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341 | @dataclass
class Z3Solver(Solver):
"""
A solver that uses Z3.
>>> from typedlogic.integrations.frameworks.pydantic import FactBaseModel
>>> class AncestorOf(FactBaseModel):
... ancestor: str
... descendant: str
>>> solver = Z3Solver()
>>> solver.add_predicate_definition(PredicateDefinition(predicate="AncestorOf", arguments={'ancestor': "str", 'descendant': "str"}))
>>> solver.add_fact(AncestorOf(ancestor='p1', descendant='p1a'))
>>> solver.add_fact(AncestorOf(ancestor='p1a', descendant='p1aa'))
>>> from typedlogic import SentenceGroup, PredicateDefinition
>>> aa = SentenceGroup(name="transitivity-of-ancestor-of")
>>> solver.add_sentence_group(aa)
>>> soln = solver.check()
"""
_wrapped_solver: Optional[z3.Solver] = None
profile: ClassVar[Profile] = MixedProfile(
Unrestricted(), SortedLogic(), MultipleModelSemantics(), OpenWorld(), AllowsComparisonTerms()
)
max_models: int = field(default=5)
# TODO: rename this
predicate_map: Optional[Dict[str, z3.FuncDecl]] = None
def __post_init__(self):
if self._wrapped_solver is None:
self._wrapped_solver = z3.Solver()
@property
def wrapped_solver(self) -> z3.Solver:
if self._wrapped_solver is None:
self._wrapped_solver = z3.Solver()
return self._wrapped_solver
def check(self) -> Solution:
result = self.wrapped_solver.check()
return Solution(satisfiable=result == z3.sat)
def models(self) -> Iterator[Model]:
results = get_models(self.wrapped_solver, self.max_models)
if not results:
raise ValueError("Not satisfiable")
for wmodel in results:
rmodel = Model(
description=str(wmodel),
source_object=wmodel,
ground_terms=[],
)
yield rmodel
return
def prove(self, sentence: Sentence) -> Optional[bool]:
s = self.wrapped_solver
s.push()
s.add(z3.Not(self.translate(sentence)))
result = s.check()
s.pop()
return result == z3.unsat
def _unroll_type(self, typ: DefinedType) -> Set[str]:
"""
Unroll a defined type into its components
:param typ:
:return:
"""
if isinstance(typ, str):
if typ in self.type_definitions:
return self._unroll_type(self.base_theory.type_definitions[typ])
return {typ}
if isinstance(typ, list):
ts: List[str] = []
for t in typ:
ts.extend(self._unroll_type(t))
return set(ts)
raise ValueError(f"Unknown type {typ}")
def _sort(self, typ: Optional[str] = None) -> Union[Callable, Type[z3.SortRef]]:
# TODO: change this to return instantiated sort, not the sort class
if not typ:
return z3.StringSort
typs = self._unroll_type(typ)
repl_map = {
"Decimal": "float",
}
typs = {repl_map.get(t, t) for t in typs}
if "float" in typs and "int" in typs:
typs = typs.difference({"int"})
if len(typs) > 1:
# unions not directly supported
# TODO: add constraints
return lambda: z3.DeclareSort(typ)
typ = list(typs)[0]
if not isinstance(typ, str):
# TODO - we should ensure types are strings
typ = typ.__name__
return SORT_MAP.get(typ, z3.StringSort)
def _const(self, value: Any, typ: str) -> z3.Const:
sort = self._sort(typ)
return z3.Const(value, sort())
def _func(self, name: str, *args) -> z3.FuncDecl:
args = tuple([args] + [z3.BoolSort()])
return z3.Function(name, *args)
def _tr(self, var: Any, bindings: dict) -> z3.ExprRef:
if var is None:
return z3.StringVal("None")
if isinstance(var, Variable):
if var.name not in bindings:
if var.name in self.constants:
pf_arg = self.constants[var.name]
else:
raise ValueError(f"Variable {var.name} not bound in {bindings} or {self.constants}")
else:
pf_arg = bindings[var.name]
return pf_arg
py_typ = type(var).__name__
z3_typ = self._sort(py_typ)
t2m_map = {
z3.StringSort: z3.StringVal,
z3.IntSort: z3.IntVal,
z3.BoolSort: z3.BoolVal,
z3.RealSort: z3.RealVal,
}
z3_valf = t2m_map.get(z3_typ, z3.StringVal)
return z3_valf(var)
def add_fact(self, fact: FactMixin) -> None:
return self.add_sentence(fact)
def add_sentence(self, sentence: Sentence) -> None:
# normalize_variables(sentence)
z3_expr = self.translate(sentence)
self.wrapped_solver.add(z3_expr)
def add_predicate_definition(self, predicate_definition: PredicateDefinition) -> None:
"""
Add a predicate definition to the solver.
E.g. `` Function('AncestorOf', StringSort(), StringSort(), BoolSort())``
:param predicate_definition:
:return:
"""
args = [self._sort(a)() for a in predicate_definition.arguments.values()]
args += [z3.BoolSort()]
p = z3.Function(predicate_definition.predicate, *args)
if not self.predicate_map:
self.predicate_map = {}
self.predicate_map[predicate_definition.predicate] = p
if not self.predicate_definitions:
self.predicate_definitions = {}
self.predicate_definitions[predicate_definition.predicate] = predicate_definition
def translate(self, sentence: Sentence, bindings: Optional[Dict[str, z3.SortRef]] = None) -> z3.ExprRef:
"""
Translate a Sentence to a Z3 expression.
:param sentence: The Sentence to translate
:param bindings: local bindings of variable names to Z3 Sorts
:return: The Z3 expression
"""
if isinstance(sentence, tlog.And):
return z3.And(*[self.translate(op, bindings) for op in sentence.operands])
if isinstance(sentence, tlog.Or):
return z3.Or(*[self.translate(op, bindings) for op in sentence.operands])
if isinstance(sentence, tlog.Xor):
return z3.Xor(*[self.translate(op, bindings) for op in sentence.operands])
if isinstance(sentence, tlog.ExactlyOne):
disj = []
for a in sentence.operands:
disj.append(
z3.And(
self.translate(a, bindings),
*[z3.Not(self.translate(b, bindings)) for b in sentence.operands if b != a],
)
)
return z3.Or(*disj)
if isinstance(sentence, tlog.Not):
return z3.Not(self.translate(sentence.operands[0], bindings))
if isinstance(sentence, tlog.Iff):
# rewrite
lhs = sentence.left
rhs = sentence.right
rewritten = tlog.And(tlog.Implies(lhs, rhs), tlog.Implies(rhs, lhs))
return self.translate(rewritten, bindings)
if isinstance(sentence, tlog.Implied):
# rewrite
lhs = sentence.operands[0]
rhs = sentence.operands[1]
return self.translate(tlog.Implies(rhs, lhs), bindings)
if isinstance(sentence, tlog.Implies):
lhs = self.translate(sentence.operands[0], bindings)
rhs = self.translate(sentence.operands[1], bindings)
return z3.Implies(lhs, rhs)
if isinstance(sentence, (tlog.Forall, tlog.Exists)):
if not bindings:
bindings = {}
args = []
for v in sentence.variables:
var_name = v.name
domain = v.domain
s = self._sort(domain)
arg = z3.Const(var_name, s()) ## TODO
bindings[var_name] = arg
args.append(arg)
inner_sentence = self.translate(sentence.sentence, bindings)
if isinstance(sentence, tlog.Exists):
return z3.Exists(args, inner_sentence)
else:
return z3.ForAll(args, inner_sentence)
if isinstance(sentence, (tlog.Term, typedlogic.pybridge.FactMixin)): # TODO: use Expression
if isinstance(sentence, typedlogic.pybridge.FactMixin):
sentence = tlog.Term(fact_predicate(sentence), fact_arg_map(sentence))
if not self.predicate_map or not self.predicate_definitions:
raise ValueError("You must add predicate definitions before adding facts")
pd = self.predicate_definitions.get(sentence.predicate)
pf = self.predicate_map.get(sentence.predicate)
if pf is None and sentence.predicate in NUMERIC_BUILTINS:
pf = NUMERIC_BUILTINS[sentence.predicate]
elif pf is None or pd is None:
raise ValueError(
f"Predicate {sentence.predicate} not found in {self.predicate_map}\n"
"Did you remember to declare these as predicates?"
)
elif sentence.positional:
# TODO: more elegant way to do this
sentence = copy(sentence)
sentence.make_keyword_indexed(list(pd.arguments.keys()))
pf_args = []
for arg_name, var in sentence.bindings.items():
if not bindings:
bindings = {}
if isinstance(var, Variable):
if var.name not in bindings:
if var.name in self.constants:
pf_arg = self.constants[var.name]
else:
raise ValueError(f"Variable {var.name} not bound in {bindings} or {self.constants}")
else:
pf_arg = bindings[var.name]
pf_args.append(pf_arg)
elif isinstance(var, Term):
args = [self._tr(a, bindings) for a in var.values]
p = var.predicate
if p == "add":
pf_args.append(args[0] + args[1])
elif p == "gt":
pf_args.append(args[0] > args[1])
else:
raise NotImplementedError(f"Term not implemented: {var}")
elif var is None:
pf_args.append(z3.StringVal("None"))
else:
py_typ = type(var).__name__
z3_typ = self._sort(py_typ)
t2m_map = {
z3.StringSort: z3.StringVal,
z3.IntSort: z3.IntVal,
z3.BoolSort: z3.BoolVal,
z3.RealSort: z3.RealVal,
}
z3_valf = t2m_map.get(z3_typ, z3.StringVal)
pf_arg = z3_valf(var)
pf_args.append(pf_arg)
try:
z3_expr = pf(*pf_args)
except Exception as e:
raise ValueError(f"Error translating {sentence} args: {pf_args} to Z3 using {pf}:\n{e}")
return z3_expr
raise NotImplementedError(f"Not implemented:{type(sentence)} :: {sentence}")
def dump(self) -> str:
return str(self.wrapped_solver)
|
