o

gapt.proofs.nd

friedman

object friedman

Source
transformation.scala
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  1. final def !=(arg0: Any): Boolean
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  2. final def ##(): Int
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  4. 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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  9. 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

  10. def frAux(formula: Formula, a: Formula): NDProof

    Creates a proof of the sequent a :- fr(formula, a).

  11. final def getClass(): Class[_]
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    Deprecated

    (Since version ) see corresponding Javadoc for more information.

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