Floyd's principle, correctness theories and program equivalence

AbstractA 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