A new formula for the execution of categorical combinators
Proc. of the 8th international conference on Automated deduction
Theoretical Computer Science
From λσ to λν: a journey through calculi of explicit substitutions
POPL '94 Proceedings of the 21st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Functional back-ends within the lambda-sigma calculus
Proceedings of the first ACM SIGPLAN international conference on Functional programming
Term rewriting and all that
Explicit substitution on the edge of strong normalization
Theoretical Computer Science
Higher order unification via explicit substitutions
Information and Computation
Typed lambda-calculi with explicit substitutions may not terminate
TLCA '95 Proceedings of the Second 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
TYPES '98 Selected papers from the International Workshop on Types for Proofs and Programs
Proof Nets and Explicit Substitutions
FOSSACS '00 Proceedings of the Third International Conference on Foundations of Software Science and Computation Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software,ETAPS 2000
Explicit Substitutions and Programming Languages
Proceedings of the 19th Conference on Foundations of Software Technology and Theoretical Computer Science
A Weak Calculus with Explicit Operators for Pattern Matching and Substitution
RTA '02 Proceedings of the 13th International Conference on Rewriting Techniques and Applications
Explicit Substitutions with de Bruijn's Levels
RTA '95 Proceedings of the 6th International Conference on Rewriting Techniques and Applications
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
A Lambda-Calculus Structure Isomorphic to Gentzen-Style Sequent Calculus Structure
CSL '94 Selected Papers from the 8th International Workshop on Computer Science Logic
CTRS '92 Proceedings of the Third International Workshop on Conditional Term Rewriting Systems
Uniform Normalisation beyond Orthogonality
RTA '01 Proceedings of the 12th International Conference on Rewriting Techniques and Applications
A λ-calculus with explicit weakening and explicit substitution
Mathematical Structures in Computer Science
Efficient reductions with director strings
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
A sequent calculus for type theory
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
Extending the explicit substitution paradigm
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
Perpetuality for Full and Safe Composition (in a Constructive Setting)
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
New Developments in Environment Machines
Electronic Notes in Theoretical Computer Science (ENTCS)
Jumping boxes: representing lambda-calculus boxes by jumps
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
From reduction-based to reduction-free normalization
AFP'08 Proceedings of the 6th international conference on Advanced functional programming
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Nested proof search as reduction in the Lambda-calculus
Proceedings of the 13th international ACM SIGPLAN symposium on Principles and practices of declarative programming
A prismoid framework for languages with resources
Theoretical Computer Science
Curry-Style explicit substitutions for the linear and affine lambda calculus
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
On Explicit Substitution with Names
Journal of Automated Reasoning
Deriving the full-reducing Krivine machine from the small-step operational semantics of normal order
Proceedings of the 15th Symposium on Principles and Practice of Declarative Programming
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Calculi with explicit substitutions (ES) are widely used in different areas of computer science. Complex systems with ES were developed these last 15 years to capture the good computational behaviour of the original systems (with meta-level substitutions) they were implementing. In this paper we first survey previous work in the domain by pointing out the motivations and challenges that guided the development of such calculi. Then we use very simple technology to establish a general theory of explicit substitutions for the lambda-calculus which enjoys fundamental properties such as simulation of one-step beta-reduction, confluence on metaterms, preservation of beta-strong normalisation, strong normalisation of typed terms and full composition. The calculus also admits a natural translation into Linear Logic's proof-nets.