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Semantic Lego
, 1995
"... Denotational semantics [Sch86] is a powerful framework for describing programming languages; however, its descriptions lack modularity: conceptually independent language features influence each others' semantics. We address this problem by presenting a theory of modular denotational semantics. Follo ..."
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Denotational semantics [Sch86] is a powerful framework for describing programming languages; however, its descriptions lack modularity: conceptually independent language features influence each others' semantics. We address this problem by presenting a theory of modular denotational semantics. Following Mosses [Mos92], we divide a semantics into two parts, a computation ADT and a language ADT (abstract data type). The computation ADT represents the basic semantic structure of the language. The language ADT represents the actual language constructs, as described by a grammar. We define the language ADT using the computation ADT; in fact, language constructs are polymorphic over many different computation ADTs. Following Moggi [Mog89a], we build the computation ADT from composable parts, using monads and monad transformers. These techniques allow us to build many different computation ADTs, and, since our language constructs are polymorphic, many different language semantics. We autom...
Synthesising Interconnections
"... In the context of the modular and incremental development of complex systems, viewed as interconnections of interacting components, new dimensions and new problems arise in the calculation of programs from specifications. A particularly important aspect for extending existing methods to address comp ..."
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In the context of the modular and incremental development of complex systems, viewed as interconnections of interacting components, new dimensions and new problems arise in the calculation of programs from specifications. A particularly important aspect for extending existing methods to address composite systems is the ability, given programs that realise component specifications, to synthesise the interconnections between them in such a way that the system specification is realised. Taking our cue from earlier work on General Systems Theory (Goguen, 1973) and more recent work on parallel program design (Fiadeiro and Maibaum, 1996), we discuss, characterise and provide solutions for the synthesis of interconnections using a categorical framework in which components are modelled as objects (either specifications or programs) and morphisms are used to express interconnections between components. * This work was partially supported by the Esprit WG 8319 (MODELAGE), JNICT through contrac...
A STUDY OF FUNCTORS ASSOCIATED WITH TOPOLOGICAL GROUPS
"... Abstract. The aim of this paper is to construct functors associated with topological groups as well as to investigate these functors. More precisely, we prove that for a given topological groups G there always exists a contravariant functor F (G) from the homotopy category of pointed topological spa ..."
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Abstract. The aim of this paper is to construct functors associated with topological groups as well as to investigate these functors. More precisely, we prove that for a given topological groups G there always exists a contravariant functor F (G) from the homotopy category of pointed topological spaces and homotopy classes of base point preserving continuous maps to the category of groups and homomorphisms. We also prove that (i) the functor F (G) is natural in G in the sense that if the topological groups G and H have the same homotopy type then the groups F (G)(X) and F (H)(X) are isomorphic, for every pointed topological space X; and (ii) the functor F (G) is homotopy type invariant in the sense that if X and Y are two pointed spaces having the same homotopy type then the groups F (G)(X) are F (G)(Y) are isomorphic. Moreover, given two topological groups G and H and a continuous homomorphism α: G → H, we show that there always exists a natural transformation between the functors F (G) and F (H) associated with topological groups G and H respectively. 1.