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

Favio Ezequiel Miranda-Perea

RAIRO - Theoretical Informatics and Applications (2009)

  • Volume: 43, Issue: 4, page 703-766
  • ISSN: 0988-3754

Abstract

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This paper presents two extensions of the second order polymorphic lambda calculus, system F, with monotone (co)inductive types supporting (co)iteration, primitive (co)recursion and inversion principles as primitives. One extension is inspired by the usual categorical approach to programming by means of initial algebras and final coalgebras; whereas the other models dialgebras, and can be seen as an extension of Hagino's categorical lambda calculus within the framework of parametric polymorphism. The systems are presented in Curry-style, and are proven to be terminating and type-preserving. Moreover their expressiveness is shown by means of several programming examples, going from usual data types to lazy codata types such as streams or infinite trees.

How to cite

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Miranda-Perea, Favio Ezequiel. "Two extensions of system F with (co)iteration and primitive (co)recursion principles." RAIRO - Theoretical Informatics and Applications 43.4 (2009): 703-766. <http://eudml.org/doc/250595>.

@article{Miranda2009,
abstract = { This paper presents two extensions of the second order polymorphic lambda calculus, system F, with monotone (co)inductive types supporting (co)iteration, primitive (co)recursion and inversion principles as primitives. One extension is inspired by the usual categorical approach to programming by means of initial algebras and final coalgebras; whereas the other models dialgebras, and can be seen as an extension of Hagino's categorical lambda calculus within the framework of parametric polymorphism. The systems are presented in Curry-style, and are proven to be terminating and type-preserving. Moreover their expressiveness is shown by means of several programming examples, going from usual data types to lazy codata types such as streams or infinite trees. },
author = {Miranda-Perea, Favio Ezequiel},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Coiteration; corecursion; iteration; primitive recursion; system F; monotone inductive type; monotone coinductive type; monotonicity witness; saturated sets; algebras; coalgebras; dialgebras.; coiteration; System F; monotonicity witness; dialgebras},
language = {eng},
month = {9},
number = {4},
pages = {703-766},
publisher = {EDP Sciences},
title = {Two extensions of system F with (co)iteration and primitive (co)recursion principles},
url = {http://eudml.org/doc/250595},
volume = {43},
year = {2009},
}

TY - JOUR
AU - Miranda-Perea, Favio Ezequiel
TI - Two extensions of system F with (co)iteration and primitive (co)recursion principles
JO - RAIRO - Theoretical Informatics and Applications
DA - 2009/9//
PB - EDP Sciences
VL - 43
IS - 4
SP - 703
EP - 766
AB - This paper presents two extensions of the second order polymorphic lambda calculus, system F, with monotone (co)inductive types supporting (co)iteration, primitive (co)recursion and inversion principles as primitives. One extension is inspired by the usual categorical approach to programming by means of initial algebras and final coalgebras; whereas the other models dialgebras, and can be seen as an extension of Hagino's categorical lambda calculus within the framework of parametric polymorphism. The systems are presented in Curry-style, and are proven to be terminating and type-preserving. Moreover their expressiveness is shown by means of several programming examples, going from usual data types to lazy codata types such as streams or infinite trees.
LA - eng
KW - Coiteration; corecursion; iteration; primitive recursion; system F; monotone inductive type; monotone coinductive type; monotonicity witness; saturated sets; algebras; coalgebras; dialgebras.; coiteration; System F; monotonicity witness; dialgebras
UR - http://eudml.org/doc/250595
ER -

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