object friedman
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- transformation.scala
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def
apply(proof: NDProof, a: Formula): NDProof
Applies the Friedman proof transformation for a formula A to a given intuitionistic natural deduction proof.
Applies the Friedman proof transformation for a formula A to a given intuitionistic natural deduction proof.
The conclusion of the resulting proof is the Friedman translation fr applied to the original conclusion.
- proof
A proof in ND for a sequent Γ :- A, without applications of the excluded middle rule
- a
The formula that we instantiate the Friedman translation with
- returns
A proof in ND for the sequent fr(Γ, a) :- fr(A, a)
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def
fr(formula: Expr, a: Formula): Formula
Applies the Friedman translation fr for a given formula a to a formula.
Applies the Friedman translation fr for a given formula a to a formula.
This function replaces every atom occurring in the formula by a disjunction formed by the atom and the formula a. The case of the negation is explained by treating ¬A as an abbreviation for A→⊥ The Bottom and Top cases are explained by observing that ⊥∨A and ⊤∨A or equivalent to A and ⊤ respectively.
- formula
input formula for the function fr
- a
formula that is disjunctively added to the atoms of the input formula
- returns
result of applying fr for a to the input formula
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def
frAux(formula: Formula, a: Formula): NDProof
Creates a proof of the sequent
a :- fr(formula, a)
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This is the API documentation for GAPT.
The main package is gapt.