Contextual Natural Deduction
نویسنده
چکیده
This paper defines the contextual natural deduction calculus ND for the implicational fragment of intuitionistic logic. ND extends the usual natural deduction calculus (here called ND) by allowing the implication introduction and elimination rules to operate on formulas that occur inside contexts. In analogy to the Curry-Howard isomorphism between ND and the simply-typed λ-calculus, an extension of the λcalculus, here called λ-calculus, is defined in order to provide compact proof-terms for ND proofs. Soundness and completeness of ND with respect to ND are proven by defining translations of proofs between these calculi. Furthermore, some ND-proofs are shown to be quadratically smaller than the smallest ND-proofs of the same theorems.
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