Confluence results for the pure strong categorical logic CCL. &lgr;-calculi as subsystems of CCL
Theoretical Computer Science
Confluence properties of weak and strong calculi of explicit substitutions
Journal of the ACM (JACM)
Explicit substitution on the edge of strong normalization
Theoretical Computer Science
Typed lambda-calculi with explicit substitutions may not terminate
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
On Explicit Substitution and Names (Extended Abstract)
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Lambda-Calculi with Explicit Substitutions and Composition Which Preserve Beta-Strong Normalization
ALP '96 Proceedings of the 5th International Conference on Algebraic and Logic Programming
Normalization for Typed Lambda Calculi with Explicit Substitution
CSL '93 Selected Papers from the 7th Workshop on Computer Science Logic
Confluence and Preservation of Strong Normalisation in an Explicit Substitutions Calculus
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Strong Normalization of Explicit Substitutions via Cut Elimination in Proof Nets
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Journal of Functional Programming
Characterising Strong Normalisation for Explicit Substitutions
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
On Explicit Substitution with Names
Journal of Automated Reasoning
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Contrary to all expectations, the λσ-calculus, the canonical simply-typed lambda-calculus with explicit substitutions, is not strongly normalising. This result has led to a proliferation of calculi with explicit substitutions. This paper shows that the reducibility method provides a general criterion when a calculus of explicit substitution is strongly normalising for all untyped lambda-terms that are strongly normalising. This result is general enough to imply preservation of strong normalisation of the calculi considered in the literature. We also propose a version of the λσ-calculus with explicit substitutions which is strongly normalising for strongly normalising λ-terms.