Titlebook: Algebraic and Coalgebraic Methods in the Mathematics of Program Construction; International Summer Roland Backhouse,Roy Crole,Jeremy Gibbon

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Galois Connections and Fixed Point Calculus,utorial also summarises the theory and application of Galois connections between partially ordered sets. In particular, the intimate relation between Galois connections and fixed point equations is amply demonstrated.

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Calculating Functional Programs, of programs, built around datatypes and their operations. Traditional algebraic methods concentrate on initial algebras, constructors, and values; dual . methods concentrate on final co-algebras, destructors, and processes. Both methods are elegant and powerful; they deserve to be combined.

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Temporal Algebra,adigms has led to an equally large number of different and, in most cases, incompatible formalisms. This diversity is of growing concern to academia and industry alike and we have reached the stage where the unification of existing theories should take priority over the invention of new ones.

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Input/Output: Interfacing the Real World,uce the notions of bisimilarity, invariance, component classes, temporal logic and refinement in a coalgebraic setting. Besides the running example of the coalgebraic specification of (possibly infinite) binary trees, a specification of Peterson’s mutual exclusion algorithm is elaborated in detail.

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Algebraic and Coalgebraic Methods in the Mathematics of Program ConstructionInternational Summer

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Ordered Sets and Complete Lattices,tist. The objective is to present the ideas as a self-contained body of material, worthy of study in its own right, and at the same time to assist the learning of algebraic and coalgebraic methods, by giving prior familiarization with some of the mathematical background that arises there. Examples d

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