def as_onestate_formula(self, index: Optional[int] = None) -> Expr:
# TODO: move to class State, this shouldn't be here
assert self.num_states == 1 or index is not None, \
'to generate a onestate formula from a multi-state model, ' + \
'you must specify which state you want'
assert index is None or (0 <= index and index < self.num_states)
if index is None:
index = 0
if index not in self.onestate_formula_cache:
prog = syntax.the_program
mut_rel_interps = self.rel_interps[index]
mut_const_interps = self.const_interps[index]
mut_func_interps = self.func_interps[index]
vs: List[syntax.SortedVar] = []
ineqs: Dict[SortDecl, List[Expr]] = {}
rels: Dict[RelationDecl, List[Expr]] = {}
consts: Dict[ConstantDecl, Expr] = {}
funcs: Dict[FunctionDecl, List[Expr]] = {}
for sort in self.univs:
vs.extend(syntax.SortedVar(v, syntax.UninterpretedSort(sort.name))
for v in self.univs[sort])
u = [syntax.Id(v) for v in self.univs[sort]]
ineqs[sort] = [syntax.Neq(a, b) for a, b in combinations(u, 2)]
for R, l in chain(mut_rel_interps.items(), self.immut_rel_interps.items()):
rels[R] = []
for tup, ans in l.items():
e: Expr = (
syntax.AppExpr(R.name, tuple(syntax.Id(col) for col in tup))
if tup else syntax.Id(R.name)
)
rels[R].append(e if ans else syntax.Not(e))
for C, c in chain(mut_const_interps.items(), self.immut_const_interps.items()):
consts[C] = syntax.Eq(syntax.Id(C.name), syntax.Id(c))
for F, fl in chain(mut_func_interps.items(), self.immut_func_interps.items()):
funcs[F] = [
syntax.Eq(syntax.AppExpr(F.name, tuple(syntax.Id(col) for col in tup)),
syntax.Id(res))
for tup, res in fl.items()
]
# get a fresh variable, avoiding names of universe elements in vs
fresh = prog.scope.fresh('x', [v.name for v in vs])
e = syntax.Exists(tuple(vs), syntax.And(
*chain(*ineqs.values(), *rels.values(), consts.values(), *funcs.values(), (
syntax.Forall((syntax.SortedVar(fresh,
syntax.UninterpretedSort(sort.name)),),
syntax.Or(*(syntax.Eq(syntax.Id(fresh), syntax.Id(v))
for v in self.univs[sort])))
for sort in self.univs
))))
assert prog.scope is not None
with prog.scope.n_states(1):
typechecker.typecheck_expr(prog.scope, e, None)
self.onestate_formula_cache[index] = e
return self.onestate_formula_cache[index]
def relaxed_program(prog: syntax.Program) -> syntax.Program:
new_decls: List[syntax.Decl] = [d for d in prog.sorts()]
actives: Dict[syntax.SortDecl, syntax.RelationDecl] = {}
for sort in prog.sorts():
name = prog.scope.fresh('active_' + sort.name)
r = syntax.RelationDecl(name, arity=[syntax.UninterpretedSort(sort.name)],
mutable=True, derived=None, annotations=[])
actives[sort] = r
new_decls.append(r)
# active relations initial conditions: always true
for sort in prog.sorts():
name = prog.scope.fresh(sort.name[0].upper())
expr = syntax.Forall([syntax.SortedVar(name, None)],
syntax.Apply(actives[sort].name, [syntax.Id(name)]))
new_decls.append(syntax.InitDecl(name=None, expr=expr))
for d in prog.decls:
if isinstance(d, syntax.SortDecl):
pass # already included above
elif isinstance(d, syntax.RelationDecl):
if d.derived_axiom is not None:
expr = syntax.relativize_quantifiers(actives, d.derived_axiom)
new_decls.append(syntax.RelationDecl(d.name, d.arity, d.mutable, expr,
d.annotations))
else:
new_decls.append(d)
elif isinstance(d, syntax.ConstantDecl):
new_decls.append(d)
elif isinstance(d, syntax.FunctionDecl):
new_decls.append(d)
elif isinstance(d, syntax.AxiomDecl):
new_decls.append(d)
elif isinstance(d, syntax.InitDecl):
new_decls.append(d)
elif isinstance(d, syntax.DefinitionDecl):
assert not isinstance(d.body, syntax.BlockStatement), \
"relax does not support transitions written in imperative syntax"
mods, expr = d.body
expr = syntax.relativize_quantifiers(actives, expr)
if d.is_public_transition:
guard = syntax.relativization_guard_for_binder(actives, d.binder)
expr = syntax.And(guard, expr)
new_decls.append(syntax.DefinitionDecl(d.is_public_transition, d.num_states, d.name,
params=d.binder.vs, body=(mods, expr)))
elif isinstance(d, syntax.InvariantDecl):
expr = syntax.relativize_quantifiers(actives, d.expr)
new_decls.append(syntax.InvariantDecl(d.name, expr=expr,
is_safety=d.is_safety, is_sketch=d.is_sketch))
else:
assert False, d
new_decls.append(relaxation_action_def(prog, actives=actives, fresh=True))
res = syntax.Program(new_decls)
res.resolve() # #sorrynotsorry
return res
def _generate_active_rels(self, scope: syntax.Scope) -> None:
for sort in scope.known_sorts():
active_name = scope.fresh('active_%s' % sort.name)
# TODO: is there a better way to get Sort out of SortDecl?
sort_not_decl = syntax.UninterpretedSort(sort.name)
typechecker.typecheck_sort(scope, sort_not_decl)
active_rel = syntax.RelationDecl(active_name,
arity=(sort_not_decl, ),
mutable=True)
self._active_rels_mapping[sort] = active_rel
def _read_first_order_structure(
struct: FirstOrderStructure
) -> Tuple[List[syntax.SortedVar], # vs
Dict[SortDecl, List[Expr]], # ineqs
Dict[RelationDecl, List[Expr]], # rels
Dict[ConstantDecl, Expr], # consts
Dict[FunctionDecl, List[Expr]], # funcs
]:
vars_by_sort: Dict[SortDecl, List[syntax.SortedVar]] = {}
ineqs: Dict[SortDecl, List[Expr]] = {}
rels: Dict[RelationDecl, List[Expr]] = {}
consts: Dict[ConstantDecl, Expr] = {}
funcs: Dict[FunctionDecl, List[Expr]] = {}
for sort in struct.univs:
vars_by_sort[sort] = [
syntax.SortedVar(v, syntax.UninterpretedSort(sort.name))
for v in struct.univs[sort]
]
u = [syntax.Id(s) for s in struct.univs[sort]]
ineqs[sort] = [
syntax.Neq(a, b) for a, b in itertools.combinations(u, 2)
]
for R, l in struct.rel_interps.items():
rels[R] = []
for tup, ans in l.items():
e: Expr
if tup:
args: List[Expr] = []
for (col, col_sort) in zip(tup, R.arity):
assert isinstance(col_sort, syntax.UninterpretedSort)
assert col_sort.decl is not None
args.append(syntax.Id(col))
e = syntax.AppExpr(R.name, tuple(args))
else:
e = syntax.Id(R.name)
e = e if ans else syntax.Not(e)
rels[R].append(e)
for C, c in struct.const_interps.items():
e = syntax.Eq(syntax.Id(C.name), syntax.Id(c))
consts[C] = e
for F, fl in struct.func_interps.items():
funcs[F] = []
for tup, res in fl.items():
e = syntax.AppExpr(F.name,
tuple(syntax.Id(col) for col in tup))
e = syntax.Eq(e, syntax.Id(res))
funcs[F].append(e)
vs = list(itertools.chain(*(vs for vs in vars_by_sort.values())))
return vs, ineqs, rels, consts, funcs
def active_rels_mapping() -> Mapping[syntax.SortDecl, syntax.RelationDecl]:
# TODO: should be read from the relaxation / the program, not fixed.
# TODO: duplicated from relaxed_program()
actives: Dict[syntax.SortDecl, syntax.RelationDecl] = {}
prog = syntax.the_program
for sort in prog.sorts():
name = 'active_' + sort.name # prog.scope.fresh('active_' + sort.name)
r = syntax.RelationDecl(name, arity=[syntax.UninterpretedSort(sort.name)],
mutable=True, derived=None, annotations=[])
actives[sort] = r
return actives
def p_sort(p: Any) -> None:
'sort : id'
p[0] = syntax.UninterpretedSort(p[1], p[1].value)
def p_sort(p: Any) -> None:
'sort : id'
tok: Token = p[1]
p[0] = syntax.UninterpretedSort(tok.value, span=span_from_tok(tok))
def relaxed_program(prog: syntax.Program) -> syntax.Program:
new_decls: List[syntax.Decl] = [d for d in prog.sorts()]
actives: Dict[syntax.SortDecl, syntax.RelationDecl] = {}
for sort in prog.sorts():
name = prog.scope.fresh('active_' + sort.name)
r = syntax.RelationDecl(name,
arity=(syntax.UninterpretedSort(sort.name), ),
mutable=True)
actives[sort] = r
new_decls.append(r)
# active relations initial conditions: always true
for sort in prog.sorts():
name = prog.scope.fresh(sort.name[0].upper())
expr = syntax.Forall((syntax.SortedVar(name, None), ),
syntax.Apply(actives[sort].name,
(syntax.Id(name), )))
new_decls.append(syntax.InitDecl(name=None, expr=expr))
for d in prog.decls:
if isinstance(d, syntax.SortDecl):
pass # already included above
elif isinstance(d, syntax.RelationDecl):
if d.derived_axiom is not None:
expr = syntax.relativize_quantifiers(actives, d.derived_axiom)
new_decls.append(
syntax.RelationDecl(d.name,
d.arity,
d.mutable,
expr,
annotations=d.annotations))
else:
new_decls.append(d)
elif isinstance(d, syntax.ConstantDecl):
new_decls.append(d)
elif isinstance(d, syntax.FunctionDecl):
new_decls.append(d)
elif isinstance(d, syntax.AxiomDecl):
new_decls.append(d)
elif isinstance(d, syntax.InitDecl):
new_decls.append(d)
elif isinstance(d, syntax.DefinitionDecl):
relativized_def = relativize_decl(d,
actives,
prog.scope,
inline_relax_actives=False)
new_decls.append(relativized_def)
elif isinstance(d, syntax.InvariantDecl):
expr = syntax.relativize_quantifiers(actives, d.expr)
new_decls.append(
syntax.InvariantDecl(d.name,
expr=expr,
is_safety=d.is_safety,
is_sketch=d.is_sketch))
else:
assert False, d
new_decls.append(relaxation_action_def(prog, actives=actives, fresh=True))
res = syntax.Program(new_decls)
typechecker.typecheck_program(res) # #sorrynotsorry
return res