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A typed, algebraic, computational lambda-calculus†

Published online by Cambridge University Press:  28 February 2013

BENOÎT VALIRON
BENOÎT VALIRON*
Affiliation:
LIPN – UMR 7030 CNRS – Université Paris 13, 99 avenue J-B Clément, F-93430 Villetaneuse, France Email: benoit.valiron@monoidal.net
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Abstract

Lambda-calculi with vectorial structures have been studied in various ways, but their semantics remain largely uninvestigated. The main contribution of this paper is to provide a categorical framework for the semantics of such algebraic lambda-calculi. We first develop a categorical analysis of a general simply typed lambda-calculus endowed with the structure of a module. We study the problems arising from the addition of a fixed-point combinator and show how to modify the equational theory to solve them. The categorical analysis carries nicely over to the modified language. We provide various concrete models for both the case without fixpoints and for the case with them.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 23 , Special Issue 2: Developments In Computational Models 2010 , April 2013 , pp. 504 - 554
Copyright
Copyright © Cambridge University Press 2013

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Footnotes

†

A preliminary version of this work appeared as Valiron (2010).

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