Call-by-Value Lambda-calculus and LJQ

Roy Dyckhoff (1) , Stéphane Lengrand (1, 2)

1 School of Computer Science [University of St Andrews]
2 PPS - Preuves, Programmes et Systèmes

LJQ is a focused sequent calculus for intuitionistic logic, with a simple restriction on the first premiss of the usual left introduction rule for implication. In a previous paper we discussed its history (going back to about 1950, or beyond) and presented its basic theory and some applications; here we discuss in detail its relation to call-by-value reduction in lambda calculus, establishing a connection between LJQ and the CBV calculus Lambda_C of Moggi. In particular, we present an equational correspondence between these two calculi forming a bijection between the two sets of normal terms, and allowing reductions in each to be simulated by reductions in the other.

Mots clés: lambda calculus; call-by-value; sequent calculus; continuation-passing-style; semantics

Domaines: Logique en informatique [cs.LO]

Roy Dyckhoff, Stéphane Lengrand. Call-by-Value Lambda-calculus and LJQ. 2007. ⟨hal-00150284⟩