Proof nets and the call-by-value λ-calculus

Beniamino Accattoli (1, 2)

1 PARSIFAL - Proof search and reasoning with logic specifications
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

This paper gives a detailed account of the relationship between (a variant of) the call-by-value lambda calculus and linear logic proof nets. The presentation is carefully tuned in order to realize an isomorphism between the two systems: every single rewriting step on the calculus maps to a single step on proof nets, and viceversa. In this way, we obtain an algebraic reformulation of proof nets. Moreover, we provide a simple correctness criterion for our proof nets, which employ boxes in an unusual way, and identify a subcalculus that is shown to be as expressive as the full calculus.

Mots clés: linear logic; graphical syntaxes; proof nets; explicit substitutions; correctness criteria; Curry-Howard isomorphism; call-by-value λ-calculus

Domaines: Logique en informatique [cs.LO]

Beniamino Accattoli. Proof nets and the call-by-value λ-calculus. Theoretical Computer Science, 2015, ⟨10.1016/j.tcs.2015.08.006⟩. ⟨hal-01244842⟩