Topic

# Explicit substitution

About: Explicit substitution is a research topic. Over the lifetime, 142 publications have been published within this topic receiving 7659 citations.

##### Papers published on a yearly basis

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30 Apr 2012

TL;DR: In this article, the Lambda-Calculus has been studied as a theory of composition and reduction, and the theory of reduction has been used to construct models of Lambda Theories.

Abstract: Towards the Theory. Introduction. Conversion. Reduction. Theories. Models. Conversion. Classical Lambda Calculus. The Theory of Combinators. Classical Lambda Calculus (Continued). The Lambda-Calculus. Bohm Trees. Reduction. Fundamental Theorems. Strongly Equivalent Reductions. Reduction Strategies. Labelled Reduction. Other Notions of Reduction. Theories. Sensible Theories. Other Lambda Theories. Models. Construction of Models. Local Structure of Models. Global Structure of Models. Combinatory Groups. Appendices: Typed Lambda Calculus. Illative Combinatory Logic. Variables. References.

2,632 citations

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01 Jan 1972

TL;DR: In this paper, a notational system for lambda calculus is developed, where occurrences of variables are indicated by integers giving the "distance" to the binding λ instead of a name attached to that λ. This convention is known to cause considerable trouble in cases of substitution.

Abstract: In ordinary lambda calculus the occurrences of a bound variable are made recognizable by the use of one and the same (otherwise irrelevant) name at all occurrences. This convention is known to cause considerable trouble in cases of substitution. In the present paper a different notational system is developed, where occurrences of variables are indicated by integers giving the “distance” to the binding λ instead of a name attached to that λ. The system is claimed to be efficient for automatic formula manipulation as well as for metalingual discussion. As an example the most essential part of a proof of the Church-Rosser theorem is presented in this namefree calculus.

919 citations

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18 Mar 1993

TL;DR: This book gives a readable but rigorous introduction to the theory of term rewriting systems, a technique used in computer science, especially functional programming, for abstract data type specification and automatic theorem-proving.

Abstract: From the Publisher:
This book, the first on the subject in English, gives a readable but rigorous introduction to the theory of term rewriting systems. These are a technique used in computer science, especially functional programming, for abstract data type specification and automatic theorem-proving. The book is self-contained, and begins with a discussion of elementary systems and progresses to the most general cases that involve concepts such as second-order lambda calculus. Exercises are included throughout, and solutions to a selection of them are provided. Complete proofs of results that are often buried in the literature are also given, so researchers in functional programming, theoretical computer science, and logic will find this book useful.

821 citations

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TL;DR: In this paper, a notational system for lambda calculus is developed, where occurrences of variables are indicated by integers giving the "distance" to the binding λ instead of a name attached to that λ. This convention is known to cause considerable trouble in cases of substitution.

Abstract: In ordinary lambda calculus the occurrences of a bound variable are made recognizable by the use of one and the same (otherwise irrelevant) name at all occurrences. This convention is known to cause considerable trouble in cases of substitution. In the present paper a different notational system is developed, where occurrences of variables are indicated by integers giving the “distance” to the binding λ instead of a name attached to that λ. The system is claimed to be efficient for automatic formula manipulation as well as for metalingual discussion. As an example the most essential part of a proof of the Church-Rosser theorem is presented in this namefree calculus.

583 citations

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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.

193 citations