Title :
Computing with Free Algebras
Author_Institution :
Dept. of Comput. Sci. & Eng., Univ. of North Texas, Denton, TX, USA
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;
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
DOI :
10.1109/SYNASC.2012.19
