The duality of computation

Hugo Herbelin (1) , Pierre-Louis Curien (2)

1 COQ - Formal Specifications and Program Validation
2 PPS - Preuves, Programmes et Systèmes

We present the lambda-bar-mu-mu-tilde-calculus, a syntax for lambda-calculus + control operators exhibiting symmetries such as program/context and call-by-name/call-by-value. This calculus is derived from implicational Gentzen's sequent calculus LK, a key classical logical system in proof theory. Under the Curry-Howard correspondence between proofs and programs, we can see LK, or more precisely a formulation called LK-mu-mu-tilde, as a syntax-directed system of simple types for lambda-bar-mu-mu-tilde-calculus. For lambda-bar-mu-mu-tilde-calculus, choosing a call-by-name or call-by-value discipline for reduction amounts to choosing one of the two possible symmetric orientations of a critical pair. Our analysis leads us to revisit the question of what is a natural syntax for call-by-value functional computation. We define a translation of lambda-mu-calculus into lambda-bar-mu-mu-tilde-calculus and two dual translations back to lambda-calculus, and we recover known CPS translations by composing these translations.

Mots clés: call-by-name; call-by-value; sequent calculus; CPS-translations; Curry-Howard-de Bruijn proof-as-program correspondence; duality; lambda-calculus

Domaines: Logique en informatique [cs.LO]; Langage de programmation [cs.PL]

Hugo Herbelin, Pierre-Louis Curien. The duality of computation. Fifth ACM SIGPLAN International Conference on Functional Programming : ICFP '00, Sep 2000, Montréal, Canada. pp.233-243. ⟨inria-00156377⟩