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Statements

Subject Item
n2:RIV%2F68407700%3A21230%2F06%3A03125206%21RIV07-GA0-21230___
rdf:type
n9:Vysledek skos:Concept
dcterms:description
Iterative theories, which were introduced by Calvin Elgot, formalise potentially infinite computations as unique solutions of recursive equations. One of the main results of Elgot and his coauthors is a description of a free iterative theory as the theory of all rational trees. Their algebraic proof of this fact is extremely complicated. In our paper we show that by starting with iterative algebras, that is, algebras admitting a unique solution of all systems of flat recursive equations, a free iterative theory is obtained as the theory of free iterative algebras. The (coalgebraic) proof we present is dramatically simpler than the original algebraic one. Despite this, our result is much more general: we describe a free iterative theory on any finitary endofunctor of every locally presentable category. Iterative theories, which were introduced by Calvin Elgot, formalise potentially infinite computations as unique solutions of recursive equations. One of the main results of Elgot and his coauthors is a description of a free iterative theory as the theory of all rational trees. Their algebraic proof of this fact is extremely complicated. In our paper we show that by starting with iterative algebras, that is, algebras admitting a unique solution of all systems of flat recursive equations, a free iterative theory is obtained as the theory of free iterative algebras. The (coalgebraic) proof we present is dramatically simpler than the original algebraic one. Despite this, our result is much more general: we describe a free iterative theory on any finitary endofunctor of every locally presentable category. Iterativni teorie, zavedene Calvinem Elgotem, formalizuji potencionalne nekonecne vypocty jako jednoznacna reseni rekursivnich rovnic. Jednim z hlavnich vysledku Elgota a jeho spoluautoru byl popis volne iterativni teorie jako teorie racionalnich stromu. Algebraicky dukaz tohoto faktu je velmi slozity. V nasi praci ukazujeme, ze pokud zacneme s iterativnimi algebrami, obdrzime volnou iterativni teorii jako teorii volnych iterativnich algeber. Nas koalgebraicky dukaz je znacne jendodussi nez puvodni algebraicky. Navic je nas vysledek obecnejsi: popisujeme volnou iterativni teorii pro libovolny finitarni endofunktor na libovolne lokalne konecne presentovane kategorii
dcterms:title
Iterativni algebry v plne sile Iterative Algebras at Work Iterative Algebras at Work
skos:prefLabel
Iterative Algebras at Work Iterative Algebras at Work Iterativni algebry v plne sile
skos:notation
RIV/68407700:21230/06:03125206!RIV07-GA0-21230___
n4:strany
1085;1131
n4:aktivita
n5:P
n4:aktivity
P(GA201/06/0664)
n4:cisloPeriodika
16
n4:dodaniDat
n16:2007
n4:domaciTvurceVysledku
n12:1462571 n12:5613078
n4:druhVysledku
n6:J
n4:duvernostUdaju
n18:S
n4:entitaPredkladatele
n13:predkladatel
n4:idSjednocenehoVysledku
480562
n4:idVysledku
RIV/68407700:21230/06:03125206
n4:jazykVysledku
n7:eng
n4:klicovaSlova
Iterative Algebras
n4:klicoveSlovo
n10:Iterative%20Algebras
n4:kodStatuVydavatele
GB - Spojené království Velké Británie a Severního Irska
n4:kontrolniKodProRIV
[4761FC6519BE]
n4:nazevZdroje
Mathematical Structures in Computer Science
n4:obor
n14:BA
n4:pocetDomacichTvurcuVysledku
2
n4:pocetTvurcuVysledku
3
n4:projekt
n15:GA201%2F06%2F0664
n4:rokUplatneniVysledku
n16:2006
n4:svazekPeriodika
2006
n4:tvurceVysledku
Adámek, Jiří Velebil, Jiří Milius, S.
s:issn
0960-1295
s:numberOfPages
47
n17:organizacniJednotka
21230