The duality of computation

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The duality of computation
We review the close relationship between abstract machines for (call-by-name or call-by-value) λ-calculi (extended with Felleisen’s C) and sequent calculus, reintroducing on the way Curien-Herbelin’s syntactic kit expressing the duality of computation. We use this kit to provide a term language for a presentation of LK (with conjunction, disjunction, and negation), and to transcribe cut elimination as (non confluent) rewriting. A key slogan here, 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 tic presentation of classical logic, that provides a quotient on (focalised)...
Pierre-Louis Curien, Hugo Herbelin
Added 01 Aug 2010
Updated 01 Aug 2010
Type Conference
Year 2000
Where ICFP
Authors Pierre-Louis Curien, Hugo Herbelin
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