## An Initial-Algebra Approach to Directed Acyclic Graphs (1995)

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### BibTeX

@MISC{Gibbons95aninitial-algebra,

author = {Jeremy Gibbons and Jeremy Gibbons},

title = {An Initial-Algebra Approach to Directed Acyclic Graphs},

year = {1995}

}

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### Abstract

. The initial-algebra 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 initial-algebra approach. Keywords. Graphs, data types, catamorphisms, initial algebras, Bird-Meertens Formalism, program derivation. 1 Introduction It is now widely recognized that the traditional ad-hoc approaches to program construction do not yield reliable software; a more systematic and formal approach is required. One such approach consists of program veri#cation---proving 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...