An abstract property of confluence applied to the study of the lazy partial lambda calculus
The partial λ-calculus, introduced by E. Moggi, is a formalism well adapted to study the logic of programs in which the evaluation mechanism is call-by-value. In this paper we consider a lazy version of the partial λ-calculus. The main result is the Church-Rosser property for the class of strongly normalizable terms. First, we find sufficient conditions for confluence in an abstract framework. Then, we prove that our calculus satisfies those conditions.
Unable to display preview. Download preview PDF.
- Barendregt, H. (1984), “The Lambda Calculus: Its Syntax and Semantics”. North-Holland. Amsterdam. 1984.Google Scholar
- Huet, G. (1980), Confluent Reductions: Abstract properties and application to term rewrite systems. Journal of ACM. vol. 27 no 4, pp797–821. 1980.Google Scholar
- Moggi, E. (1988), The Partial Lambda Calculus, Ph.D. Thesis, University of Edinburgh.Google Scholar
- Pino Pérez, R. (1991), A Strict Partial Combinatory Algebra Based on Lambda Terms. In “Proceedings of the Symposium Mathematical Foundations of Computer Science' 91”. September 9–13, 1991. Kazimierz Dolny, Poland. Lecture Notes in Computer Science. Vol. 520. Springer-Verlag. Berlin. 1991Google Scholar
- Pino Pérez, R. (1992), Contribution à l'étude du Lambda Calcul Partiel, Ph.D. Thesis, University of Paris VII.Google Scholar
- Plotkin, G. (1975), Call-by-name, call-by-value and the λ-calculus. Theoretical Computer Science (1), 1975.Google Scholar
- Sethi, R. (1974), Testing for Church-Rosser Property. Journal of ACM. vol. 21, pp797–821. 1974.Google Scholar