B. Jacobs. Exercises in coalgebraic specication. To appear in the proceedings of the Mathematics for Information Technology Summer School and Workshop on Algebraic and Coalgebraic Methods in the Mathematics of Program Construction, 2000. Home/Search Document Not in Database Summary Related Articles Check |
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Assertional and Behavioural Refinement in Coalgebraic.. - Jacobs, Tews (2001) (3 citations) Self-citation (Jacobs Coalgebraic) (Correct)
....the transition is obvious . Similarly, the last formal speci cation should be so concrete that actually producing a corresponding program is obvious . However, in practice these rst and last steps are not so clear. We shall be working within the context of so called coalgebraic speci cation [15,26]. This formalism is particularly suited for the abstract speci cation of classes in object oriented languages, in functional style. A key feature is that the speci cation describes a state space, commonly called Self, which is considered as a black box. This set of states Self carries a number of ....
....and with taking the opposite relation. The remaining items are obtained by similar basic properties of predicate and relation lifting. 2 3 Coalgebraic Speci cations This section gives a brief introduction to coalgebraic speci cation, mainly via examples. A more thorough account may be found in [15] and [26] At this stage we use ad hoc notation. Later, in Section 6 a formal language ccsl for such speci cations will be described. ccsl is used in the examples in Section 7. Example 3.1 In this illustration of a coalgebraic speci cation we use the set 2 = f0; 1g of bits, or Boolean values, ....
B. Jacobs. Exercises in coalgebraic specication. To appear in the proceedings of the Mathematics for Information Technology Summer School and Workshop on Algebraic and Coalgebraic Methods in the Mathematics of Program Construction, 2000.
Towards a Duality Result in the Modal Logic of Coalgebras - Jacobs (2000) (2 citations) Self-citation (Jacobs) (Correct)
....ourselves to set based coalgebras. Here we use so called polynomial functors, which are built up from the identity and constant functors using products, coproducts and exponents (with a constant) These functors suce for describing many interfaces of classes in object oriented languages, see [Jac96, Jac00]. For a functor T there is a category CoAlg(T ) of coalgebras X T (X) with interface T . This paper introduces a category BAO(T ) of Boolean algebras with operators of (polynomial) type T . The main result (see Theorem 8.4) 1 is then an adjunction of the form: BAO(T ) spec a CoAlg(T ....
....stacks that we concentrate on will be given in two parts: one for the operations (also called methods) and one for the assertions. The methods are described in Figure 1. The style of speci cation is as in the experimental language CCSL 2 (for Coalgebraic Class Speci cation Language) see [HHJT98, Jac00]. BEGIN BoundedStack[D : TYPE, N : N] METHOD size: Self f0; 1; Ng push: Self D Self Self pop: Self Self (D Self) ASSERTION [ See Figure 2 ] END BoundedStack Figure 1: Methods of the bounded stack speci cation 2 Although the speci c modal operators that we use here are ....
B. Jacobs. Exercises in coalgebraic specication. To appear in the proceedings of the Mathematics for Information Technology Summer School and Workshop on Algebraic and Coalgebraic Methods in the Mathematics of Program Construction, 2000.
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