A Tutorial on (Co)Algebras and (Co)Induction

by: Bart Jacobs, Jan Rutten

Bulletin of the European Association for Theoretical Computer Science, Vol. 62 (1997), pp. 222-259.

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Abstract

. Algebraic structures which are generated by a collection of constructors--- like natural numbers (generated by a zero and a successor) or finite lists and trees--- are of well-established importance in computer science. Formally, they are initial algebras. Induction is used both as a definition principle, and as a proof principle for such structures. But there are also important dual "coalgebraic" structures, which do not come equipped with constructor operations but with what are sometimes...

@article{citeulike:405057, abstract = {. Algebraic structures which are generated by a collection of constructors--- like natural numbers (generated by a zero and a successor) or finite lists and trees--- are of well-established importance in computer science. Formally, they are initial algebras. Induction is used both as a definition principle, and as a proof principle for such structures. But there are also important dual \"coalgebraic\" structures, which do not come equipped with constructor operations but with what are sometimes...}, author = {Jacobs, Bart and Rutten, Jan }, citeulike-article-id = {405057}, journal = {Bulletin of the European Association for Theoretical Computer Science}, keywords = {algebra, coalgebra, coinduction}, pages = {222--259}, posted-at = {2008-06-14 18:05:04}, priority = {2}, title = {A Tutorial on (Co)Algebras and (Co)Induction}, url = {http://citeseer.ist.psu.edu/jacobs97tutorial.html}, volume = {62}, year = {1997} }

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TY - JOUR ID - citeulike:405057 L3 - citeulike-article-id:405057 TI - A Tutorial on (Co)Algebras and (Co)Induction JF - Bulletin of the European Association for Theoretical Computer Science VL - 62 SP - 222 EP - 259 N2 - . Algebraic structures which are generated by a collection of constructors--- like natural numbers (generated by a zero and a successor) or finite lists and trees--- are of well-established importance in computer science. Formally, they are initial algebras. Induction is used both as a definition principle, and as a proof principle for such structures. But there are also important dual "coalgebraic" structures, which do not come equipped with constructor operations but with what are sometimes... KW - algebra KW - coalgebra KW - coinduction AU - Jacobs, Bart AU - Rutten, Jan PY - 1997/// UR - http://citeseer.ist.psu.edu/jacobs97tutorial.html ER -

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