• Action notation includes a data notation for general use.

• Standard data consists of tuples, truth-values, numbers, characters, strings, lists, trees, sets, and maps.

• Some of the operations of data notation are intended for use mainly on proper sorts, rather than on mere individuals.

• Appendix E gives the full algebraic specification of data notation.

Consider an implementation of a high-level programming language. When a program is run, the information processed by it is represented entirely by sequences of bits: O's and 1's. The programmer, however, does not usually have to deal with this representation directly. The program can be regarded as processing abstract entities, such as numbers, arrays, and sets. Indeed, standards for high-level programming languages generally leave the binary representation of information unspecified. Recall from Chapter 1 that the semantics of a program is an entity which represents the implementation-independent aspects of its information processing behaviour, and that the semantics of a phrase is an entity which represents its contribution to overall behaviour. In action semantics, these entities are generally actions. The information processed by programs is represented by items of data, which correspond directly to abstract entities such as numbers rather than to bit sequences.

Various sorts of data are needed for the semantics of general-purpose high-level programming languages, not only ‘mathematical’ values such as numbers and lists, but also abstract entities of computational origins such as variables, procedures, packages, and so on.