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Additional sort classes like BOOL SORT and LIST SORT are then declared by extending VALUE with injections for their respective sort types. We can then, for instance, use BOOL SORT to constrain constructs requiring the presence of Booleans, and use the injections to produce correctly typed model values. A concrete model will usually consist of datatypes for the value and type spaces, and functions for the typing relation and definedness predicate, which instantiate the value model. As in [19], we model variables explicitly, and with [27] also encode type data so bindings can impose well-typedness.
Unifying theories of programming in Isabelle. , Zhu, H. ) Theories of Programming. LNCS, vol. 8050, pp. 109–155. Springer, Heidelberg (2013) 13. : Normal design algebra. The Journal of Logic and Algebraic Programming 79(2), 144–173 (2010) 14. : Communicating Sequential Processes. Prentice-Hall (1985) 15. : Unifying Theories of Programming. Prentice-Hall (1998) 16. : Lifting and transfer: a modular design for quotients in Isabelle/HOL. , Norrish, M. ) CPP 2013. LNCS, vol. 8307, pp. 131–146. Springer, Heidelberg (2013) 17.
UTP is based on the alphabetised predicate calculus, and so its mechanisation requires a semantic model in which the predicate operators can be denoted. Moreover to allow generic theory composition, it must be possible to compose predicates with different alphabets. A common predicate model used since the earliest embeddings of Z in HOL is the binding set [3], where a binding is a mapping from variables to values. g. x > 1 = {x → 2, x → 3, · · · }. This approach is used by both ProofPower-Z UTP and Isabelle/Circus.