The categorical abstract machine
Proc. of a conference on Functional programming languages and computer architecture
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
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
The geometry of optimal lambda reduction
POPL '92 Proceedings of the 19th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A natural semantics for lazy evaluation
POPL '93 Proceedings of the 20th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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
Confluence properties of weak and strong calculi of explicit substitutions
Journal of the ACM (JACM)
Analysis and caching of dependencies
Proceedings of the first ACM SIGPLAN international conference on Functional programming
Escape analysis: correctness proof, implementation and experimental results
POPL '98 Proceedings of the 25th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Combinatory weak reduction in lambda calculus
Theoretical Computer Science
Minimal and Optimal Computations of Recursive Programs
Journal of the ACM (JACM)
Categorical Combinators, Sequential Algorithms and Funtional Programming
Categorical Combinators, Sequential Algorithms and Funtional Programming
Typed lambda-calculi with explicit substitutions may not terminate
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Combinatory Reduction Systems with Explicit Substitution that Preserve Strong Nomalisation
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
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
Functional runtime systems within the lambda-sigma calculus
Journal of Functional Programming
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
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Extending the explicit substitution paradigm
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
Sharing in the weak lambda-calculus
Processes, Terms and Cycles
The theory of calculi with explicit substitutions revisited
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
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The λ-calculus has been much used to study the theory of substitution in logical systems and programming languages. However, with explicit substitutions, it is possible to get finer properties with respect to gradual implementations of substitutions as effectively done in runtimes of programming languages. But the theory of explicit substitutions has some defects such as non-confluence or the nontermination of the typed case. In this paper, we stress on the sub-theory of weak substitutions, which is sufficient to analyze most of the properties of programming languages, and which preserves many of the nice theorems of the λ-calculus.