86 lines
2.0 KiB
Python
86 lines
2.0 KiB
Python
"""
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This module hosts propositions.
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"""
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from __future__ import annotations
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from .terms import Term
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from dataclasses import dataclass
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class Prop:
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"""
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A proposition is a logical statement. It can be proven by the proof
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checker, or it can be used as a hypothesis to prove another
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proposition.
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"""
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def as_assumption(self, goal : Prop) -> list[list[tuple[list[Prop], Prop]]]:
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"""
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Propositions can simplify the proof by creating simpler theorems
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and sub-lemmas to prove instead. If this proposition is part of
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the assumptions, this function helps transform the goal into
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simpler sub-goals.
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:return: Tuples of added assumptions with a new goal.
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:rtype: list[list[tuple[list[Prop], Prop]]]
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"""
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return []
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def as_proof(self) -> list[list[tuple[list[Prop], Prop]]]:
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"""
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Determine which hypotheses are required in the context to prove
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this proposition.
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The function returns a list of various methods to prove the
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proposition. If any of the methods is an empty list, it means
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the proposition requires no assumptions and can instead be
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computed.
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:return: Methods to prove this proposition.
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:rtype: list[tuple[list[Prop], Prop]]
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"""
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return []
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@dataclass(frozen=True)
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class And(Prop):
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"""
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The logical and-operator `P ^ Q`.
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"""
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P : Prop
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Q : Prop
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class Eq(Prop):
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"""
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Compare whether two terms are equal.
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"""
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x : Term
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y : Term
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def as_assumption(self, goal: Prop) -> list[list[tuple[list[Prop], Prop]]]:
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return []
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def as_proof(self) -> list[list[tuple[list[Prop], Prop]]]:
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return super().as_proof()
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@dataclass(frozen=True)
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class Implies(Prop):
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"""
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The logical operator `P -> Q`.
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"""
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P : Prop
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Q : Prop
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@dataclass(frozen=True)
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class Or(Prop):
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"""
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The logical and-operator `P v Q`.
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"""
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P : Prop
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Q : Prop
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