Generalized Hypersubstitutions of Many-Sorted Algebras

Dawan Chumpungam, Sorasak Leeratanavalee

Abstract

The concept of many-sorted algebras or heterogeneous algebras is useful for abstract data type specifications in Theoretical Computer Science. It is used to explain for abstract data types. Modules and vector spaces are examples of many-sorted algebras. In this paper we extend the concept of a generalized hypersubstitution from one-sorted algebras or homogeneous algebras to many-sorted algebras. We define the $I$-sortede set of all $\Sigma$-generalized hypersubstitutions on special type and define a binary operation on this set. We show that this set together with the binary operation forms a monoid.