def point(name: str) -> NamedOpetope.OCMT:
"""
The :math:`\\textbf{OptSet${}^!_m$}` :math:`\\texttt{point}` rule.
Introduces a :math:`0`-variable with name ``x``.
"""
t = NamedOpetope.Typing(NamedOpetope.Term(NamedOpetope.Variable(name, 0)),
NamedOpetope.Type([NamedOpetope.Term()]))
return NamedOpetope.OCMT(NamedOpetope.EquationalTheory(),
NamedOpetope.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)
def setUp(self):
self.term1 = NamedOpetope.Term(NamedOpetope.Variable("a", 0))
self.term2 = NamedOpetope.Term(NamedOpetope.Variable("f", 1))
self.term3 = NamedOpetope.Term(NamedOpetope.Variable("α", 2))
self.term4 = NamedOpetope.Term(NamedOpetope.Variable("A", 3))
self.typing1 = NamedOpetope.Type([NamedOpetope.Term()])
self.typing2 = NamedOpetope.Type([self.term1, NamedOpetope.Term()])
self.typing3 = NamedOpetope.Type(
[self.term2, self.term1,
NamedOpetope.Term()])
self.typing4 = NamedOpetope.Type(
[self.term3, self.term2, self.term1,
NamedOpetope.Term()])
self.ctx1 = NamedOpetope.Context()
self.ctx2 = self.ctx1 + NamedOpetope.Typing(self.term1, self.typing1)
self.ctx3 = self.ctx2 + NamedOpetope.Typing(self.term2, self.typing2)
self.ctx4 = self.ctx3 + NamedOpetope.Typing(self.term3, self.typing3)
self.ctx5 = self.ctx4 + NamedOpetope.Typing(self.term4, self.typing4)
def zero() -> NamedOpetope.OCMT:
"""
The :math:`\\textbf{OptSet${}^!$}` :math:`\\texttt{zero}` rule.
"""
return NamedOpetope.OCMT(NamedOpetope.EquationalTheory(),
NamedOpetope.Context())