Pl. Curien et G. Ghelli, DECIDABILITY AND CONFLUENCE OF BETA-ETA-TOP(LESS-THAN-OR-EQUAL-TO) REDUCTION IN F(LESS-THAN-OR-EQUAL-TO), Information and computation, 109(1-2), 1994, pp. 57-114
Citations number
21
Categorie Soggetti
Information Science & Library Science",Mathematics,"Computer Science Information Systems
We contribute to the syntactic study of F less-than-or-equal-to a vari
ant of second-order lambda-calculus F which appears as a paradigmatic
kernel language for polymorphism and subtyping. The type system of F l
ess-than-or-equal-to has a maximum type Top and bounded quantification
. We endow this language with the beta-rules (for terms and types), to
which we add eta-rules (for terms and types) and a rule which equates
all terms of type Top. These rules are suggested by the axiomatizatio
n of cartesian closed categories. We exhibit a weakly normalizing and
confluent reduction system for this theory betaeta top less-than-or-eq
ual-to and show that it is decidable. It is also confluent, but decida
bility does not follow from confluence, since reduction is not effecti
ve. Our proofs rely on the confluence and decidability of a correspond
ing system on F1 (the extension of F with a terminal type). (C) 1994 A
cademic Press, Inc.