Logic programming in the LF logical framework
Logical frameworks
Constructive logics: Part I: a tutorial on proof systems and typed &lgr;-calculi
Theoretical Computer Science
Computational interpretations of linear logic
Theoretical Computer Science - Special volume of selected papers of the Sixth Workshop on the Mathematical Foundations of Programming Semantics, Kingston, Ont., Canada, May 1990
Categorical combinators, sequential algorithms, and functional programming (2nd ed.)
Categorical combinators, sequential algorithms, and functional programming (2nd ed.)
Confluence properties of weak and strong calculi of explicit substitutions
Journal of the ACM (JACM)
Functional back-ends within the lambda-sigma calculus
Proceedings of the first ACM SIGPLAN international conference on Functional programming
Basic proof theory
Permutability of proofs in intuitionistic sequent calculi
Theoretical Computer Science - Special issue: Gentzen
Terminiation of permutative conversions in intuitionistic Gentzen calculi
Theoretical Computer Science - Special issue: Gentzen
Computing in Systems Described by Equations
Computing in Systems Described by Equations
A Term Calculus for Intuitionistic Linear Logic
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
A Lambda-Calculus `a la de Bruijn with Explicit Substitutions
PLILPS '95 Proceedings of the 7th International Symposium on Programming Languages: Implementations, Logics and Programs
On the Intuitionistic Force of Classical Search (Extended Abstract)
TABLEAUX '96 Proceedings of the 5th International Workshop on Theorem Proving with Analytic Tableaux and Related Methods
A Lambda-Calculus Structure Isomorphic to Gentzen-Style Sequent Calculus Structure
CSL '94 Selected Papers from the 8th International Workshop on Computer Science Logic
LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
Higher-order Unification via Explicit Substitutions
LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
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
Pattern Matching as Cut Elimination
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Addendum to ``New Notions of Reduction and Non-Semantic Proofs of Beta Strong Normalization in Typed Lambda Calculi''''
Journal of Functional Programming
The Calculi of Lambda Conversion. (AM-6) (Annals of Mathematics Studies)
The Calculi of Lambda Conversion. (AM-6) (Annals of Mathematics Studies)
Pattern matching as cut elimination
Theoretical Computer Science
Resource operators for λ-calculus
Information and Computation
Extending the explicit substitution paradigm
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
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We introduce a method to associate calculi of proof terms and rewrite rules with cut elimination procedures for logical deduction systems (i.e., Gentzen-style sequent calculi) in the case of intuitionistic logic. We illustrate this method using two different versions of the cut rule for a variant of the intuitionistic fragment of Kleene's logical deduction system G3.Our systems are in fact calculi of explicit substitution, where the cut rule introduces an explicit substitution and the left-→ rule introduces a binding of the result of a function application. Cut propagation steps of cut elimination correspond to propagation of explicit substitutions, and propagation of weakening (to eliminate it) corresponds to propagation of index-updating operations. We prove various subject reduction, termination, and confluence properties for our calculi.Our calculi improve on some earlier calculi for logical deduction systems in a number of ways. By using de Bruijn indices, our calculi qualify as first-order term rewriting systems (TRS's), allowing us to use correctly certain results for TRS's about termination. Unlike in some other calculi, each of our calculi has only one cut rule and we do not need unusual features of sequents.We show that the substitution and index-updating mechanisms of our calculi work the same way as the substitution and index-updating mechanisms of Kamareddine and Ríos' λs and λt, two well-known systems of explicit substitution for the standard λ-calculus. By a change in the format of sequents, we obtain similar results for a known λ-calculus with variables and explicit substitutions, Rose's λbxgc.