def add_common_objects(self):
self.a = common_vars.a()
self.b = common_vars.b()
self.c = common_vars.c()
self.d = common_vars.d()
self.e = common_vars.e()
self.b_of_a = formula.Always(formula.Holds(self.a, self.b))
self.a_of_b = formula.Always(formula.Holds(self.b, self.a))
self.a_of_a = formula.Always(formula.Holds(self.a, self.a))
self.b_of_c = formula.Always(formula.Holds(self.c, self.b))
self.d_of_c = formula.Always(formula.Holds(self.c, self.d))
self.e_of_e = formula.Always(formula.Holds(self.e, self.e))
self.and_b_of_a_functor = endofunctor.And(side=endofunctor.left,
other=self.b_of_a)
self.b_of_a_and_functor = endofunctor.And(side=endofunctor.right,
other=self.b_of_a)
self.or_d_of_c_functor = endofunctor.Or(side=endofunctor.left,
other=self.d_of_c)
self.d_of_c_or_functor = endofunctor.Or(side=endofunctor.right,
other=self.d_of_c)
self.exists_a_functor = endofunctor.Exists(variable=self.a)
self.exists_b_functor = endofunctor.Exists(variable=self.b)
self.exists_c_functor = endofunctor.Exists(variable=self.c)
self.exists_d_functor = endofunctor.Exists(variable=self.d)
self.not_not_functor = endofunctor.not_functor.compose(endofunctor.not_functor)
self.equivalence = variable.StringVariable('equiv')
def add_common_objects(self):
self.a = common_vars.a()
self.b = common_vars.b()
self.c = common_vars.c()
self.d = common_vars.d()
self.e = common_vars.e()
self.A = constructors.Always(constructors.Holds(self.a, self.a))
self.B = constructors.Always(constructors.Holds(self.b, self.b))
self.W = constructors.Always(constructors.Holds(self.a, self.b))
self.X = constructors.Always(constructors.Holds(self.a, self.c))
self.Y = constructors.Always(constructors.Holds(self.a, self.d))
self.Z = constructors.Always(constructors.Holds(self.a, self.e))
self.a_in_domain_b = constructors.Always(constructors.Holds(self.a,
variable.ApplySymbolVariable(self.b, common_symbols.domainSymbol)))
self.and_W = endofunctor.And(values = [self.W], index = 0)
self.W_and = endofunctor.And(values = [self.W], index = 1)
self.X_and_and_Y = endofunctor.And(values = [self.X, self.Y], index = 1)
self.W_and_X = constructors.And([self.W, self.X])
self.X_and_Y_and_Z = constructors.Always(constructors.And([self.X, self.Y, self.Z]))
self.W_AND_X_and_Y_and_Z = constructors.And([self.W, self.X_and_Y_and_Z])
self.exists_a_in_domain_b_X_and_Y_and_Z = constructors.Exists(
[constructors.BoundedVariableBinding(self.a, self.b)], self.X_and_Y_and_Z)
self.exists_wd_a_in_domain_b_X_and_Y_and_Z = constructors.Exists(
[constructors.WelldefinedVariableBinding(self.a, self.b)], self.X_and_Y_and_Z)
self.exists_d = endofunctor.Exists([constructors.OrdinaryVariableBinding(self.d)])
self.exists_e = endofunctor.Exists([constructors.OrdinaryVariableBinding(self.e)])
self.exists_d_e = endofunctor.Exists([ constructors.OrdinaryVariableBinding(self.d)
, constructors.OrdinaryVariableBinding(self.e)])
def Plus(a, b):
return variable.ApplySymbolVariable(
variable.ProductVariable([(common_symbols.leftSymbol, a), (common_symbols.rightSymbol, b)]), plus
)
def ExpandPlus(a, b, c):
base = And([Equal(natural.zero, a), Equal(b, c)])
z = common_vars.z()
step = ExistsNatural([z], And([Equal(S(z), a), Equal(S(Plus(z, b)), c)]))
return Or([base, step])
a = common_vars.a()
b = common_vars.b()
c = common_vars.c()
define_plus = Always(ForallNatural([a, b, c], Iff(left=Equal(Plus(a, b), c), right=ExpandPlus(a, b, c))))
a = common_vars.a()
b = common_vars.b()
plus_natural = Always(ForallNatural([a, b], natural.Natural(Plus(a, b))))
# define multiplication
times = variable.StringVariable("*", infix=(common_symbols.leftSymbol, common_symbols.rightSymbol))
def Times(a, b):
return variable.ApplySymbolVariable(
variable.ProductVariable([(common_symbols.leftSymbol, a), (common_symbols.rightSymbol, b)]), times
)