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A Categorical Manifesto
 Mathematical Structures in Computer Science
, 1991
"... : This paper tries to explain why and how category theory is useful in computing science, by giving guidelines for applying seven basic categorical concepts: category, functor, natural transformation, limit, adjoint, colimit and comma category. Some examples, intuition, and references are given for ..."
Abstract

Cited by 99 (5 self)
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: This paper tries to explain why and how category theory is useful in computing science, by giving guidelines for applying seven basic categorical concepts: category, functor, natural transformation, limit, adjoint, colimit and comma category. Some examples, intuition, and references are given for each concept, but completeness is not attempted. Some additional categorical concepts and some suggestions for further research are also mentioned. The paper concludes with some philosophical discussion. 0 Introduction This paper tries to explain why category theory is useful in computing science. The basic answer is that computing science is a young field that is growing rapidly, is poorly organised, and needs all the help it can get, and that category theory can provide help with at least the following: ffl Formulating definitions and theories. In computing science, it is often more difficult to formulate concepts and results than to give a proof. The seven guidelines of this paper can h...
Relative Complexity of Algebras
, 1981
"... A simple algebraic model is proposed fr measuring the relative complexity of programming systems. The appropriateness of this model is illustrated by its use as a framework for the statement and proof of results dealing with codingindependent limitations on the relative complexity of basic alge ..."
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Cited by 2 (0 self)
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A simple algebraic model is proposed fr measuring the relative complexity of programming systems. The appropriateness of this model is illustrated by its use as a framework for the statement and proof of results dealing with codingindependent limitations on the relative complexity of basic algebras.
Twisted Systems and the Logic of Imperative Programs
, 1998
"... Following Burstall, a flow diagram can be represented by a pair consisting of a graph and a functor from the free category to the category of sets and relations. A program is verified by incorporating the assertions of the FloydNaur proof method into a second functor and exhibiting a natural transf ..."
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Cited by 1 (1 self)
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Following Burstall, a flow diagram can be represented by a pair consisting of a graph and a functor from the free category to the category of sets and relations. A program is verified by incorporating the assertions of the FloydNaur proof method into a second functor and exhibiting a natural transformation to the program. A broader range of properties is obtained by substituting spans for relations and introducing oplaxness into both the functors representing programs and the natural transformations in the morphisms between programs. The apparent complexity of this generalization is overcome by the observation that an oplax functor J Sp(C) is essentially the same as a functor e J C where e J is the twisted arrow category of J. Thus, a program is a presheaf F (G) Set as are the properties of the program. By analogy with categorical models of firstorder logic, a program and the properties which pertain to it are subobjects of a suitably chosen base object. In this setting safety ...