This paper suggests that input and output are basic primitives of programming and that parallel composition of communicating sequential processes is a fundamental program structuring method. When combined with a development of Dijkstra's guarded command, these concepts are surprisingly versatile. Their use is illustrated by sample solutions of a variety of a familiar programming exercises.

/pdf/communicating-sequential-processes-2j6tdrg5nx.pdf

Communicating sequential processes

https://www.inf.ed.ac.uk/teaching/courses/seoc/2005_2006/resources/statecharts.pdf

Statecharts: A visual formalism for complex systems

https://cmi.ac.in/~madhavan/courses/verification-2011/alur-dill-tcs-94.pdf

A theory of timed automata

A program denotes computations in some universe of objects. Abstract interpretation of programs consists in using that denotation to describe computations in another universe of abstract objects, so that the results of abstract execution give some information on the actual computations. An intuitive example (which we borrow from Sintzoff [72]) is the rule of signs. The text -1515 * 17 may be understood to denote computations on the abstract universe {(+), (-), (±)} where the semantics of arithmetic operators is defined by the rule of signs. The abstract execution -1515 * 17 → -(+) * (+) → (-) * (+) → (-), proves that -1515 * 17 is a negative number. Abstract interpretation is concerned by a particular underlying structure of the usual universe of computations (the sign, in our example). It gives a summary of some facets of the actual executions of a program. In general this summary is simple to obtain but inaccurate (e.g. -1515 + 17 → -(+) + (+) → (-) + (+) → (±)). Despite its fundamentally incomplete results abstract interpretation allows the programmer or the compiler to answer questions which do not need full knowledge of program executions or which tolerate an imprecise answer, (e.g. partial correctness proofs of programs ignoring the termination problems, type checking, program optimizations which are not carried in the absence of certainty about their feasibility, …).

/pdf/abstract-interpretation-a-unified-lattice-model-for-static-2jfaix0dre.pdf

Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints

A unified approach to program verification is suggested, which applies to both sequential and parallel programs. The main proof method suggested is that of temporal reasoning in which the time dependence of events is the basic concept. Two formal systems are presented for providing a basis for temporal reasoning. One forms a formalization of the method of intermittent assertions, while the other is an adaptation of the tense logic system Kb, and is particularly suitable for reasoning about concurrent programs.

The temporal logic of programs

Unifying theories: a personal statement

Towards the Verifying Compiler.

It was my early experience in industry that triggered my interest in assertions and their in-program proofs; and my subsequent research at university extended the idea into a methodology for the specification and design of programs. Now that I have returned to work in industry, I have looked into the current role of assertions in industrial program development. My personal perspective illustrates the complementary roles of pure research, aimed at academic ideals of excellence, and the unexpected ways in which the results of such research contribute to the gradual improvement of engineering practice.

Assertions: a personal perspective

A theory of programming provides a scientific basis for programming practices that lead to predictable delivery of programs of high quality. A top-down theory starts with a specification of the intended behaviour of a program; and a bottom-up theory starts with a description of how the program is executed. The aim of both theories is to prove theorems (often algebraic laws) that will be helpful in the design, development, compilation, testing, optimisation and maintainance of all kinds of program. The most mature theories are those that are presented both in bottom-up and top-down fashion, where essentially the same laws are valid in both presentations.

C. A. R. Hoare

Papers

Unifying theories: a personal statement

Towards the Verifying Compiler.

Assertions: a personal perspective

Theories of Programming: Top-Down and Bottom-Up and Meeting in the Middle

Let's make models