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Theoretical Computer Science
A representation of Lambda terms suitable for operations on their intensions
LFP '90 Proceedings of the 1990 ACM conference on LISP and functional programming
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POPL '94 Proceedings of the 21st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Confluence properties of weak and strong calculi of explicit substitutions
Journal of the ACM (JACM)
A notation for lambda terms. A generalization of environment
Theoretical Computer Science
A Lambda-Calculus `a la de Bruijn with Explicit Substitutions
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A λ-calculus with explicit weakening and explicit substitution
Mathematical Structures in Computer Science
Journal of Functional Programming
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The aim of this paper is to give abstract properties of some calculi with explicit substitution which will be sufficient to prove their confluence. We define a property that we call ''implementing a good notion of substitution.'' We show that calculi with explicit substitution having this property are confluent and their substitution reductions are also confluent. We test our theory with the well-known calculi of explicit substitution @ls, @l@u and @lse. The latter is @ls with open terms. The property of implementing a good substitution is natural and characterizes a large number of calculi. Two conditions of this property are usually checked as an initial step in the proof for confluence. The third condition is new and is the key for our proofs of confluence.