About: On second-order iterative monads

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	B. Courcelle studied algebraic trees as precisely the solutions of all recursive program schemes for a given signature in Set. He proved that the corresponding monad is iterative. We generalize this to recursive program schemes over a given unitary endofunctor H of a %22suitable%22 category. A monad is called second-order iterative if every guarded recursive program scheme has a unique solution in it. We construct two second-order iterative monads: one, called the second-order rational monad, S(H), is proved to be the initial second-order iterative monad. The other one, called the context-free monad, C(H), is a quotient of S(H) and in the original case of a polynomial endofunctor H of Set we prove that C(H) is the monad studied by B. Courcelle. The question whether these two monads are equal is left open. (C) 2011 Elsevier B.V. All rights reserved. B. Courcelle studied algebraic trees as precisely the solutions of all recursive program schemes for a given signature in Set. He proved that the corresponding monad is iterative. We generalize this to recursive program schemes over a given unitary endofunctor H of a %22suitable%22 category. A monad is called second-order iterative if every guarded recursive program scheme has a unique solution in it. We construct two second-order iterative monads: one, called the second-order rational monad, S(H), is proved to be the initial second-order iterative monad. The other one, called the context-free monad, C(H), is a quotient of S(H) and in the original case of a polynomial endofunctor H of Set we prove that C(H) is the monad studied by B. Courcelle. The question whether these two monads are equal is left open. (C) 2011 Elsevier B.V. All rights reserved. (en)
Title	On second-order iterative monads On second-order iterative monads (en)
skos:prefLabel	On second-order iterative monads On second-order iterative monads (en)
skos:notation	RIV/68407700:21230/11:00181889!RIV12-MSM-21230___
http://linked.open...avai/predkladatel	Fakulta elektrotechnická
http://linked.open...avai/riv/aktivita	Z
http://linked.open...avai/riv/aktivity	Z(MSM6840770014)
http://linked.open...iv/cisloPeriodika	38
http://linked.open...vai/riv/dodaniDat	2012
http://linked.open...aciTvurceVysledku	Velebil, Jiří
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	České vysoké učení technické v Praze / Fakulta elektrotechnická
http://linked.open...dnocenehoVysledku	218129
http://linked.open...ai/riv/idVysledku	RIV/68407700:21230/11:00181889
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Algebraic trees; Recursive program schemes; Ideal theory; Monads; INFINITE-TREES; ALGEBRAS; FINITARY (en)
http://linked.open.../riv/klicoveSlovo	ALGEBRAS Algebraic trees FINITARY INFINITE-TREES Ideal theory Monads Recursive program schemes
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[1732D688D9FE]
http://linked.open...i/riv/nazevZdroje	Theoretical Computer Science
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...UplatneniVysledku	2011
http://linked.open...v/svazekPeriodika	412
http://linked.open...iv/tvurceVysledku	Velebil, Jiří Adámek, J. Milius, S.
http://linked.open...ain/vavai/riv/wos	000294317000002
http://linked.open...n/vavai/riv/zamer	Výzkum perspektivních informačních a komunikačních technologií
issn	0304-3975
number of pages	20 (xsd:int)
http://bibframe.org/vocab/doi	10.1016/j.tcs.2011.04.027
http://localhost/t...ganizacniJednotka	21230
is http://linked.open...avai/riv/vysledek of	On second-order iterative monads On second-order iterative monads

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