Implement substitution
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ir.py
80
ir.py
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@ -1,6 +1,24 @@
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from dataclasses import dataclass
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from typing import Sequence, TypeAlias
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@dataclass(frozen=True)
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class Subst:
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"""
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A substitution which may be performed on a term.
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Only variables may be substituted, but they may be substituted with any term. That
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is, `x1/Chris` is valid, but `Chris/x1` is not.
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It is strongly recommended to avoid recursive substitutions, that is, substitutions
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which contain the variable they are replacing
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"""
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variable: str
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replacement: 'IRTerm'
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def __str__(self) -> str:
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return repr(self)
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def __repr__(self) -> str:
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return f'{self.variable}/{self.replacement}'
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@dataclass(frozen=True)
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class IRProp:
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"""
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@ -10,12 +28,32 @@ class IRProp:
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distinction is made between predicates (n-arity, logical statements), functions
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(positive-arity functions over objects), and constants (stand-ins for objects)
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"""
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name: str
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"""
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The identifier of this thing, including its location in the source
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"""
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arguments: 'Sequence[IRTerm]'
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arguments: 'Sequence[IRTerm]' = tuple()
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def subst(self, subst: Subst) -> 'IRTerm':
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"""
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Perform substitution on a proposition
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Returns the same proposition, but with any instances of the variable named in the
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substitution replaced with the contents of the substitution.
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>>> original = IRProp('angry', (IRVar('x1'),))
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>>> original
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angry(*x1)
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>>> original.subst(Subst('x1', IRProp('Alex')))
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angry(Alex())
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"""
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return IRProp(self.name, [arg.subst(subst) for arg in self.arguments])
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def __str__(self) -> str:
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return repr(self)
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def __repr__(self) -> str:
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return f'{self.name}({",".join(str(arg) for arg in self.arguments)})'
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@dataclass(frozen=True)
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@ -24,7 +62,26 @@ class IRVar:
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A variable which may be substituted for any other term
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"""
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name: str
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def subst(self, subst: Subst) -> 'IRTerm':
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"""
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Perform substitution on a proposition
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Returns the same proposition, but with any instances of the variable named in the
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substitution replaced with the contents of the substitution.
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>>> IRVar('x1').subst(Subst('x1', IRProp('Alex')))
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Alex()
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>>> IRVar('x1').subst(Subst('x2', IRProp('Alex')))
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*x1
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"""
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if self.name == subst.variable:
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return subst.replacement
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else:
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return self
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def __str__(self) -> str:
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return repr(self)
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def __repr__(self) -> str:
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return f'*{self.name}'
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@dataclass(frozen=True)
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@ -33,7 +90,28 @@ class IRNeg:
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A negated proposition
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"""
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inner: 'IRTerm'
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def subst(self, subst: Subst) -> 'IRTerm':
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"""
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Perform substitution on a proposition
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Returns the same proposition, but with any instances of the variable named in the
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substitution replaced with the contents of the substitution.
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>>> original = IRNeg(IRProp('happy', [IRVar('x1')]))
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>>> original
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¬happy(*x1)
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>>> original.subst(Subst('x1', IRProp('parent', [IRProp('Susie')])))
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¬happy(parent(Susie()))
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"""
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return IRNeg(self.inner.subst(subst))
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def __str__(self) -> str:
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return repr(self)
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def __repr__(self) -> str:
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return f'¬{self.inner}'
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IRTerm: TypeAlias = IRVar | IRProp | IRNeg
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if __name__ == '__main__':
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import doctest
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doctest.testmod()
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