Year: 2020
Type: preprint
Abstract: Factorization -- a simple form of standardization -- is concerned with reduction strategies, i.e. how a result is computed. We present a new technique for proving factorization theorems for compound rewriting systems in a modular way, which is inspired by the Hindley-Rosen technique for confluence. Specifically, our technique is well adapted to deal with extensions of the call-by-name and call-by-value lambda-calculi. The technique is first developed abstractly. We isolate a sufficient condition (called linear swap) for lifting factorization from components to the compound system, and which is compatible with beta-reduction. We then closely analyze some common factorization schemas for the lambda-calculus. Concretely, we apply our technique to diverse extensions of the lambda-calculus, among which de' Liguoro and Piperno's non-deterministic lambda-calculus and -- for call-by-value -- Carraro and Guerrieri's shuffling calculus. For both calculi the literature contains factorization theorems. In both cases, we give a new proof which is neat, simpler than the original, and strikingly shorter.
Source: arXiv (Cornell University)
Institutions: Institut national de recherche en sciences et technologies du numérique, École Polytechnique, Laboratoire d'Informatique de l'École Polytechnique, Centre National de la Recherche Scientifique, Université Paris Cité, Institut de Recherche en Informatique Fondamentale, University of Bath
Language: English
Subfield: Software
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3021989208