Algebraic transformation of unary partial algebras II: single-pushout approach

The single-pushout approach to graph transformation is extended to the algebraic transformation of partial many-sorted unary algebras. The main result presented in this article is an algebraic characterization of the single-pushout transformation in the categories of all conformisms, all closed quomorphisms, and all closed-domain closed quomorphisms of unary partial algebras over a given signature, together with a corresponding operational characterization that may serve as a basis for implementation. Moreover, all three categories are shown to satisfy all of the HLR (High Level Replacement) conditions for parallelism, taking as occurrences the total morphisms in each category. Another important result presented in this article is the definition of HLR conditions for amalgamation, which are also satisfied by the categories of partial homomorphisms considered here, taking again the corresponding total morphisms as occurrences