Floyd's principle, correctness theories and program equivalence

A programming system is a language made from a fixed class of data abstractions and a selection of familiar deterministic control and assignment constructs. It is shown that the sets of all ‘before-after’ first-order assertions which are true of programs in any such language can uniquely determine the input-output semantics of the language providing one allows the use of auxiliary operators on its ground types. After this, we study programming systems wherein the data types are syntactically defined using a first-order specification language with the objective of eliminating these auxiliary operators. Especial attention is paid to algebraic specifications, complete first-order specifications; and to arithmetical computation in the context of a specified programming system