Modelling the algebra of weakest preconditions

In expounding the notions of pre- and postconditions, of termination and nontermination, of correctness and of predicate transformers I found that the same trivalent distinction played a major role in all contexts. Namely: Initialisation properties: An execution of a program always, sometimes or never starts from an initial state. Termination/nontermination properties: If it starts, the execution always, sometimes or never terminates. Clean-/messy termination properties: A terminating execution always, sometimes or never terminates cleanly. Final state properties: All, some or no final states of α from s have a given property

Another characterization of weakest preconditions

We present an approach to the study of nondeterministic programs, consisting essentially in using binary relations as semantic objects representing the input-out-put behaviour of programs. These relations include an explicit representation of non--terminating computations. Based on the relational model we introduce a weakest pre-condition total correctness predicate transformer. We then show how to build up this predicate transformer starting from others of a more e1ementar kind. Fina11y,we obtain a,characterization of its healthiness properties in terms of set-theoretical propert~ ies of the relations involved. 1