Semantics of a Typed Algebraic Lambda-Calculus
Logic in Computer Science
2010-06-09 v1
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.
Cite
@article{arxiv.1006.1433,
title = {Semantics of a Typed Algebraic Lambda-Calculus},
author = {Benoît Valiron},
journal= {arXiv preprint arXiv:1006.1433},
year = {2010}
}