Universal algebra

Abstract

The most basic assumption in work on algebraic specification is that programs are modelled as algebras. This point of view abstracts from the concrete details of code and algorithms, and regards the input/output behaviour of functions and the representation of data as of primary importance. Representing programs in terms of sets (of data values) and ordinary mathematical functions over these sets greatly simplifies the task of reasoning about program correctness. The necessary underpinnings are offered by universal algebra, necessarily in a many-sorted variant, building on the classical single-sorted version. This chapter summarizes the basic concepts and results concerning many-sorted algebras that will be required for the rest of this book.