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نویسنده
چکیده
Functional languages are renowned for their mathematical tractability, clarity of expression, abstraction powers, and more. There are problem domains, however, that still present real challenges to functional languages. One notoriously difficult problem domain is graph algorithms. Graph algorithms have been studied for a long time with conventional von Neumann languages. The emphasis has primarily been on the efficiency of the algorithm. Concerns such as clarity of the algorithm have been secondary. Although the underpinnings of algorithms generally have a solid theoretical foundation, there is still some distance between computer program and proof of correctness. This thesis is an investigation of graph algorithms in the non-strict purely functional language Haskell. Emphasis is placed on the importance of achieving an asymptotic complexity as good as with conventional languages. This is achieved by using the monadic model for including actions on the state. Work on the monadic. model was carried out at Glasgow University by Wadler, Peyton Jones, and Launchbury in the early nineties and has opened up many diverse application areas. One area is the ability to express data structures that require sharing. Although graphs are not presented in this style, data structures that graph algorithms use are expressed in this style. Several examples of stateful algorithms are given including union/find for disjoint sets, and the linear time sort binsort. The graph algorithms presented are not new, but are traditional algorithms recast in a functional setting. Examples include strongly connected components, biconnected components, Kruskal's minimum cost spanning tree, and Dijkstra's shortest paths. The presentation is lucid giving more insight than usual. The functional setting allows for complete calculational style correctness proofs which is demonstrated with many examples. The benefits of using a functional language for expressing graph algorithms are quantified by looking at the issues of execution times, asymptotic complexity, correctness, and clarity, in comparison with traditional approaches. The intention is to be as objective as possible, pointing out both the weaknesses and the strengths of using a functional language.
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