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arXiv · 1006.1433

Semantics of a Typed Algebraic Lambda-Calculus

Benoît Valiron
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Abstract

Algebraic lambda-calculi have been studied in various ways, but their semantics remain mostly untouched. In this paper we propose a semantic analysis of a general simply-typed lambda-calculus endowed with a structure of vector space. We sketch the relation with two established vectorial lambda-calculi. Then we study the problems arising from the addition of a fixed point combinator and how to modify the equational theory to solve them. We sketch an algebraic vectorial PCF and its possible denotational interpretations.

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Benoît Valiron. 2010-06-08. Semantics of a Typed Algebraic Lambda-Calculus. https://doi.org/10.4204/eptcs.26.14

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