Proofs as Description of Computation

A proof of ∀x∃yϕ(x,y) can serve as a description of an algorithm which satisfies the specification given by ϕ. A variety of techniques from proof theory may be used to execute such a proof — that is, to take the proof and a value for x, and compute a value for y such that ϕ(x,y) holds. Proofs differ from ordinary programs in that they formalize information about algorithms beyond what is needed for the simple execution of the algorithm. This paper concerns (I) the uses of this additional information in the automatic transformation of algorithms, and in particular, in the adaptation of algorithms to special situations, and (2) efficient methods for executing and transforming proofs. A system for manipulating proofs has been implemented. Results of experiments on the specialization of a bin-packing algorithm are described.

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