Evidenced Frames: A Unifying Framework Broadening Realizability Models

Liron Cohen, Etienne Miquey, Ross Tate

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Constructive foundations have for decades been built upon realizability models for higher-order logic and type theory. However, traditional realizability models have a rather limited notion of computation, which only supports non-termination and avoids many other commonly used effects. Work to address these limitations has typically overlaid structure on top of existing models, such as by using powersets to represent non-determinism, but kept the realizers themselves deterministic. This paper alternatively addresses these limitations by making the structure underlying realizability models more flexible. To this end, we introduce evidenced frames: a general-purpose framework for building realizability models that support diverse effectful computations. We demonstrate that this flexibility permits models wherein the realizers themselves can be effectful, such as λ-terms that can manipulate state, reduce non-deterministically, or fail entirely. Beyond the broader notions of computation, we demonstrate that evidenced frames form a unifying framework for (realizability) models of higher-order dependent predicate logic. In particular, we prove that evidenced frames are complete with respect to these models, and that the existing completeness construction for implicative algebras - another foundational framework for realizability - factors through our simpler construction. As such, we conclude that evidenced frames offer an ideal domain for unifying and broadening realizability models.

Original languageEnglish
Title of host publication2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2021
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781665448956
DOIs
StatePublished - 29 Jun 2021
Event36th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2021 - Virtual, Online
Duration: 29 Jun 20212 Jul 2021

Publication series

NameProceedings - Symposium on Logic in Computer Science
Volume2021-June
ISSN (Print)1043-6871

Conference

Conference36th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2021
CityVirtual, Online
Period29/06/212/07/21

ASJC Scopus subject areas

  • Software
  • Mathematics (all)

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