o

gapt.proofs.lk.transformations

makeTheoryAxiomsExplicit

object makeTheoryAxiomsExplicit

Given a list of formulas Π, this transforms a proof π of Σ :- Δ into a proof π' of Π, Σ :- Δ.

It replaces theory axioms on sequents S that are subsumed by Π with propositional proofs of Π, S.

Source
makeTheoryAxiomsExplicit.scala
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  4. def apply(proof: LKProof)(implicit ctx: Context): LKProof
  5. def apply(formulas: Formula*)(proof: LKProof): LKProof

    Eliminates some theory axioms from proof, namely those subsumed by formulas.

    Eliminates some theory axioms from proof, namely those subsumed by formulas.

    formulas

    A list of Formulas. Each must be of the form ∀x1 ... ∀xn F' with F' quantifier-free.

    proof

    An LKProof.

    returns

    An LKProof proof' with the following properties: Every theory axiom in proof that is subsumed by formulas is removed in proof' and elements of formula may occur in the antecedent of the end sequent of proof'.

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  22. def withSequentConnector(formulas: Formula*)(proof: LKProof): (LKProof, SequentConnector)

    Eliminates some theory axioms from proof, namely those subsumed by formulas.

    Eliminates some theory axioms from proof, namely those subsumed by formulas.

    formulas

    A list of Formulas. Each must be of the form ∀x1 ... ∀xn F' with F' quantifier-free.

    proof

    An LKProof.

    returns

    A pair (proof', conn) with the following properties: Every theory axiom in proof that is subsumed by formulas is removed in proof' and elements of formulas may occur in the antecedent of the end sequent of proof'; conn is an SequentConnector relating proof and proof'.

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