research-article

Combining proofs and programs in a dependently typed language

Authors:

Chris Casinghino,

Vilhelm Sjöberg,

Stephanie WeirichAuthors Info & Claims

POPL '14: Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

Pages 33 - 45

https://doi.org/10.1145/2535838.2535883

Published: 08 January 2014 Publication History

Abstract

Most dependently-typed programming languages either require that all expressions terminate (e.g. Coq, Agda, and Epigram), or allow infinite loops but are inconsistent when viewed as logics (e.g. Haskell, ATS, Ωmega. Here, we combine these two approaches into a single dependently-typed core language. The language is composed of two fragments that share a common syntax and overlapping semantics: a logic that guarantees total correctness, and a call-by-value programming language that guarantees type safety but not termination. The two fragments may interact: logical expressions may be used as programs; the logic may soundly reason about potentially nonterminating programs; programs can require logical proofs as arguments; and "mobile" program values, including proofs computed at runtime, may be used as evidence by the logic. This language allows programmers to work with total and partial functions uniformly, providing a smooth path from functional programming to dependently-typed programming.

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Index Terms

Combining proofs and programs in a dependently typed language
1. Software and its engineering
  1. Software notations and tools
    1. Formal language definitions
2. Theory of computation
  1. Formal languages and automata theory

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cover image ACM Conferences

POPL '14: Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

January 2014

702 pages

ISBN:9781450325448

DOI:10.1145/2535838

General Chair:
Suresh Jagannathan
Purdue University, USA
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Program Chair:
Peter Sewell
University of Cambridge, UK

ACM SIGPLAN Notices Volume 49, Issue 1
POPL '14
January 2014
661 pages
ISSN:0362-1340
EISSN:1558-1160
DOI:10.1145/2578855
Editor:
Mark W. Bailey
Hamilton College, Clinton, NY
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Published: 08 January 2014

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https://dl.acm.org/doi/10.1145/3704253.3706135
Malewski MMaillard KTabareau NTanter É(2024)Gradual Indexed Inductive TypesProceedings of the ACM on Programming Languages10.1145/36746448:ICFP(544-572)Online publication date: 15-Aug-2024
https://dl.acm.org/doi/10.1145/3674644
SEKIYAMA TTSUKADA TIGARASHI A(2024)Signature restriction for polymorphic algebraic effectsJournal of Functional Programming10.1017/S095679682400005434Online publication date: 27-May-2024
https://doi.org/10.1017/S0956796824000054
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