A Proof-Theoretic Account of Primitive Recursion and Primitive Iteration
AbstractWe 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.
How to Cite
Chiarabini, L., & Danvy, O. (2011). A Proof-Theoretic Account of Primitive Recursion and Primitive Iteration. Journal of Formalized Reasoning, 4(1), 85-109. https://doi.org/10.6092/issn.1972-5787/2225
Copyright (c) 2011 Luca Chiarabini, Olivier Danvy
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