Computing with Free Algebras

descriptionPublicationkeyboard_double_arrow_right Article , Conference object 01 Sep 2012Publisher:IEEEJournal:2012 14th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing

Authors: Paul Tarau;

doi: 10.1109/synasc.2012.19

Computing with Free Algebras

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Abstract

We describe arithmetic computations in terms of operations on some well known free algebras (S1S, S2S and ordered rooted binary trees) while emphasizing the common structure present in all of them when seen as isomorphic with the set of natural numbers. Constructors and deconstructors seen through an initial algebra semantics are generalized to recursively defined functions obeying similar laws. Implementations using GHC's "view" construct are discussed, based on the free algebra of rooted ordered binary trees.

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University of North Texas
United States

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