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 _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 functions_total_axioms(prog: syntax.Program) -> List[Expr]:
res = []
for func in prog.functions():
# TODO: generation of part of the formula duplicated from relaxation_action_def.
# TODO: would be best to beef up the expression-generation library
names: List[str] = []
params = []
for arg_sort in func.arity:
arg_sort_decl = syntax.get_decl_from_sort(arg_sort)
name = prog.scope.fresh(arg_sort_decl.name[0].upper(),
also_avoid=names)
names.append(name)
params.append(syntax.SortedVar(name, arg_sort))
ap_func = syntax.Apply(func.name,
tuple(syntax.Id(v.name) for v in params))
name = prog.scope.fresh('y', also_avoid=names)
ax = syntax.Forall(
tuple(params),
syntax.Exists((syntax.SortedVar(name, func.sort), ),
syntax.Eq(syntax.Id(name), ap_func)))
with prog.scope.n_states(1):
typechecker.typecheck_expr(prog.scope, ax, syntax.BoolSort)
res.append(ax)
return res
def consts_exist_axioms(prog: syntax.Program) -> List[Expr]:
res = []
for c in prog.constants():
name = prog.scope.fresh('e_%s' % c.name)
ax = syntax.Exists((syntax.SortedVar(name, c.sort), ),
syntax.Eq(syntax.Id(c.name), syntax.Id(name)))
with prog.scope.n_states(1):
typechecker.typecheck_expr(prog.scope, ax, syntax.BoolSort)
res.append(ax)
return res
def load_relaxed_trace_from_updr_cex(prog: Program, s: Solver) -> logic.Trace:
import xml.dom.minidom # type: ignore
collection = xml.dom.minidom.parse(
"paxos_derived_trace.xml").documentElement
components: List[syntax.TraceComponent] = []
xml_decls = reversed(collection.childNodes)
seen_first = False
for elm in xml_decls:
if isinstance(elm, xml.dom.minidom.Text): # type: ignore
continue
if elm.tagName == 'state':
diagram = parser.parse_expr(elm.childNodes[0].data)
typechecker.typecheck_expr(prog.scope, diagram, syntax.BoolSort)
assert isinstance(
diagram, syntax.QuantifierExpr) and diagram.quant == 'EXISTS'
active_clauses = [
relaxed_traces.active_var(v.name, str(v.sort))
for v in diagram.get_vs()
]
if not seen_first:
# restrict the domain to be subdomain of the diagram's existentials
seen_first = True
import itertools # type: ignore
for sort, vars in itertools.groupby(
diagram.get_vs(),
lambda v: v.sort): # TODO; need to sort first
free_var = syntax.SortedVar(
syntax.the_program.scope.fresh("v_%s" % str(sort)),
None)
# TODO: diagram simplification omits them from the exists somewhere
consts = list(
filter(lambda c: c.sort == sort, prog.constants()))
els: Sequence[Union[syntax.SortedVar, syntax.ConstantDecl]]
els = list(vars)
els += consts
restrict_domain = syntax.Forall(
(free_var, ),
syntax.Or(*(syntax.Eq(syntax.Id(free_var.name),
syntax.Id(v.name))
for v in els)))
active_clauses += [restrict_domain]
diagram_active = syntax.Exists(
diagram.get_vs(), syntax.And(diagram.body, *active_clauses))
typechecker.typecheck_expr(prog.scope, diagram_active,
syntax.BoolSort)
components.append(syntax.AssertDecl(expr=diagram_active))
elif elm.tagName == 'action':
action_name = elm.childNodes[0].data.split()[0]
tcall = syntax.TransitionCalls(
calls=[syntax.TransitionCall(target=action_name, args=None)])
components.append(syntax.TraceTransitionDecl(transition=tcall))
else:
assert False, "unknown xml tagName"
trace_decl = syntax.TraceDecl(components=components, sat=True)
migrated_trace = bmc_trace(
prog,
trace_decl,
s,
lambda s, ks: logic.check_solver(s, ks, minimize=True),
log=False)
assert migrated_trace is not None
import pickle
pickle.dump(migrated_trace, open("migrated_trace.p", "wb"))
return migrated_trace
def as_expr(self, els_trans: Callable[[str],str]) -> Expr:
e = syntax.AppExpr(None, self._func.name, [syntax.Id(None, els_trans(e)) for e in self._params_els])
return syntax.Eq(e, syntax.Id(None, els_trans(self._res_elm)))
