def pd(ocmt: NamedOpetope.OCMT, name: str) -> NamedOpetope.Sequent:
"""
The :math:`\\textbf{OptSet${}^!_m$}` :math:`\\texttt{pd}` rule.
Introduces the trivial non degenerate pasting diagram on a given variable.
"""
var = ocmt.context[name]
t = NamedOpetope.Typing(NamedOpetope.Term(var), ocmt.context.typeOf(var))
return NamedOpetope.Sequent(deepcopy(ocmt.theory), deepcopy(ocmt.context),
t)
def degen(ocmt: NamedOpetope.OCMT, name: str) -> NamedOpetope.Sequent:
"""
The :math:`\\textbf{OptSet${}^!_m$}` :math:`\\texttt{degen}` rule.
Introduces the degenerate pasting diagram on a given variable.
"""
var = ocmt.context[name]
type = ocmt.context.typeOf(var)
t = NamedOpetope.Typing(
NamedOpetope.Term(var, True),
NamedOpetope.Type([NamedOpetope.Term(var)] + type.terms))
return NamedOpetope.Sequent(deepcopy(ocmt.theory), deepcopy(ocmt.context),
t)
def setUp(self):
self.a1 = NamedOpetope.Variable("a1", 0)
self.b1 = NamedOpetope.Variable("b1", 0)
self.c1 = NamedOpetope.Variable("c1", 0)
self.a2 = NamedOpetope.Variable("a2", 0)
self.b2 = NamedOpetope.Variable("b2", 0)
self.c2 = NamedOpetope.Variable("c2", 0)
self.f = NamedOpetope.Variable("f", 1)
self.g = NamedOpetope.Variable("g", 1)
self.h = NamedOpetope.Variable("h", 1)
self.i = NamedOpetope.Variable("h", 1)
ctx = NamedOpetope.Context() + \
NamedOpetope.Typing(
NamedOpetope.Term(self.a1),
NamedOpetope.Type([NamedOpetope.Term()])) + \
NamedOpetope.Typing(
NamedOpetope.Term(self.b1),
NamedOpetope.Type([NamedOpetope.Term()])) + \
NamedOpetope.Typing(
NamedOpetope.Term(self.c1),
NamedOpetope.Type([NamedOpetope.Term()])) + \
NamedOpetope.Typing(
NamedOpetope.Term(self.f),
NamedOpetope.Type(
[NamedOpetope.Term(self.a2),
NamedOpetope.Term()])) + \
NamedOpetope.Typing(
NamedOpetope.Term(self.g),
NamedOpetope.Type(
[NamedOpetope.Term(self.b2), NamedOpetope.Term()])) + \
NamedOpetope.Typing(
NamedOpetope.Term(self.h),
NamedOpetope.Type(
[NamedOpetope.Term(self.c2), NamedOpetope.Term()]))
eqth = NamedOpetope.EquationalTheory() + \
(self.b1, self.b2) + \
(self.c1, self.c2) + \
(self.h, self.i)
self.sequent = NamedOpetope.Sequent(eqth, ctx, None)
self.fg = self.sequent.graft(NamedOpetope.Term(self.g), self.b2,
NamedOpetope.Term(self.f))
self.gh = self.sequent.graft(NamedOpetope.Term(self.h), self.c2,
NamedOpetope.Term(self.g))
self.fgh1 = self.sequent.graft(self.gh, self.b2,
NamedOpetope.Term(self.f))
self.fgh2 = self.sequent.graft(NamedOpetope.Term(self.h), self.c2,
self.fg)
