Elgot Theories: A new Perspective of Iteration Theories (Extended Abstract)

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F09%3A00157080" target="_blank" >RIV/68407700:21230/09:00157080 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Elgot Theories: A new Perspective of Iteration Theories (Extended Abstract)

Popis výsledku v původním jazyce

The concept of iteration theory of Bloom and ´Esik summarizes all equational properties that iteration has in usual applications, e.g., in Domain Theory where to every system of recursive equations the least solution is assigned. However, this assignmentin Domain Theory is also functorial. Yet, functoriality is not included in the definition of iteration theory. Pity: functorial iteration theories have a particularly simple axiomatization, and most of examples of iteration theories are functorial. Thereason for excluding functoriality was the view that this property cannot be called equational. This is true from the perspective of the category Sgn of signatures as the base category: whereas iteration theories are monadic (thus, equationally presentable) over Sgn, functorial iteration theories are not. In the present paper we propose to change the perspective and work, in lieu of Sgn, in the category of sets in context (the presheaf category of finite sets and functions). We p

Název v anglickém jazyce

Elgot Theories: A new Perspective of Iteration Theories (Extended Abstract)

Popis výsledku anglicky

The concept of iteration theory of Bloom and ´Esik summarizes all equational properties that iteration has in usual applications, e.g., in Domain Theory where to every system of recursive equations the least solution is assigned. However, this assignmentin Domain Theory is also functorial. Yet, functoriality is not included in the definition of iteration theory. Pity: functorial iteration theories have a particularly simple axiomatization, and most of examples of iteration theories are functorial. Thereason for excluding functoriality was the view that this property cannot be called equational. This is true from the perspective of the category Sgn of signatures as the base category: whereas iteration theories are monadic (thus, equationally presentable) over Sgn, functorial iteration theories are not. In the present paper we propose to change the perspective and work, in lieu of Sgn, in the category of sets in context (the presheaf category of finite sets and functions). We p

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

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Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2009

Kód důvěrnosti údajů

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

Název periodika

Electronic Notes in Theoretical Computer Science

ISSN

1571-0661

e-ISSN

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Svazek periodika

2009

Číslo periodika v rámci svazku

249

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

21

Strana od-do

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Kód UT WoS článku

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EID výsledku v databázi Scopus

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