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An InitialAlgebra Approach to Directed Acyclic Graphs
, 1995
"... . The initialalgebra approach to modelling datatypes consists of giving constructors for building larger objects of that type from smaller ones, and laws identifying di#erentways of constructing the same object. The recursive decomposition of objects of the datatype leads directly to a recursiv ..."
Abstract

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. The initialalgebra approach to modelling datatypes consists of giving constructors for building larger objects of that type from smaller ones, and laws identifying di#erentways of constructing the same object. The recursive decomposition of objects of the datatype leads directly to a recursive pattern of computation on those objects, whichisvery helpful for both functional and parallel programming. We showhow to model a particular kind of directed acyclic graph using this initialalgebra approach. Keywords. Graphs, data types, catamorphisms, initial algebras, BirdMeertens Formalism, program derivation. 1 Introduction It is now widely recognized that the traditional adhoc approaches to program construction do not yield reliable software; a more systematic and formal approach is required. One such approach consists of program veri#cationproving after the fact that a given program satis#es its formal speci#cation. This approach turns out to be di#cult to implement, not lea...