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Towards Concurrent Type Theory (2012)

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by Luís Caires , Frank Pfenning , Bernardo Toninho
Venue:INVITED TALK AT TLDI’12
Citations:7 - 6 self
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BibTeX

@MISC{Caires12towardsconcurrent,
    author = {Luís Caires and Frank Pfenning and Bernardo Toninho},
    title = { Towards Concurrent Type Theory},
    year = {2012}
}

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Abstract

We review progress in a recent line of research that provides a concurrent computational interpretation of (intuitionistic) linear logic. Propositions are interpreted as session types, sequent proofs as processes in the π-calculus, cut reductions as process reductions, and vice versa. The strong proof-theoretic foundation of this type system provides immediate opportunities for uniform generalization, specifically, to embed terms from a functional type theory. The resulting system satisfies the properties of type preservation, progress, and termination, as expected from a language derived via a Curry-Howard isomorphism. While very expressive, the language is strictly stratified so that dependent types for functional terms can be enforced during communication, but neither processes nor channels can appear in functional terms. We briefly speculate on how this limitation might be overcome to arrive at a fully dependent concurrent type theory.

Citations

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290 Functions as processes - Milner - 1992
272 Computational interpretations of linear logic - Abramsky - 1993
184 Combinatory Logic - Curry, Feys - 1958
162 Language primitives and type disciplines for structured communication-based programming - Honda, Vasconcelos, et al. - 1998
80 On asynchrony in name-passing calculi - Merro, Sangiorgi - 1998
76 Constable et al. Implementing Mathematics with the Nuprl Proof Development System - L - 1986
70 Types for dyadic interaction - Honda - 1993
63 Some properties of conversion - Church, Rosser
40 A judgmental analysis of linear logic - Chang, Chaudhuri, et al. - 2003
34 Linear Type Theories, Semantics and Action Calculi - Barber - 1997
16 Propositions as [types - Awodey, Bauer
15 dialogue games and PCF - Pi-calculus - 1995
12 A linear logic of affirmation and knowledge - Garg, Bauer, et al. - 2006
11 logic. Theoretical Computer Science, 50:1–102 - Linear - 1987
7 The formulae-as-types notion of construction. Unpublished note. An annotated version appeared in - Howard - 1980
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