# The Duality of Computation under Focus

1 PI.R2 - Design, study and implementation of languages for proofs and programs
PPS - Preuves, Programmes et Systèmes, Inria Paris-Rocquencourt, UPD7 - Université Paris Diderot - Paris 7, CNRS - Centre National de la Recherche Scientifique : UMR7126
Abstract : We review the relationship between abstract machines for (call-by-name or call-by-value) λ-calculi (extended with Felleisen's $\mathcal C$) and sequent calculus, reintroducing on the way Curien-Herbelin's syntactic kit of the duality of computation. We provide a term language for a presentation of LK (with conjunction, disjunction, and negation), and we transcribe cut elimination as (non confluent) rewriting. A key slogan, which may appear here in print for the first time, is that commutative cut elimination rules are explicit substitution propagation rules. We then describe the focalised proof search discipline (in the classical setting), and narrow down the language and the rewriting rules to a confluent calculus (a variant of the second author's focalising system L). We then define a game of patterns and counterpatterns, leading us to a fully focalised finitary syntax for a synthetic presentation of classical logic, that provides a quotient on (focalised) proofs, abstracting out the order of decomposition of negative connectives.
Document type :
Conference papers

Cited literature [24 references]

https://hal.inria.fr/inria-00491236
Contributor : Hal Ifip Connect in order to contact the contributor
Submitted on : Wednesday, August 6, 2014 - 4:26:02 PM
Last modification on : Friday, January 21, 2022 - 3:21:44 AM
Long-term archiving on: : Wednesday, November 26, 2014 - 1:01:16 AM

### File

03230167.pdf
Files produced by the author(s)

### Citation

Pierre-Louis Curien, Guillaume Munch-Maccagnoni. The Duality of Computation under Focus. 6th IFIP TC 1/WG 2.2 International Conference on Theoretical Computer Science (TCS) / Held as Part of World Computer Congress (WCC), Sep 2010, Brisbane, Australia. pp.165-181, ⟨10.1007/978-3-642-15240-5_13⟩. ⟨inria-00491236v2⟩

Record views