Extracting constructive content from classical logic via control-like reductions
Recently there has been much interest in the problem of finding the computational content of classical reasoning. One of the most appealing directions for the computer scientist to tackle such a problem is the relation which has been established between classical logic and lambda calculi with control operators, like Felleisen's control operator C. In this paper we introduce a typed lambda calculus with the C operator corresponding to Peano Arithmetic, and a set of reduction rules related to the ones of the usual control calculi with C. We show how these rules, which are proved to be strongly normalizing, can be used to extract witnesses from proofs of ∑ 1 0 sentences in Peano Arithmetic.
KeywordsClassical Logic Main Branch Reduction Rule Natural Deduction Peano Arithmetic
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