Recursion from Iteration (1994)
| Venue: | Lisp and Symbolic Computation |
| Citations: | 10 - 0 self |
BibTeX
@INPROCEEDINGS{Filinski94recursionfrom,
author = {Andrzej Filinski},
title = {Recursion from Iteration},
booktitle = {Lisp and Symbolic Computation},
year = {1994},
pages = {11--38}
}
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Abstract
. In a simply-typed, call-by-value (CBV) language with first-class continuations, the usual CBV fixpoint operator can be defined in terms of a simple, infinitelylooping iteration primitive. We first consider a natural but flawed definition, based on exceptions and "iterative deepening" of finite unfoldings, and point out some of its shortcomings. Then we present the proper construction using full first-class continuations, with both an informal derivation and a proof that the behavior of the defined operator faithfully mimics a "built-in" recursion primitive. In fact, given an additional uniformity assumption, the construction is a two-sided inverse of the usual definition of iteration from recursion. Continuing, we show that the CBV looping primitive is in fact the direct-style equivalent of a continuation-passing-style fixpoint, and that this correspondence extends all the way to traditional definitions of these operators in terms of reflexive types. 1. Introduction 1.1. Background ...
