On explicit substitutions and names (extended abstract)
Calculi with explicit substitutions have found widespread acceptance as a basis for abstract machines for functional languages. In this paper we investigate the relations between variants with de Bruijnnumbers, with variable names, with reduction based on raw expressions and calculi with equational judgements. We show the equivalence between these variants, which is crucial in establishing the correspondence between the semantics of the calculus and its implementations.
KeywordsNormal Form Free Variable Reduction Rule Abstract Machine Substitution Variable
Unable to display preview. Download preview PDF.
- 1.M. Abadi, L. Cardelli, P.-L. Curien, and J.-J. Lévy. Explicit substitutions. Journal of Functional Programming, 1(4):375–416, 1991.Google Scholar
- 2.R. Bloo and K.H. Rose. Preesrvation of strong normalisation in named lambda calculi with explicit substitution and garbage collection. In Proc. CSN'95 — Computer Science in the Netherlands, pages 62–72, 1995.Google Scholar
- 3.C. Coquand. From semantics to rules: A machine assisted analysis. In CSL'93, volume 832 of LNCS, 1994.Google Scholar
- 6.Herman Geuvers. Logics and Type Systems. PhD thesis, Univ. of Nijmegen, 1993.Google Scholar
- 8.F. Kamareddine and A. Rios. A lambda-calculus a la de bruijn with explicit substitutions. In PLILP'95, volume 982 of LNCS, 1995.Google Scholar
- 9.P. Lescanne. From λσ to λυ: a journey through calculi of explicit substitutions. POPL'94, pages 60–69, Portland, Oregon, 1994.Google Scholar
- 10.Per Martin-Löf. Intuitionistic Type Theory. Bibliopolis, Napoli, 1984.Google Scholar
- 11.P.-A. Mellies. Typed λ-calculi with explicit substitution may not terminate. TLCA'95, pages 328–334. LNCS No. 902, 1995.Google Scholar
- 12.E. Ritter and V. de Paiva. On explicit substitution and names. Technical report, Univ. of Birmingham, School of Computer Science, 1997.Google Scholar
- 13.Eike Ritter. Normalization for typed lambda calculi with explicit substitution. CSL'93, pages 295–304. LNCS No. 832, 1994.Google Scholar
- 14.Thomas Streicher. Correctness and Completeness of a Categorical Semantics of the Calculus of Constructions. PhD thesis, Universität Passau, June 1989.Google Scholar
- 15.A. Tasistro. Formulation of Martin-Löf's theory types with explicit substitutions. Licenciate Thesis, Chalmers University, Dept. of Computer Science, May 1993.Google Scholar