Abstract

We build a confluent, local, asynchronous reduction on -terms, using infinite objects (partial injections of Girard's algebra L*), which is simple (only one move), intelligible (semantic setting of the reduction), general (based on a largescale decomposition of fi), and may be mechanized. ' Equipe de Logique Math'ematique UFR de math'ematiques Couloir 45-55, 5`eme 'etage Universit'e de Paris 7 2 place Jussieu 75251 Paris Cedex 05 FRANCE Phone: (33-1) 43 29 77 26 Introduction Captatio Benevolentiae. -calculus certainly is the simplest syntax ever developed for proof denotation & normalization in intuitionistic logic. Discovered by Church, rediscovered by Gentzen (under the guise of natural deduction), turned into a functional language by McCarthy (LISP), and nowadays clearly seen to be extendable to classical logic as well, - calculus is a fair syntax. Longing for a mathematical account of fi-reduction. Albeit the computation rule of - calculus, fi-reduction, is simple, understood...

Citations