def __init__(self, FOL: SimpleNamespace, ST: SimpleNamespace):
self._defined = ST.Nin
vars = VarBuilder()
self._formula = (FOL.Forall(
vars.universal('u'),
FOL.Forall(
vars.universal('v'),
FOL.Equiv(ST.In(vars['u'], vars['v']),
FOL.Not(ST.Nin(vars['u'], vars['v']))))))
pass
def __init__(self, index: int, FOL: SimpleNamespace, ST: SimpleNamespace):
def recurse_create_forall(count: int,
vars: VarBuilder,
index: int = 0) -> Node:
if index == count:
return None
else:
return FOL.Forall(
vars.universal("u_{}".format(index)),
recurse_create_forall(count, vars, index+1))
def recurse_create_or(count: int,
check_var: str,
vars: VarBuilder,
index: int = 0) -> Node:
eq_formula = FOL.Eq(vars[check_var], vars["u_{}".format(index)])
if index + 1 == count:
return eq_formula
else:
return FOL.Or(
eq_formula,
recurse_create_or(count, check_var, vars, index+1))
self._defined = (ST.InductiveFormation, 3)
vars = VarBuilder()
root_member_foralls = recurse_create_forall(index, vars)
tail_member_foralls = root_member_foralls
while tail_member_foralls.right() is not None:
tail_member_foralls = tail_member_foralls.right()
members = vars.values()
tail_member_foralls.set_right(
FOL.Forall(
vars.universal("Set"),
FOL.Equiv(
FOL.Eq(
vars["Set"],
ST.InductiveFormation(index, *members)
),
FOL.Forall(
vars.universal("x"),
FOL.Equiv(
ST.In(vars["x"], vars["Set"]),
recurse_create_or(index, "x", vars)
)
)
)
)
)
self._formula = root_member_foralls
pass
def __init__(self, FOL: SimpleNamespace, ST: SimpleNamespace):
self._defined = ST.Subset
vars = VarBuilder()
self._formula = (FOL.Forall(
vars.universal("Set"),
FOL.Forall(
vars.universal("Subset"),
FOL.Equiv(
ST.Subset(vars["Subset"], vars["Set"]),
FOL.Forall(
vars.universal("u"),
FOL.Impl(
ST.In(vars["u"], vars["Subset"]),
ST.In(vars["u"], vars["Set"]),
))))))
pass
def recurse_create_forall(count: int,
vars: VarBuilder,
index: int = 0) -> Node:
if index == count:
return None
else:
return FOL.Forall(
vars.universal("u_{}".format(index)),
recurse_create_forall(count, vars, index+1))
def __init__(self, FOL: SimpleNamespace, ST: SimpleNamespace):
self._defined = FOL.DefOp
vars = VarBuilder()
# TODO: the problem here that this node depends on the function being defined
# So it can only be applied based on a concrete function definition? or can we provide
# a recipe?
# making this work nicely needs a refactoring, every entity eg function must be expressible as a partially-expanded parametrizable
# node
# TBC
self._formula = (
FOL.Forall(
vars.universal("f"),
FOL.Equiv(
FOL.Eq(
vars["f"],
None
),
None
)
)
)
pass
def __init__(self, FOL: SimpleNamespace, ST: SimpleNamespace):
vars = VarBuilder()
self._formula = (FOL.Forall(
vars.universal('u'),
FOL.Forall(
vars.universal('v'),
FOL.Exists(
vars.existential('Pair'),
FOL.Forall(
vars.existential('x'),
FOL.Equiv(
ST.In(vars['x'], vars['Pair']),
FOL.Or(
FOL.Eq(vars['x'], vars['u']),
FOL.Eq(vars['x'], vars['v']),
)))))))
pass
def __init__(self, FOL: SimpleNamespace, ST: SimpleNamespace):
vars = VarBuilder()
self._formula = (FOL.Forall(vars.universal('u'),
ST.Nin(vars['u'], ST.Empty())))