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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.
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.
The question of how to combine monads arises naturally in many areas with much recent interest focusing on the coproduct of two monads. In general, the coproduct of arbitrary monads does not always exist. Although a rather general construction was given by Kelly [Bull. Austral. Math. Soc. 22 (1980) 1–83], its generality is reflected in its complexity which limits the applicability of this construction. Following our own research [C. Lüth and N. Ghani, Lect. Notes Artif. Intell. 2309 (2002) 18–32],...
The question of how to combine monads arises naturally in many areas
with much recent interest focusing on the coproduct of two monads.
In general, the coproduct of arbitrary monads does not always exist.
Although a rather general construction was given by
Kelly [Bull. Austral. Math. Soc.22 (1980) 1–83], its generality is reflected in its
complexity which limits the applicability of this construction.
Following our own research [C. Lüth and N. Ghani,
Lect. Notes Artif. Intell.2309 (2002)...
It is well known that, given an endofunctor on a category , the initial -algebras (if existing), i.e., the algebras of (wellfounded) -terms over different variable supplies , give rise to a monad with substitution as the extension operation (the free monad induced by the functor ). Moss [17] and Aczel, Adámek, Milius and Velebil [2] have shown that a similar monad, which even enjoys the additional special property of having iterations for all guarded substitution rules (complete iterativeness),...
It is well known that, given an endofunctor H on a category C ,
the initial (A+H-)-algebras (if existing), i.e. , the algebras
of (wellfounded) H-terms over different variable supplies A,
give rise to a monad with substitution as the extension operation
(the free monad induced by the functor H). Moss [17]
and Aczel, Adámek, Milius and Velebil [12] have shown
that a similar monad, which even enjoys the additional special
property of having iterations for all guarded substitution rules
(complete...
Algebraic systems of equations define functions using recursion where parameter passing is permitted. This generalizes the notion of a rational system of equations where parameter passing is prohibited. It has been known for some time that algebraic systems in Greibach Normal Form have unique solutions. This paper presents a categorical approach to algebraic systems of equations which generalizes the traditional approach in two ways i) we define algebraic equations for locally finitely presentable...
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