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

RAIRO - Theoretical Informatics and Applications (2009)

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

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topMiranda-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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