The primary aim of the definition sequence is to establish the mathematical platform for software development in particular with a view towards array-based logic. The secondary aim is to establish an approach for teaching array theory. The definition sequence has been developed in the spirit of array theory developed by dr. Trenchard More. In order to check the definition sequence we made a comparison to APL2, Iverson's J language, functional programming languages and Backus' FP. The establishment of the set of primitives is considered as an engineering design project. The result of this is that from eight primitives which can be related to the axioms of Zermelo-Fraenkel's set theory we can build all the functions of the pure array theory.