Introduction to higher order categorical logic
Introduction to higher order categorical logic
Introduction to combinators and &lgr;-calculus
Introduction to combinators and &lgr;-calculus
Proof of termination of the rewriting system SUBST on CCL
Theoretical Computer Science
The categorical abstract machine
Science of Computer Programming
Church-Rosser theorem for a rewriting system on categorical combinators
Theoretical Computer Science
Confluence results for the pure strong categorical logic CCL. &lgr;-calculi as subsystems of CCL
Theoretical Computer Science
On laziness and optimality in lambda interpreters: tools for specification and analysis
POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
An algorithm for optimal lambda calculus reduction
POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Optimal derivations in weak lambda-calculi and in orthogonal term rewriting systems
POPL '91 Proceedings of the 18th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
An abstract frame work for environment machines
Theoretical Computer Science
Lambda-calculi for (strict) parallel functions
Information and Computation
Minimal and Optimal Computations of Recursive Programs
Journal of the ACM (JACM)
Strong Normalization of Substitutions
MFCS '92 Proceedings of the 17th International Symposium on Mathematical Foundations of Computer Science
Layer sharing: an improved structure-sharing framework
POPL '93 Proceedings of the 20th 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
A Polymorphic Environment Calculus and its Type-Inference Algorithm
Higher-Order and Symbolic Computation
Proof-term synthesis on dependent-type systems via explicit substitutions
Theoretical Computer Science
External Rewriting for Skeptical Proof Assistants
Journal of Automated Reasoning
Binding Logic: Proofs and Models
LPAR '02 Proceedings of the 9th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Characterising Explicit Substitutions which Preserve Termination
TLCA '99 Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications
Programming and Computing in HOL
TPHOLs '00 Proceedings of the 13th International Conference on Theorem Proving in Higher Order Logics
TYPES '98 Selected papers from the International Workshop on Types for Proofs and Programs
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
A Framework for Defining Object-Calculi
FM '99 Proceedings of the Wold Congress on Formal Methods in the Development of Computing Systems-Volume II
Closed Reductions in the lambda-Calculus
CSL '99 Proceedings of the 13th International Workshop and 8th Annual Conference of the EACSL on Computer Science Logic
Higher-order unification and matching
Handbook of automated reasoning
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
Journal of Automated Reasoning
Reductions, intersection types, and explicit substitutions
Mathematical Structures in Computer Science
HOL-λσ: an intentional first-order expression of higher-order logic
Mathematical Structures in Computer Science
Dependent types and explicit substitutions: a meta-theoretical development
Mathematical Structures in Computer Science
Cut rules and explicit substitutions
Mathematical Structures in Computer Science
An environment machine for the λμ-calculus
Mathematical Structures in Computer Science
Journal of Functional Programming
Functional runtime systems within the lambda-sigma calculus
Journal of Functional Programming
Journal of Functional Programming
A syntactic correspondence between context-sensitive calculi and abstract machines
Theoretical Computer Science
A ρ-calculus of explicit constraint application
Higher-Order and Symbolic Computation
A concrete framework for environment machines
ACM Transactions on Computational Logic (TOCL)
Explaining the lazy Krivine machine using explicit substitution and addresses
Higher-Order and Symbolic Computation
Strongly reducing variants of the Krivine abstract machine
Higher-Order and Symbolic Computation
Inter-deriving Semantic Artifacts for Object-Oriented Programming
WoLLIC '08 Proceedings of the 15th international workshop on Logic, Language, Information and Computation
Encoding the Pure Lambda Calculus into Hierarchical Graph Rewriting
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Sequent calculi and abstract machines
ACM Transactions on Programming Languages and Systems (TOPLAS)
Abstract Conditions for the Confluence of Explicit Substitution Calculi
Electronic Notes in Theoretical Computer Science (ENTCS)
Reductions, intersection types, and explicit substitutions
TLCA'01 Proceedings of the 5th international conference on Typed lambda calculi and applications
Efficient reductions with director strings
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
A finite first-order presentation of set theory
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
Confluence of pattern-based calculi
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
Inter-deriving semantic artifacts for object-oriented programming
Journal of Computer and System Sciences
Sharing in the weak lambda-calculus
Processes, Terms and Cycles
On Explicit Substitution with Names
Journal of Automated Reasoning
Strong reduction for typed lambda calculus with first-class environments
ICICA'12 Proceedings of the Third international conference on Information Computing and Applications
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Categorical combinators [Curien 1986/1993; Hardin 1989; Yokouchi 1989] and more recently &lgr;&sgr;-calculus [Abadi 1991; Hardin and Le´vy 1989], have been introduced to provide an explicit treatment of substitutions in the &lgr;-calculus. We reintroduce here the ingredients of these calculi in a self-contained and stepwise way, with a special emphasis on confluence properties. The main new results of the paper with respect to Curien [1986/1993], Hardin [1989], Abadi [1991], and Hardin and Le´vy [1989] are the following:(1) We present a confluent weak calculus of substitutions, where no variable clashes can be feared;(2) We solve a conjecture raised in Abadi [1991]: &lgr;&sgr;-calculus is not confluent (it is confluent on ground terms only).This unfortunate result is “repaired” by presenting a confluent version of &lgr;&sgr;-calculus, named the &lgr;Env-caldulus in Hardin and Le´vy [1989], called here the confluent &lgr;&sgr;-calculus.