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Journal of Logic and Computation Advance Access originally published online on September 21, 2007
Journal of Logic and Computation 2007 17(6):1109-1134; doi:10.1093/logcom/exm037
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© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Articles

Call-by-Value {lambda}-calculus and LJQ

Roy Dyckhoff and Stéphane Lengrand

School of Computer Science, University of St Andrews, St Andrews, Fife, KY16 9SX, Scotland.

E-mail: rd{at}dcs.st-and.ac.uk, sl{at}dcs.st-and.ac.uk

Received 29 October 2006.


  Abstract

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.

Keywords: Lambda calculus; call-by-value; sequent calculus; continuation-passing; semantics


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