def rename_and_pull(f, quant, old_var1, old_var2, arg1, arg2):
""" Helper function that renames given variable in a formula. """
# when both variables are to be renamed, re-use the variable name
# eg. (forall x: P(x) & forall y: Q(y)) <-> (forall x: P(x) & Q(x))
new_var = None
if old_var1: # rename left?
new_var = variant(old_var1, fvars(f))
a1 = subst({old_var1: new_var}, arg1)
else:
a1 = arg1
if old_var2: # rename right?
if not new_var:
new_var = variant(old_var2, fvars(f))
a2 = subst({old_var2: new_var}, arg2)
else:
a2 = arg2
return Quantifier(quant, new_var, pullquants(Expr(f.op, a1 , a2)))
def helper(f, used, substs):
if is_variable(f):
if f in substs: return substs[f]
else: return f
if is_quantified(f):
# does this quantifier use a variable that is already used?
clashing = (used & set(f.vars)) # set intersection
if len(clashing) > 0:
for var in clashing:
existing = used.union(*list(map(vars, substs.values())))
# rename any clashing variable
var2 = variant(var, existing)
substs[var] = var2
used.update(f.vars)
arg = helper(f.args[0], used, substs)
return Quantifier(f.op,
[subst(substs, x) for x in f.vars],
*[subst(substs, x) for x in f.args])
else:
used.update(f.vars)
arg = helper(f.args[0], used, substs)
return Quantifier(f.op, f.vars, arg)
else:
return Expr(f.op, *[helper(x, used, substs) for x in f.args])