Recursion versus iteration at higher-orders

Abstract

We extend the well-known analysis of recursion-removal in first-order program schemes to a higher-order language of finitely typed and polymorphically typed functional programs, the semantics of which is based on call-by-name parameter-passing. We introduce methods for recursion-removal, i.e. for translating higher-order recursive programs into higher-order iterative programs, and determine conditions under which this translation is possible. Just as finitely typed recursive programs are naturally classified by their orders, so are finitely typed iterative programs. This syntactic classification of recursive and iterative programs corresponds to a semantic (or computational) classification: the higher the order of programs, the more functions they can compute.KeywordsFinite TypeFunction DefinitionFunctional ProgramRecursive ProcedureGround TypeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.