def localize(property:SpecProperty):
""" sound, but incomplete
forall(i) a_i -> forall(j) g_j
=>
forall(i) (a_i -> g_i)
forall(i,j) a_i_j -> forall(k) g_k
=>
forall(i,j) (a_i_j -> g_i)
"""
if not is_quantified_property(property):
return property
normalized_ass = normalize_conjuncts(property.assumptions)
normalized_gua = normalize_conjuncts(property.guarantees)
binding_indices_ass = _get_indices(normalized_ass)
binding_indices_gua = _get_indices(normalized_gua)
if len(binding_indices_ass) > len(binding_indices_gua):
max_expr, other_expr = normalized_ass, normalized_gua
else:
max_expr, other_expr = normalized_gua, normalized_ass
assert isinstance(max_expr, ForallExpr)
max_binding_indices = max_expr.arg1
ass_newindex_by_old = dict((o, max_binding_indices[i]) for i, o in enumerate(binding_indices_ass))
gua_newindex_by_old = dict((o, max_binding_indices[i]) for i, o in enumerate(binding_indices_gua))
replaced_ass = _replace_indices(ass_newindex_by_old, normalized_ass)
replaced_gua = _replace_indices(gua_newindex_by_old, normalized_gua)
replaced_underlying_ass = replaced_ass.arg2 if is_quantified_expr(replaced_ass) else replaced_ass
replaced_underlying_gua = replaced_gua.arg2 if is_quantified_expr(replaced_gua) else replaced_gua
new_gua = ForallExpr(max_binding_indices,
BinOp('->', replaced_underlying_ass, replaced_underlying_gua))
new_property = SpecProperty([Bool(True)], [new_gua])
return new_property
def _denormalize(conjunct:Expr) -> list:
"""
Forall(i) a_i and b_i
replaced by
Forall(i) a_i and Forall(i) b_i
"""
normalized_conjunct = normalize_conjuncts([conjunct])
if not is_quantified_property(SpecProperty([normalized_conjunct], [])):
return [normalized_conjunct]
#: :type: ForallExpr
forall_expr = conjunct
quantified_expr = forall_expr.arg2
conjunctions = _get_conjuncts(quantified_expr)
return [_reduce_quantifiers(ForallExpr(forall_expr.arg1, c))
for c in conjunctions]
def _get_rank(property:SpecProperty) -> int:
if not is_quantified_property(property):
return 0
#forall(i) a_i -> g_0
# since the initial token distribution is random
# <=>
#forall(i) a_i -> forall(i) g_i, which is 2-indexed
# a_0 -> forall(i) g_i
# <=> ???
# (exists(i) a_i) -> forall(i) g_i, which is 2-indexed
#
# Currently we forbid concrete assumptions/guarantees
ass_max_len = max(map(lambda e: len(e.arg1) if is_quantified_expr(e) else 0, property.assumptions))
gua_max_len = max(map(lambda e: len(e.arg1) if is_quantified_expr(e) else 0, property.guarantees))
rank = ass_max_len + gua_max_len
return rank
def _get_rank(property: SpecProperty) -> int:
if not is_quantified_property(property):
return 0
#forall(i) a_i -> g_0
# since the initial token distribution is random
# <=>
#forall(i) a_i -> forall(i) g_i, which is 2-indexed
# a_0 -> forall(i) g_i
# <=> ???
# (exists(i) a_i) -> forall(i) g_i, which is 2-indexed
#
# Currently we forbid concrete assumptions/guarantees
ass_max_len = max(
map(lambda e: len(e.arg1)
if is_quantified_expr(e) else 0, property.assumptions))
gua_max_len = max(
map(lambda e: len(e.arg1)
if is_quantified_expr(e) else 0, property.guarantees))
rank = ass_max_len + gua_max_len
return rank
def is_quantified_expr(expr: Expr):
return is_quantified_property(SpecProperty([], [expr]))
def is_quantified_expr(expr:Expr):
return is_quantified_property(SpecProperty([], [expr]))