Coalgebras have been proposed as formal basis for the semantics of objects in the sense of object-oriented programming. This paper shows that this semantics provides a smooth interpretation for subtyping, a central notion in object-oriented programming. We show that different characterisations of behavioural subtyping found in the literature can conveniently be expressed in coalgebraic terms. We also investigate the subtle difference between behavioural subtyping and refinement.

@article{ITA_2001__35_1_61_0, author = {Poll, Erik}, title = {A coalgebraic semantics of subtyping}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, publisher = {EDP-Sciences}, volume = {35}, number = {1}, year = {2001}, pages = {61-81}, zbl = {0990.18004}, mrnumber = {1845875}, language = {en}, url = {http://www.numdam.org/item/ITA_2001__35_1_61_0} }

Poll, Erik. A coalgebraic semantics of subtyping. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 35 (2001) no. 1, pp. 61-81. http://www.numdam.org/item/ITA_2001__35_1_61_0/

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