Book ChapterDOI
Strong Normalization of Substitutions
Pierre-Louis Curien,Thérèse Hardin,Alejandro Ríos +2 more
- pp 209-217
TLDR
The strong normalization of its subcalculus σ which computes substitutions is proved, which proves that λσ-calculus is an extended λ-Calculus where substitutions are handled explicity.Abstract:
λσ-calculus is an extended λ-calculus where substitutions are handled explicity. We prove the strong normalization of its subcalculus σ which computes substitutions.read more
Citations
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Book
Advanced Topics in Term Rewriting
TL;DR: In this paper, the so-called confluence and termination hierarchies play a key role, and it is shown that for every implication X = Y in the hierarchies, the property X is undecidable for all term rewriting systems satisfying Y.
Journal ArticleDOI
Termination of term rewriting
TL;DR: Termination is proved to be persistent for the class of term rewriting systems for which not both duplicating rules and collapsing rules occur, generalizing a similar result of Rusinowitch for modularity.
Journal ArticleDOI
Termination Of Term Rewriting By Semantic Labelling
TL;DR: A new kind of transformation of term rewriting systems (TRS) is proposed, depending on a choice for a model for the TRS, which provides a new technique for proving termination, making classical techniques like path orders and polynomial interpretations applicable even for non-simplifying TRS’s.
Termination of term rewriting by semantic labelling
TL;DR: In this article, a new kind of transformation of term rewriting systems (TRS) is proposed, depending on a choice for a model for the TRS, which is obtained from the original one by labelling operation symbols, possibly creating extra copies of some rules.
Journal ArticleDOI
Confluence properties of weak and strong calculi of explicit substitutions
TL;DR: The main new results of the paper are a confluent weak calculus of substitutions, where no variable clashes can be feared, and a conjecture raised in Abadi [1991]: λ&sgr;-calculus is not confluent (it is confluent on ground terms only).
References
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Journal ArticleDOI
Confluence properties of weak and strong calculi of explicit substitutions
TL;DR: The main new results of the paper are a confluent weak calculus of substitutions, where no variable clashes can be feared, and a conjecture raised in Abadi [1991]: λ&sgr;-calculus is not confluent (it is confluent on ground terms only).
Journal ArticleDOI
Confluence results for the pure strong categorical logic CCL. l-calculi as subsystems of CCL
TL;DR: The Strong Categorical Combinatory Logic, developed by Curien (1986) is, when typed and augmented with a rule defining a terminal object, a presentation of Cartesian Closed Categories, and is equationally equivalent to the Lambda-calculus with explicit couples and Surjective Pairing.
Journal ArticleDOI
Proof of termination of the rewriting system SUBST on CCL
TL;DR: Curien (1985) defines a translation of the λ c -calculus in the Pure Combinatory Categorical Logic and establishes an equivalence theorem between these two theories and shows that this system is locally confluent and also noetherian.