Factorization and Normalization, Essentially

Beniamino Accattoli, Claudia Faggian, Giulio Guerrieri

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

λ-calculi come with no fixed evaluation strategy. Different strategies may then be considered, and it is important that they satisfy some abstract rewriting property, such as factorization or normalization theorems. In this paper we provide simple proof techniques for these theorems. Our starting point is a revisitation of Takahashi’s technique to prove factorization for head reduction. Our technique is both simpler and more powerful, as it works in cases where Takahashi’s does not. We then pair factorization with two other abstract properties, defining essential systems, and show that normalization follows. Concretely, we apply the technique to four case studies, two classic ones, head and the leftmost-outermost reductions, and two less classic ones, non-deterministic weak call-by-value and least-level reductions.
Original languageEnglish
Title of host publicationAPLAS 2019: Programming Languages and Systems
PublisherSpringer Verlag
Pages159–180
Number of pages22
ISBN (Electronic)9783030341756
ISBN (Print)9783030341749
DOIs
Publication statusPublished - 31 Dec 2019

Publication series

NameLecture Notes in Computer Science
Volume11893
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Projects

Cite this

Accattoli, B., Faggian, C., & Guerrieri, G. (2019). Factorization and Normalization, Essentially. In APLAS 2019: Programming Languages and Systems (pp. 159–180). (Lecture Notes in Computer Science; Vol. 11893). Springer Verlag. https://doi.org/10.1007/978-3-030-34175-6_9