Computing with Free Algebras

Author

Tarau, P.

Author_Institution

Dept. of Comput. Sci. & Eng., Univ. of North Texas, Denton, TX, USA

fYear

2012

Firstpage

15

Lastpage

22

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.

Keywords

digital arithmetic; functional languages; number theory; process algebra; programming language semantics; recursive functions; trees (mathematics); GHC view construct; algebra semantics; arithmetic computations; constructors; deconstructors; free algebras; natural numbers; rooted ordered binary trees; Algebra; Binary trees; Complexity theory; Computer science; Generators; Semantics; arithmetic computations with free algebras; bijective Goedel numberings and algebraic datatypes; declarative modeling of computational phenomena; generalized constructors;

fLanguage

English

Publisher

ieee

Conference_Titel

Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), 2012 14th International Symposium on

Conference_Location

Timisoara

Print_ISBN

978-1-4673-5026-6

Type

conf

DOI

10.1109/SYNASC.2012.19

Filename

6481006