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A Coalgebraic Semantics of Subtyping

Erik Poll (2010)

RAIRO - Theoretical Informatics and Applications

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.

A coalgebraic semantics of subtyping

Erik Poll (2001)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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.

A duality between infinitary varieties and algebraic theories

Jiří Adámek, Václav Koubek, Jiří Velebil (2000)

Commentationes Mathematicae Universitatis Carolinae

A duality between λ -ary varieties and λ -ary algebraic theories is proved as a direct generalization of the finitary case studied by the first author, F.W. Lawvere and J. Rosick’y. We also prove that for every uncountable cardinal λ , whenever λ -small products commute with 𝒟 -colimits in Set , then 𝒟 must be a λ -filtered category. We nevertheless introduce the concept of λ -sifted colimits so that morphisms between λ -ary varieties (defined to be λ -ary, regular right adjoints) are precisely the functors...

A logic of orthogonality

Jiří Adámek, Michel Hébert, Lurdes Sousa (2006)

Archivum Mathematicum

A logic of orthogonality characterizes all “orthogonality consequences" of a given class Σ of morphisms, i.e. those morphisms s such that every object orthogonal to Σ is also orthogonal to s . A simple four-rule deduction system is formulated which is sound in every cocomplete category. In locally presentable categories we prove that the deduction system is also complete (a) for all classes Σ of morphisms such that all members except a set are regular epimorphisms and (b) for all classes Σ , without...

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