Semantics of a Typed Algebraic Lambda-Calculus

Details Semantics of a Typed Algebraic Lambda-Calculus Semantics of a Typed Algebraic Lambda-Calculus

2010-06-08

arxiv.org/abs/1006.1433v1

EPTCS 26, 2010, pp. 147-158

Computer Science

Logic in Computer Science

Scientific paper

10.4204/EPTCS.26.14

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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