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Mixed relations as enriched semiringal categories
 Journal of Universal Computer Science
, 2000
"... Abstract: A study of the classes of nite relations as enriched strict monoidal categories is presented in [CaS91]. The relations there are interpreted as connections in owchart schemes, hence an \angelic " theory of relations is used. Finite relations may be used to model the connections betwee ..."
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Abstract: A study of the classes of nite relations as enriched strict monoidal categories is presented in [CaS91]. The relations there are interpreted as connections in owchart schemes, hence an \angelic " theory of relations is used. Finite relations may be used to model the connections between the components of data ow networks [BeS98, BrS96], as well. The corresponding algebras are slightly di erent enriched strict monoidal categories modeling a \forwarddemonic " theory of relations. In order to obtain a full model for parallel programs one needs to mix control and reactive parts, hence a richer theory of nite relations is needed. In this paper we (1) de ne a model of such mixed nite relations, (2) introduce enriched (weak) semiringal categories as an abstract algebraic model for these relations, and (3) show that the initial model of the axiomatization (it always exists) is isomorphic to the de ned one of mixed relations. Hence the axioms gives a sound and complete axiomatization for the these relations. Key Words: parallel programs; mixed relations; network algebra; (enriched) semiringal
Functional programming with structured graphs
 In Proceedings of the 17th ACM SIGPLAN international conference on Functional programming, ICFP ’12
, 2012
"... This paper presents a new functional programming model for graph structures called structured graphs. Structured graphs extend conventional algebraic datatypes with explicit definition and manipulation of cycles and/or sharing, and offer a practical and convenient way to program graphs in functional ..."
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This paper presents a new functional programming model for graph structures called structured graphs. Structured graphs extend conventional algebraic datatypes with explicit definition and manipulation of cycles and/or sharing, and offer a practical and convenient way to program graphs in functional programming languages like Haskell. The representation of sharing and cycles (edges) employs recursive binders and uses an encoding inspired by parametric higherorder abstract syntax. Unlike traditional approaches based on mutable references or node/edge lists, wellformedness of the graph structure is ensured statically and reasoning can be done with standard functional programming techniques. Since the binding structure is generic, we can define many useful generic combinators for manipulating structured graphs. We give applications and show how to reason about structured graphs.
Calculating with Relations for Graph Algorithmics
, 1997
"... Much emphasis has been placed in recent years on deriving or calculating programs rather than proving them correct. Adequate calculational frameworks are needed to support such an approach. The present work explores the use of a calculus of relations to express and reason about graph properties ..."
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Much emphasis has been placed in recent years on deriving or calculating programs rather than proving them correct. Adequate calculational frameworks are needed to support such an approach. The present work explores the use of a calculus of relations to express and reason about graph properties in an algorithmic context. We take a generic program that computes a maximal set, over some universe, satisfying some predicate P and calculate two instances of it: the computation of maximal independent sets of vertices in a graph, and the computation of maximal sets of edges without cycles (i.e. maximal forests).