A Proof-Theoretic Account of Primitive Recursion and Primitive Iteration

Luca Chiarabini, Olivier Danvy


We revisit both the usual ``going-up'' induction principle and Manna and Waldinger's ``going-down'' induction principle for primitive recursion,`a la Goedel, and primitive iteration, `a la Church. We use 'Kleene's trick' to show that primitive recursion and primitive iiteration are as expressive as the other, even in the presence of accumulators. As a result, we can directly extract a variety of recursive and iterative functional programs of the kind usually written or optimized by hand.

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DOI: 10.6092/issn.1972-5787/2225

Copyright (c) 2011 Luca Chiarabini, Olivier Danvy

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