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Two extensions of system Fwith (co)iteration and primitive(co)recursion principles

Published online by Cambridge University Press:  01 September 2009

Favio Ezequiel Miranda-Perea
Favio Ezequiel Miranda-Perea*
Affiliation:
Departamento de Matemáticas, Facultad de Ciencias UNAM, Circuito Exterior S/N. Ciudad Universitaria, 04510 México, D.F. México; favio@ciencias.unam.mx
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Abstract

This paper presents two extensions of the second order polymorphiclambda calculus, system F, with monotone (co)inductive types supporting(co)iteration, primitive (co)recursion and inversion principles asprimitives. One extension is inspired by the usual categoricalapproach to programming by means of initial algebras and finalcoalgebras; whereas the other models dialgebras, and can be seen as an extension of Hagino'scategorical lambda calculus within the framework of parametricpolymorphism. The systems are presented in Curry-style, and are proven to be terminating andtype-preserving. Moreovertheir expressiveness is shown by means of several programmingexamples, going from usual data types to lazy codata types such as streamsor infinite trees.

Keywords

Coiterationcorecursioniterationprimitive recursionsystem Fmonotone inductive typemonotone coinductive typemonotonicity witnesssaturated setsalgebrascoalgebrasdialgebras.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 43 , Issue 4 , October 2009 , pp. 703 - 766
Copyright
© EDP Sciences, 2009

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