We introduce a framework that generalizes algebraic specifications by equipping algebras with descriptions of evaluation strategies. The resulting abstract mathematical description allows one to model the implementation of algebras on various platforms in a way that is independent of the function-oriented specifications.

We study algebras with associated data dependencies. The latter provide separate means for modelling computational aspects apart from the functional specifications captured by an algebra. The formalization of evaluation strategies (1) introduces increased portability among different hardware platforms, and (2) allows a potential increase in execution efficiency, since a chosen evaluation strategy may be tailored to a particular platform. We present the development process where algebraic specifications are equipped with data dependencies, the latter are refined, and, finally, mapped to actual hardware architectures.

In this paper we investigate and compare four variants of the double-pushout approach to graph transformation. As well as the traditional approach with arbitrary matching and injective right-hand morphisms, we consider three variations by employing injective matching and/or arbitrary right-hand morphisms in rules. We show that injective matching provides additional expressiveness in two respects: for generating graph languages by grammars without non-terminals and for computing graph functions by convergent graph transformation systems. Then we clarify for each of the three variations whether the well-known commutativity, parallelism and concurrency theorems are still valid and – where this is not the case – give modified results. In particular, for the most general approach with injective matching and arbitrary right-hand morphisms, we establish sequential and parallel commutativity by appropriately strengthening sequential and parallel independence.