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Computational Effects and Operations: An Overview
, 2004
"... We overview a programme to provide a unified semantics for computational effects based upon the notion of a countable enriched Lawvere theory. We define the notion of countable enriched Lawvere theory, show how the various leading examples of computational effects, except for continuations, give ris ..."
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Cited by 26 (8 self)
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We overview a programme to provide a unified semantics for computational effects based upon the notion of a countable enriched Lawvere theory. We define the notion of countable enriched Lawvere theory, show how the various leading examples of computational effects, except for continuations, give rise to them, and we compare the definition with that of a strong monad. We outline how one may use the notion to model three natural ways in which to combine computational effects: by their sum, by their commutative combination, and by distributivity. We also outline a unified account of operational semantics. We present results we have already shown, some partial results, and our plans for further development of the programme.
Monoidal functor categories and graphic Fourier transforms, arXiv: math/0612496v1 [math. QA
, 2006
"... Abstract. This article represents a preliminary attempt to link Kan extensions, and some of their further developments, to Fourier theory and quantum algebra through ∗autonomous monoidal categories and related structures. There is a close resemblance to convolution products and the Wiener algebra ( ..."
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Cited by 3 (1 self)
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Abstract. This article represents a preliminary attempt to link Kan extensions, and some of their further developments, to Fourier theory and quantum algebra through ∗autonomous monoidal categories and related structures. There is a close resemblance to convolution products and the Wiener algebra (of transforms) in functional analysis. The analysis term “kernel ” (of a distribution) has also been adapted below in connection with certain special types of “distributors ” (in the terminology of J. Bénabou) or “modules” (in the terminology of R. Street) in category theory. In using the term “graphic”, in a very broad sense, we are clearly distinguishing the categorical methods employed in this article from standard Fourier and wavelet mathematics. The term “graphic ” also applies to promultiplicative graphs, and related concepts, which can feature prominently in the theory.
Diagrammatic Representations in DomainSpecific Languages
, 2000
"... One emerging approach to reducing the labour and costs of software development favours the specialisation of techniques to particular application domains. The rationale is that programs within a given domain often share enough common features and assumptions to enable the incorporation of substantia ..."
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Cited by 1 (1 self)
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One emerging approach to reducing the labour and costs of software development favours the specialisation of techniques to particular application domains. The rationale is that programs within a given domain often share enough common features and assumptions to enable the incorporation of substantial support mechanisms into domainspecific programming languages and associated tools. Instead of being machineoriented, algorithmic implementations, programs in many domainspecific languages (DSLs) are rather userlevel, problemoriented specifications of solutions. Taken further, this view suggests that the most appropriate representation of programs in many domains is diagrammatic, in a way which derives from existing design notations in the domain. This thesis conducts an investigation, using mathematical techniques and supported by case studies, of issues arising from the use of diagrammatic representations in DSLs. Its structure is conceptually divided into two parts: the first is co...