U. Hensel and D. Spooner. A view on implementing processes: Categories of circuits. In M. Haveraaen, O. Owe, and O. Dahl, editors, Recent Trends in Data Types Specification, volume 1130 of LNCS, pages 237--255. Springer Verlag, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... 1 Introduction In recent years there has been a growing interest in the theory of coalgebras, motivated by the fact that they are particularly suitable to specify, in an implementation independent way, a wide class of systems, typically discrete dynamical systems with a hidden state space [Rut96, Jac96b, Jac96a, Rei95, HS95]. Examples include various kinds of transition systems, deterministic and nondeterministic automata, concurrent) objects, hybrid systems, and (possibly) infinite data structures like streams and trees. In the theory of algebraic specification, an abstract data type is specified by a set of ....

U. Hensel and D. Spooner. A view on implementing processes: Categories of circuits. In M. Haveraaen, O. Owe, and O. Dahl, editors, Recent Trends in Data Types Specification, volume 1130 of LNCS, pages 237--255. Springer Verlag, 1995.

....DGS Cat. ut Equivalent notions of dgs monoidal categories have surfaced quite frequently in recent years. A (bicategorical) presentation is used as a description of the (bi)category of relations already in [5] which forms the basis for some recent work on the categorical description of circuits [21, 17]: Arrows are processes, and the bicategorical structure allows to relate specifications which are equivalent but show a different internal structure (a different implementation, so to say) Intuitively, the arrow a can be interpreted as the new operator, creating a pointer to a new name of sort ....

U. Hensel and D. Spooner. A view on implementing processes: Categories of circuits. In M. Haveraaen, O. Owe, and O. Dahl, editors, Recent Trends in Data Types Specification, volume 1130 of LNCS, pages 237--255. Springer Verlag, 1995.

....the transformation is replaced by two binary projections, possibly non natural in one of the arguments. A detailed analysis of these kinds of categories, including many equivalent equational and nonequational charaterizations, is presented in [13] Also close to ours are the copy categories of [19], and the premonoidal categories of [35] Fact 4.1 (from cartesian to gs monoidal categories, and back) The inclusion functors I C : C Cat , GM Cat and I G : GM Cat , GSM Cat have obvious left adjoints F C : GM Cat C Cat and FG : GSM Cat GM Cat, respectively. Informally, FG turns a ....

U. Hensel and D. Spooner. A view on implementing processes: Categories of circuits. In M. Haveraaen, O. Owe, and O. Dahl, editors, Recent Trends in Data Types Specication, volume 1130 of LNCS, pages 237-255. Springer Verlag, 1995.

....that try to recover which is the extra structure we need on a category for it to be a well behaved category of partial maps. To this aim, they introduce p categories, which were very close to ours if we required r to be natural. Also related to ours are the copy categories introduced in [28]. Walters et al..ii investigate the algebraic structure of relations, regarded as arrows of suitable categories of spans [36, 37] They have on the operational side an interpretation in terms of processes, and on the categorical side suitable bicategories. Interestingly, the axiomatisation of ....

U. Hensel and D. Spooner. A view on implementing processes: Categories of circuits. In M. Haveraaen, O. Owe, and O. Dahl, editors, Recent Trends in Data Types Specification, volume 1130 of LNCS, pages 237--255. Springer Verlag, 1995.

....category where transformations r and are natural. Instead, by requiring just r to be natural (and not ) we obtain structures which are very similar to the dht categories of the pioneering [7, 8] More recently, analogous constructions are the p categories of [15] or the copy categories of [6]: We call them g monoidal categories, where g stays for garbage, for reasons that will be explained later on. Definition 5 (from gs monoidal to cartesian categories) A g monoidal category is a gs monoidal category where transformation r is natural. The full sub category of GSM Cat containing ....

U. Hensel and D. Spooner. A view on implementing processes: Categories of circuits. In M. Haveraaen, O. Owe, and O. Dahl, editors, Recent Trends in Data Types Specification, volume 1130 of LNCS, pages 237--255. Springer Verlag, 1995.

....of the algebra, but which is not necessarily an equivalence relation. For example, a congruence R N Theta N on the natural numbers satisfies R(0; 0) and R(x; y) R(S(x) S(y) for all x; y 2 N. This (recent) interest in the logic of initial algebras and terminal coalgebras (see for example [6, 2, 22, 26, 7, 28, 9, 8, 12, 27]) is also motivated by the increasing use of powerful and expressive proof tools, like pvs, isabelle, hol, larch, lego, coq etc. in which users may introduce their own inductively (and sometimes also coinductively) defined type. And, this is of most relevance, the tool 3 then automatically ....

U. Hensel and D. Spooner. A view on implementing processes: Categories of circuits. In M. Haveraaen, O. Owe, and O.-J. Dahl, editors, Recent Trends in Data Type Specification, number 1130 in Lect. Notes Comp. Sci., pages 237--254. Springer, Berlin, 1996.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC