Semantics of higher-order recursion schemes

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F11%3A00179796" target="_blank" >RIV/68407700:21230/11:00179796 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.2168/LMCS-7(1:15)2011" target="_blank" >http://dx.doi.org/10.2168/LMCS-7(1:15)2011</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.2168/LMCS-7(1:15)2011" target="_blank" >10.2168/LMCS-7(1:15)2011</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Semantics of higher-order recursion schemes

Popis výsledku v původním jazyce

Higher-order recursion schemes are recursive equations defining new operations from given ones called terminals. Every such recursion scheme is proved to have a least interpreted semantics in every Scott's model of lambda-calculus in which the terminalsare interpreted as continuous operations. For the uninterpreted semantics based on infinite lambda-terms we follow the idea of Fiore, Plotkin and Turi and work in the category of sets in context, which are presheaves on the category of finite sets. Fioreet al showed how to capture the type of variable binding in lambda-calculus by an endofunctor H and they explained simultaneous substitution of lambda-terms by proving that the presheaf of lambda-terms is an initial H-monoid. Here we work with the presheaf of rational infinite lambda-terms and prove that this is an initial iterative H-monoid. We conclude that every guarded higher-order recursion scheme has a unique uninterpreted solution in this monoid.

Název v anglickém jazyce

Semantics of higher-order recursion schemes

Popis výsledku anglicky

Higher-order recursion schemes are recursive equations defining new operations from given ones called terminals. Every such recursion scheme is proved to have a least interpreted semantics in every Scott's model of lambda-calculus in which the terminalsare interpreted as continuous operations. For the uninterpreted semantics based on infinite lambda-terms we follow the idea of Fiore, Plotkin and Turi and work in the category of sets in context, which are presheaves on the category of finite sets. Fioreet al showed how to capture the type of variable binding in lambda-calculus by an endofunctor H and they explained simultaneous substitution of lambda-terms by proving that the presheaf of lambda-terms is an initial H-monoid. Here we work with the presheaf of rational infinite lambda-terms and prove that this is an initial iterative H-monoid. We conclude that every guarded higher-order recursion scheme has a unique uninterpreted solution in this monoid.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

—

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2011

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Logical Methods in Computer Science

ISSN

1860-5974

e-ISSN

—

Svazek periodika

2011

Číslo periodika v rámci svazku

7

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

43

Strana od-do

1-43

Kód UT WoS článku

000290278900015

EID výsledku v databázi Scopus

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