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On the Expressive Power of Schemes (2304.11892v1)
Published 24 Apr 2023 in cs.LO
Abstract: We present a calculus, called the scheme-calculus, that permits to express natural deduction proofs in various theories. Unlike $\lambda$-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 $\lambda$-calculi.