Retrospective and Prospective for Unifying Theories of Programming

Abstract

This paper presents a personal account of developments leading to Unifying Theories of Programming, and some opinions about the direction the work should take in the future. It also speculates on consequences the work will have for all of computer science. UTP and meMy introduction to formal methods was the book a Discipline of Programming [2] by Edsger Dijkstra in 1976. I wrote a small contribution in a paper named do considered od [14] in that same year. In that paper I proposed recursive refinement as a way of composing programs, and a different way of generating the sequence of approximations for loop semantics that is more general than the one in Dijkstra's book, applying to all looping constructs, including general recursion.It was standard in semantics work then (and for some people, it remains so today) to use a meaning function (sometimes written as double square brackets) that maps program text to its meaning. In Dijkstra's book, he used the wp function to map a program text and postcondition to a precondition. If S is some program text, and R is a postcondition, then wp(S, R) is the exact precondition for execution of 1 S to terminate and establish postcondition R . In my 1976 paper, I made the The English meaning of "precondition" is "something that is necessary 1 beforehand". Dijkstra was using it to mean "something that is sufficient beforehand". In Dijkstra's use, the "weakest precondition" wp was the weakest sufficient condition, i.e. the necessary and sufficient condition. To avoid misusing the word "precondition", I am saying "exact precondition" to mean the condition that is both necessary and sufficient.

Unifying Theories of Programming That Distinguish Nontermination and Abort

“…In a timed design one can place specific requirements on the final time τ , whereas in an extended design one can only refer to termination (term ), which effectively abstracts all finite restrictions of τ in a timed design simply to τ = ∞. Timed designs making use of abstract time are closely related to Hehner's timed models [10,28,29].…”

“…To discuss timing issues one can introduce an observation representing the current time, as done by Hehner [10,28,29] and Abadi and Lamport [30]. An extended design can be generalised to a timed design by replacing the observations term and term by the observations τ and τ , representing the initial and final times, respectively.…”

Contracts in CML

“…It can be described as follows: researchers propose programming theories and practitioners use pragmatic programming paradigms; what is the relationship between them? UTP, based on predicative programming [23], gives three principal ways to study such relationships: (i) by computational paradigm, identifying common concepts; (ii) by level of abstraction, from requirements, through architectures and components, to platform-specic implementation technologies; and (iii) by method of presentationnamely, denotational, algebraic, and operational semanticsand their mutual embeddings.…”

Unifying Theories of Programming in Isabelle

“…UTP can trace its origins back to the work on predicative programming, which was started by Hehner; see [12] for a summary. It gives three principal ways to study such relationships: (i) by computational paradigm; (ii) by level of abstraction; and (iii) by method of presentation.…”