On the Expressive Power of Schemes

04/24/2023

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by   Gilles Dowek, et al.

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We present a calculus, called the scheme-calculus, that permits to express natural deduction proofs in various theories. Unlike λ-calculus, the syntax of this calculus sticks closely to the syntax of proofs, in particular, no names are introduced for the hypotheses. We show that despite its non-determinism, some typed scheme-calculi have the same expressivity as the corresponding typed λ-calculi.