, Z3_probe p2)
Return a probe that evaluates to "true" when the value returned by p1 is equal to the value returned ...
def declare(self, name, args)
def assert_exprs(self, args)
def set_option(args, kws)
Z3_param_descrs Z3_API Z3_simplifier_get_param_descrs(Z3_context c, Z3_simplifier t)
Return the parameter description set for the given simplifier object.
Z3_ast Z3_API Z3_substitute(Z3_context c, Z3_ast a, unsigned num_exprs, Z3_ast const from[], Z3_ast const to[])
Substitute every occurrence of from[i] in a with to[i], for i smaller than num_exprs. The result is the new AST. The arrays from and to must have size num_exprs. For every i smaller than num_exprs, we must have that sort of from[i] must be equal to sort of to[i].
Z3_ast Z3_API Z3_mk_pbeq(Z3_context c, unsigned num_args, Z3_ast const args[], int const coeffs[], int k)
Pseudo-Boolean relations.
Z3_optimize Z3_API Z3_mk_optimize(Z3_context c)
Create a new optimize context.
void Z3_API Z3_optimize_assert(Z3_context c, Z3_optimize o, Z3_ast a)
Assert hard constraint to the optimization context.
void Z3_API Z3_del_context(Z3_context c)
Delete the given logical context.
Z3_ast Z3_API Z3_mk_app(Z3_context c, Z3_func_decl d, unsigned num_args, Z3_ast const args[])
Create a constant or function application.
bool Z3_API Z3_is_eq_sort(Z3_context c, Z3_sort s1, Z3_sort s2)
compare sorts.
bool Z3_API Z3_get_finite_domain_sort_size(Z3_context c, Z3_sort s, uint64_t *r)
Store the size of the sort in r. Return false if the call failed. That is, Z3_get_sort_kind(s) == Z3_...
unsigned Z3_API Z3_get_decl_num_parameters(Z3_context c, Z3_func_decl d)
Return the number of parameters associated with a declaration.
bool Z3_API Z3_is_eq_ast(Z3_context c, Z3_ast t1, Z3_ast t2)
Compare terms.
def assert_exprs(self, args)
Z3_probe Z3_API Z3_mk_probe(Z3_context c, Z3_string name)
Return a probe associated with the given name. The complete list of probes may be obtained using the ...
Z3_solver Z3_API Z3_mk_solver_for_logic(Z3_context c, Z3_symbol logic)
Create a new solver customized for the given logic. It behaves like Z3_mk_solver if the logic is unkn...
Z3_decl_kind Z3_API Z3_get_decl_kind(Z3_context c, Z3_func_decl d)
Return declaration kind corresponding to declaration.
Z3_string Z3_API Z3_get_tactic_name(Z3_context c, unsigned i)
Return the name of the idx tactic.
def lower_values(self, obj)
void Z3_API Z3_optimize_inc_ref(Z3_context c, Z3_optimize d)
Increment the reference counter of the given optimize context.
Z3_ast Z3_API Z3_func_decl_to_ast(Z3_context c, Z3_func_decl f)
Convert a Z3_func_decl into Z3_ast. This is just type casting.
Z3_ast Z3_API Z3_mk_add(Z3_context c, unsigned num_args, Z3_ast const args[])
Create an AST node representing args[0] + ... + args[num_args-1].
Z3_stats Z3_API Z3_fixedpoint_get_statistics(Z3_context c, Z3_fixedpoint d)
Retrieve statistics information from the last call to Z3_fixedpoint_query.
Z3_ast Z3_API Z3_simplify_ex(Z3_context c, Z3_ast a, Z3_params p)
Interface to simplifier.
Z3_context Z3_API Z3_mk_context_rc(Z3_config c)
Create a context using the given configuration. This function is similar to Z3_mk_context. However, in the context returned by this function, the user is responsible for managing Z3_ast reference counters. Managing reference counters is a burden and error-prone, but allows the user to use the memory more efficiently. The user must invoke Z3_inc_ref for any Z3_ast returned by Z3, and Z3_dec_ref whenever the Z3_ast is not needed anymore. This idiom is similar to the one used in BDD (binary decision diagrams) packages such as CUDD.
Z3_string Z3_API Z3_simplifier_get_help(Z3_context c, Z3_simplifier t)
Return a string containing a description of parameters accepted by the given simplifier.
Z3_apply_result Z3_API Z3_tactic_apply(Z3_context c, Z3_tactic t, Z3_goal g)
Apply tactic t to the goal g.
def register_relation(self, relations)
Z3_sort Z3_API Z3_mk_finite_domain_sort(Z3_context c, Z3_symbol name, uint64_t size)
Create a named finite domain sort.
Z3_parameter_kind Z3_API Z3_get_decl_parameter_kind(Z3_context c, Z3_func_decl d, unsigned idx)
Return the parameter type associated with a declaration.
Z3_ast Z3_API Z3_get_app_arg(Z3_context c, Z3_app a, unsigned i)
Return the i-th argument of the given application.
void Z3_API Z3_parser_context_dec_ref(Z3_context c, Z3_parser_context pc)
Decrement the reference counter of the given Z3_parser_context object.
bool Z3_API Z3_global_param_get(Z3_string param_id, Z3_string_ptr param_value)
Get a global (or module) parameter.
Z3_symbol Z3_API Z3_get_decl_symbol_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the double value associated with an double parameter.
Z3_func_decl Z3_API Z3_get_app_decl(Z3_context c, Z3_app a)
Return the declaration of a constant or function application.
void Z3_API Z3_fixedpoint_assert(Z3_context c, Z3_fixedpoint d, Z3_ast axiom)
Assert a constraint to the fixedpoint context.
void Z3_API Z3_parser_context_add_decl(Z3_context c, Z3_parser_context pc, Z3_func_decl f)
Add a function declaration.
Z3_apply_result Z3_API Z3_tactic_apply_ex(Z3_context c, Z3_tactic t, Z3_goal g, Z3_params p)
Apply tactic t to the goal g using the parameter set p.
void Z3_API Z3_append_log(Z3_string string)
Append user-defined string to interaction log.
unsigned Z3_API Z3_get_index_value(Z3_context c, Z3_ast a)
Return index of de-Bruijn bound variable.
def is_finite_domain_sort(s)
Z3_lbool Z3_API Z3_optimize_check(Z3_context c, Z3_optimize o, unsigned num_assumptions, Z3_ast const assumptions[])
Check consistency and produce optimal values.
def z3_error_handler(c, e)
void Z3_API Z3_optimize_set_params(Z3_context c, Z3_optimize o, Z3_params p)
Set parameters on optimization context.
Z3_tactic Z3_API Z3_tactic_or_else(Z3_context c, Z3_tactic t1, Z3_tactic t2)
Return a tactic that first applies t1 to a given goal, if it fails then returns the result of t2 appl...
Z3_ast Z3_API Z3_optimize_get_upper(Z3_context c, Z3_optimize o, unsigned idx)
Retrieve upper bound value or approximation for the i'th optimization objective.
Z3_ast_kind Z3_API Z3_get_ast_kind(Z3_context c, Z3_ast a)
Return the kind of the given AST.
bool Z3_API Z3_open_log(Z3_string filename)
Log interaction to a file.
void Z3_API Z3_set_ast_print_mode(Z3_context c, Z3_ast_print_mode mode)
Select mode for the format used for pretty-printing AST nodes.
void Z3_API Z3_optimize_assert_and_track(Z3_context c, Z3_optimize o, Z3_ast a, Z3_ast t)
Assert tracked hard constraint to the optimization context.
Z3_probe Z3_API Z3_probe_not(Z3_context x, Z3_probe p)
Return a probe that evaluates to "true" when p does not evaluate to true.
Z3_param_descrs Z3_API Z3_simplify_get_param_descrs(Z3_context c)
Return the parameter description set for the simplify procedure.
Z3_func_decl Z3_API Z3_mk_func_decl(Z3_context c, Z3_symbol s, unsigned domain_size, Z3_sort const domain[], Z3_sort range)
Declare a constant or function.
def get_rule_names_along_trace(self)
def simplify_param_descrs()
void Z3_API Z3_fixedpoint_inc_ref(Z3_context c, Z3_fixedpoint d)
Increment the reference counter of the given fixedpoint context.
void Z3_API Z3_probe_inc_ref(Z3_context c, Z3_probe p)
Increment the reference counter of the given probe.
Z3_func_decl Z3_API Z3_get_decl_func_decl_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the expression value associated with an expression parameter.
Z3_sort Z3_API Z3_mk_uninterpreted_sort(Z3_context c, Z3_symbol s)
Create a free (uninterpreted) type using the given name (symbol).
void Z3_API Z3_apply_result_inc_ref(Z3_context c, Z3_apply_result r)
Increment the reference counter of the given Z3_apply_result object.
void Z3_API Z3_dec_ref(Z3_context c, Z3_ast a)
Decrement the reference counter of the given AST. The context c should have been created using Z3_mk_...
void Z3_API Z3_del_config(Z3_config c)
Delete the given configuration object.
Z3_simplifier Z3_API Z3_simplifier_using_params(Z3_context c, Z3_simplifier t, Z3_params p)
Return a simplifier that applies t using the given set of parameters.
void Z3_API Z3_optimize_push(Z3_context c, Z3_optimize d)
Create a backtracking point.
def convert_model(self, model)
Z3_ast Z3_API Z3_substitute_vars(Z3_context c, Z3_ast a, unsigned num_exprs, Z3_ast const to[])
Substitute the variables in a with the expressions in to. For every i smaller than num_exprs...
def __init__(self, args, kws)
Z3_ast Z3_API Z3_optimize_get_lower(Z3_context c, Z3_optimize o, unsigned idx)
Retrieve lower bound value or approximation for the i'th optimization objective.
void Z3_API Z3_optimize_register_model_eh(Z3_context c, Z3_optimize o, Z3_model m, void *ctx, Z3_model_eh model_eh)
register a model event handler for new models.
void Z3_API Z3_parser_context_add_sort(Z3_context c, Z3_parser_context pc, Z3_sort s)
Add a sort declaration.
def using_params(self, args, keys)
double Z3_API Z3_get_decl_double_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the double value associated with an double parameter.
unsigned Z3_API Z3_get_ast_hash(Z3_context c, Z3_ast a)
Return a hash code for the given AST. The hash code is structural but two different AST objects can m...
def Extract(high, low, a)
Z3_string Z3_API Z3_optimize_to_string(Z3_context c, Z3_optimize o)
Print the current context as a string.
def solve_using(s, args, keywords)
Z3_string Z3_API Z3_get_full_version(void)
Return a string that fully describes the version of Z3 in use.
Z3_ast_vector Z3_API Z3_fixedpoint_from_file(Z3_context c, Z3_fixedpoint f, Z3_string s)
Parse an SMT-LIB2 file with fixedpoint rules. Add the rules to the current fixedpoint context...
def set_predicate_representation(self, f, representations)
Z3_ast_vector Z3_API Z3_parser_context_from_string(Z3_context c, Z3_parser_context pc, Z3_string s)
Parse a string of SMTLIB2 commands. Return assertions.
unsigned Z3_API Z3_get_app_num_args(Z3_context c, Z3_app a)
Return the number of argument of an application. If t is an constant, then the number of arguments is...
Z3_tactic Z3_API Z3_tactic_par_and_then(Z3_context c, Z3_tactic t1, Z3_tactic t2)
Return a tactic that applies t1 to a given goal and then t2 to every subgoal produced by t1...
Z3_string Z3_API Z3_fixedpoint_get_reason_unknown(Z3_context c, Z3_fixedpoint d)
Retrieve a string that describes the last status returned by Z3_fixedpoint_query. ...
def RecFunction(name, sig)
Z3_ast Z3_API Z3_sort_to_ast(Z3_context c, Z3_sort s)
Convert a Z3_sort into Z3_ast. This is just type casting.
void Z3_API Z3_set_error_handler(Z3_context c, Z3_error_handler h)
Register a Z3 error handler.
void Z3_API Z3_enable_trace(Z3_string tag)
Enable tracing messages tagged as tag when Z3 is compiled in debug mode. It is a NOOP otherwise...
Strings, Sequences and Regular expressions.
void Z3_API Z3_fixedpoint_dec_ref(Z3_context c, Z3_fixedpoint d)
Decrement the reference counter of the given fixedpoint context.
def apply(self, goal, arguments, keywords)
def solve(args, keywords)
def __init__(self, opt, value, is_max)
def check(self, assumptions)
Z3_ast_vector Z3_API Z3_fixedpoint_get_rules(Z3_context c, Z3_fixedpoint f)
Retrieve set of rules from fixedpoint context.
int Z3_API Z3_get_symbol_int(Z3_context c, Z3_symbol s)
Return the symbol int value.
def __call__(self, goal, arguments, keywords)
void Z3_API Z3_optimize_dec_ref(Z3_context c, Z3_optimize d)
Decrement the reference counter of the given optimize context.
double Z3_API Z3_probe_apply(Z3_context c, Z3_probe p, Z3_goal g)
Execute the probe over the goal. The probe always produce a double value. "Boolean" probes return 0...
unsigned Z3_API Z3_optimize_assert_soft(Z3_context c, Z3_optimize o, Z3_ast a, Z3_string weight, Z3_symbol id)
Assert soft constraint to the optimization context.
def prove(claim, show=False, keywords)
unsigned Z3_API Z3_get_num_tactics(Z3_context c)
Return the number of builtin tactics available in Z3.
def is_finite_domain_value(a)
Z3_string Z3_API Z3_get_numeral_string(Z3_context c, Z3_ast a)
Return numeral value, as a decimal string of a numeric constant term.
def get_rules_along_trace(self)
Z3_ast Z3_API Z3_simplify(Z3_context c, Z3_ast a)
Interface to simplifier.
Z3_model Z3_API Z3_optimize_get_model(Z3_context c, Z3_optimize o)
Retrieve the model for the last Z3_optimize_check.
void Z3_API Z3_interrupt(Z3_context c)
Interrupt the execution of a Z3 procedure. This procedure can be used to interrupt: solvers...
Z3_param_descrs Z3_API Z3_fixedpoint_get_param_descrs(Z3_context c, Z3_fixedpoint f)
Return the parameter description set for the given fixedpoint object.
def assert_and_track(self, a, p)
def translate(self, target)
def __radd__(self, other)
def from_file(self, filename)
unsigned Z3_API Z3_fixedpoint_get_num_levels(Z3_context c, Z3_fixedpoint d, Z3_func_decl pred)
Query the PDR engine for the maximal levels properties are known about predicate. ...
Z3_ast Z3_API Z3_get_decl_ast_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the expression value associated with an expression parameter.
def query_from_lvl(self, lvl, query)
Z3_tactic Z3_API Z3_tactic_using_params(Z3_context c, Z3_tactic t, Z3_params p)
Return a tactic that applies t using the given set of parameters.
Z3_sort Z3_API Z3_mk_type_variable(Z3_context c, Z3_symbol s)
Create a type variable.
Z3_sort Z3_API Z3_get_domain(Z3_context c, Z3_func_decl d, unsigned i)
Return the sort of the i-th parameter of the given function declaration.
void Z3_API Z3_fixedpoint_add_cover(Z3_context c, Z3_fixedpoint d, int level, Z3_func_decl pred, Z3_ast property)
Add property about the predicate pred. Add a property of predicate pred at level. It gets pushed forw...
void Z3_API Z3_optimize_pop(Z3_context c, Z3_optimize d)
Backtrack one level.
unsigned Z3_API Z3_get_ast_id(Z3_context c, Z3_ast t)
Return a unique identifier for t. The identifier is unique up to structural equality. Thus, two ast nodes created by the same context and having the same children and same function symbols have the same identifiers. Ast nodes created in the same context, but having different children or different functions have different identifiers. Variables and quantifiers are also assigned different identifiers according to their structure.
Z3_config Z3_API Z3_mk_config(void)
Create a configuration object for the Z3 context object.
def to_string(self, queries)
Z3_sort Z3_API Z3_get_range(Z3_context c, Z3_func_decl d)
Return the range of the given declaration.
void Z3_API Z3_fixedpoint_update_rule(Z3_context c, Z3_fixedpoint d, Z3_ast a, Z3_symbol name)
Update a named rule. A rule with the same name must have been previously created. ...
Z3_tactic Z3_API Z3_tactic_repeat(Z3_context c, Z3_tactic t, unsigned max)
Return a tactic that keeps applying t until the goal is not modified anymore or the maximum number of...
Z3_stats Z3_API Z3_optimize_get_statistics(Z3_context c, Z3_optimize d)
Retrieve statistics information from the last call to Z3_optimize_check.
Z3_tactic Z3_API Z3_tactic_cond(Z3_context c, Z3_probe p, Z3_tactic t1, Z3_tactic t2)
Return a tactic that applies t1 to a given goal if the probe p evaluates to true, and t2 if p evaluat...
Z3_tactic Z3_API Z3_tactic_par_or(Z3_context c, unsigned num, Z3_tactic const ts[])
Return a tactic that applies the given tactics in parallel.
Z3_ast Z3_API Z3_mk_pble(Z3_context c, unsigned num_args, Z3_ast const args[], int const coeffs[], int k)
Pseudo-Boolean relations.
def set_on_model(self, on_model)
def parse_string(self, s)
Z3_solver Z3_API Z3_mk_simple_solver(Z3_context c)
Create a new incremental solver.
Z3_tactic Z3_API Z3_tactic_try_for(Z3_context c, Z3_tactic t, unsigned ms)
Return a tactic that applies t to a given goal for ms milliseconds. If t does not terminate in ms mil...
void Z3_API Z3_set_param_value(Z3_config c, Z3_string param_id, Z3_string param_value)
Set a configuration parameter.
def get_ground_sat_answer(self)
Z3_ast_vector Z3_API Z3_optimize_get_assertions(Z3_context c, Z3_optimize o)
Return the set of asserted formulas on the optimization context.
def declare_var(self, vars)
void Z3_API Z3_parser_context_inc_ref(Z3_context c, Z3_parser_context pc)
Increment the reference counter of the given Z3_parser_context object.
Z3_probe Z3_API Z3_probe_lt(Z3_context x, Z3_probe p1, Z3_probe p2)
Return a probe that evaluates to "true" when the value returned by p1 is less than the value returned...
Z3_string Z3_API Z3_fixedpoint_get_help(Z3_context c, Z3_fixedpoint f)
Return a string describing all fixedpoint available parameters.
void Z3_API Z3_simplifier_inc_ref(Z3_context c, Z3_simplifier t)
Increment the reference counter of the given simplifier.
Z3_tactic Z3_API Z3_tactic_fail_if(Z3_context c, Z3_probe p)
Return a tactic that fails if the probe p evaluates to false.
Z3_string Z3_API Z3_optimize_get_help(Z3_context c, Z3_optimize t)
Return a string containing a description of parameters accepted by optimize.
Z3_string Z3_API Z3_get_symbol_string(Z3_context c, Z3_symbol s)
Return the symbol name.
Z3_goal Z3_API Z3_apply_result_get_subgoal(Z3_context c, Z3_apply_result r, unsigned i)
Return one of the subgoals in the Z3_apply_result object returned by Z3_tactic_apply.
Z3_sort_kind Z3_API Z3_get_sort_kind(Z3_context c, Z3_sort t)
Return the sort kind (e.g., array, tuple, int, bool, etc).
def __rmul__(self, other)
Z3_param_descrs Z3_API Z3_get_global_param_descrs(Z3_context c)
Retrieve description of global parameters.
def RecAddDefinition(f, args, body)
Z3_ast Z3_API Z3_mk_pbge(Z3_context c, unsigned num_args, Z3_ast const args[], int const coeffs[], int k)
Pseudo-Boolean relations.
void Z3_API Z3_apply_result_dec_ref(Z3_context c, Z3_apply_result r)
Decrement the reference counter of the given Z3_apply_result object.
Z3_ast_vector Z3_API Z3_fixedpoint_get_assertions(Z3_context c, Z3_fixedpoint f)
Retrieve set of background assertions from fixedpoint context.
Z3_ast Z3_API Z3_mk_atleast(Z3_context c, unsigned num_args, Z3_ast const args[], unsigned k)
Pseudo-Boolean relations.
Z3_ast Z3_API Z3_fixedpoint_get_cover_delta(Z3_context c, Z3_fixedpoint d, int level, Z3_func_decl pred)
unsigned Z3_API Z3_get_num_probes(Z3_context c)
Return the number of builtin probes available in Z3.
Z3_ast Z3_API Z3_translate(Z3_context source, Z3_ast a, Z3_context target)
Translate/Copy the AST a from context source to context target. AST a must have been created using co...
void Z3_API Z3_get_version(unsigned *major, unsigned *minor, unsigned *build_number, unsigned *revision_number)
Return Z3 version number information.
Z3_lbool Z3_API Z3_fixedpoint_query(Z3_context c, Z3_fixedpoint d, Z3_ast query)
Pose a query against the asserted rules.
Z3_string Z3_API Z3_optimize_get_reason_unknown(Z3_context c, Z3_optimize d)
Retrieve a string that describes the last status returned by Z3_optimize_check.
Z3_solver Z3_API Z3_solver_add_simplifier(Z3_context c, Z3_solver solver, Z3_simplifier simplifier)
Attach simplifier to a solver. The solver will use the simplifier for incremental pre-processing...
Z3_string Z3_API Z3_tactic_get_help(Z3_context c, Z3_tactic t)
Return a string containing a description of parameters accepted by the given tactic.
void Z3_API Z3_global_param_reset_all(void)
Restore the value of all global (and module) parameters. This command will not affect already created...
unsigned Z3_API Z3_optimize_minimize(Z3_context c, Z3_optimize o, Z3_ast t)
Add a minimization constraint.
def get_num_levels(self, predicate)
Z3_string Z3_API Z3_simplify_get_help(Z3_context c)
Return a string describing all available parameters.
Z3_ast Z3_API Z3_mk_eq(Z3_context c, Z3_ast l, Z3_ast r)
Create an AST node representing l = r.
Z3_ast Z3_API Z3_mk_atmost(Z3_context c, unsigned num_args, Z3_ast const args[], unsigned k)
Pseudo-Boolean relations.
Z3_symbol Z3_API Z3_mk_int_symbol(Z3_context c, int i)
Create a Z3 symbol using an integer.
void Z3_API Z3_add_rec_def(Z3_context c, Z3_func_decl f, unsigned n, Z3_ast args[], Z3_ast body)
Define the body of a recursive function.
def __init__(self, result, ctx)
def set(self, args, keys)
Z3_ast Z3_API Z3_mk_ite(Z3_context c, Z3_ast t1, Z3_ast t2, Z3_ast t3)
Create an AST node representing an if-then-else: ite(t1, t2, t3).
Z3_solver Z3_API Z3_mk_solver_from_tactic(Z3_context c, Z3_tactic t)
Create a new solver that is implemented using the given tactic. The solver supports the commands Z3_s...
Z3_ast_vector Z3_API Z3_optimize_get_upper_as_vector(Z3_context c, Z3_optimize o, unsigned idx)
Retrieve upper bound value or approximation for the i'th optimization objective.
Z3_string Z3_API Z3_benchmark_to_smtlib_string(Z3_context c, Z3_string name, Z3_string logic, Z3_string status, Z3_string attributes, unsigned num_assumptions, Z3_ast const assumptions[], Z3_ast formula)
Convert the given benchmark into SMT-LIB formatted string.
def add_cover(self, level, predicate, property)
int Z3_API Z3_get_decl_int_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the integer value associated with an integer parameter.
unsigned Z3_API Z3_get_arity(Z3_context c, Z3_func_decl d)
Alias for Z3_get_domain_size.
Z3_sort Z3_API Z3_get_sort(Z3_context c, Z3_ast a)
Return the sort of an AST node.
Z3_parser_context Z3_API Z3_mk_parser_context(Z3_context c)
Create a parser context.
void Z3_API Z3_probe_dec_ref(Z3_context c, Z3_probe p)
Decrement the reference counter of the given probe.
void Z3_API Z3_optimize_from_file(Z3_context c, Z3_optimize o, Z3_string s)
Parse an SMT-LIB2 file with assertions, soft constraints and optimization objectives. Add the parsed constraints and objectives to the optimization context.
Z3_symbol Z3_API Z3_get_sort_name(Z3_context c, Z3_sort d)
Return the sort name as a symbol.
Z3_ast_vector Z3_API Z3_optimize_get_lower_as_vector(Z3_context c, Z3_optimize o, unsigned idx)
Retrieve lower bound value or approximation for the i'th optimization objective. The returned vector ...
void Z3_API Z3_fixedpoint_set_params(Z3_context c, Z3_fixedpoint f, Z3_params p)
Set parameters on fixedpoint context.
void Z3_API Z3_fixedpoint_set_predicate_representation(Z3_context c, Z3_fixedpoint d, Z3_func_decl f, unsigned num_relations, Z3_symbol const relation_kinds[])
Configure the predicate representation.
Z3_string Z3_API Z3_probe_get_descr(Z3_context c, Z3_string name)
Return a string containing a description of the probe with the given name.
def set(self, args, keys)
void Z3_API Z3_fixedpoint_register_relation(Z3_context c, Z3_fixedpoint d, Z3_func_decl f)
Register relation as Fixedpoint defined. Fixedpoint defined relations have least-fixedpoint semantics...
void Z3_API Z3_inc_ref(Z3_context c, Z3_ast a)
Increment the reference counter of the given AST. The context c should have been created using Z3_mk_...
Z3_ast Z3_API Z3_mk_numeral(Z3_context c, Z3_string numeral, Z3_sort ty)
Create a numeral of a given sort.
Z3_ast_vector Z3_API Z3_optimize_get_unsat_core(Z3_context c, Z3_optimize o)
Retrieve the unsat core for the last Z3_optimize_check The unsat core is a subset of the assumptions ...
def substitute_funs(t, m)
Z3_string Z3_API Z3_tactic_get_descr(Z3_context c, Z3_string name)
Return a string containing a description of the tactic with the given name.
unsigned Z3_API Z3_optimize_maximize(Z3_context c, Z3_optimize o, Z3_ast t)
Add a maximization constraint.
unsigned Z3_API Z3_apply_result_get_num_subgoals(Z3_context c, Z3_apply_result r)
Return the number of subgoals in the Z3_apply_result object returned by Z3_tactic_apply.
def check(self, assumptions)
Z3_ast Z3_API Z3_fixedpoint_get_answer(Z3_context c, Z3_fixedpoint d)
Retrieve a formula that encodes satisfying answers to the query.
Z3_string Z3_API Z3_fixedpoint_to_string(Z3_context c, Z3_fixedpoint f, unsigned num_queries, Z3_ast queries[])
Print the current rules and background axioms as a string.
Z3_lbool Z3_API Z3_fixedpoint_query_relations(Z3_context c, Z3_fixedpoint d, unsigned num_relations, Z3_func_decl const relations[])
Pose multiple queries against the asserted rules.
def is_algebraic_value(a)
void Z3_API Z3_tactic_dec_ref(Z3_context c, Z3_tactic g)
Decrement the reference counter of the given tactic.
Z3_func_decl Z3_API Z3_mk_rec_func_decl(Z3_context c, Z3_symbol s, unsigned domain_size, Z3_sort const domain[], Z3_sort range)
Declare a recursive function.
Z3_ast Z3_API Z3_substitute_funs(Z3_context c, Z3_ast a, unsigned num_funs, Z3_func_decl const from[], Z3_ast const to[])
Substitute functions in from with new expressions in to.
Z3_simplifier Z3_API Z3_mk_simplifier(Z3_context c, Z3_string name)
Return a simplifier associated with the given name. The complete list of simplifiers may be obtained ...
Z3_sort Z3_API Z3_get_decl_sort_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the sort value associated with a sort parameter.
void Z3_API Z3_optimize_from_string(Z3_context c, Z3_optimize o, Z3_string s)
Parse an SMT-LIB2 string with assertions, soft constraints and optimization objectives. Add the parsed constraints and objectives to the optimization context.
Z3_ast Z3_API Z3_mk_fresh_const(Z3_context c, Z3_string prefix, Z3_sort ty)
Declare and create a fresh constant.