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

In this paper an attempt is made to explore the logical foundations of computer programming by use of techniques which were first applied in the study of geometry and have later been extended to other branches of mathematics. This involves the elucidation of sets of axioms and rules of inference which can be used in proofs of the properties of computer programs. Examples are given of such axioms and rules, and a formal proof of a simple theorem is displayed. Finally, it is argued that important advantages, both theoretical and practical, may follow from a pursuance of these topics.

/pdf/an-axiomatic-basis-for-computer-programming-e3ajn2qiu2.pdf

An axiomatic basis for computer programming

This paper develops Brinch-Hansen's concept of a monitor as a method of structuring an operating system. It introduces a form of synchronization, describes a possible method of implementation in terms of semaphores and gives a suitable proof rule. Illustrative examples include a single resource scheduler, a bounded buffer, an alarm clock, a buffer pool, a disk head optimizer, and a version of the problem of readers and writers.

/pdf/monitors-an-operating-system-structuring-concept-4uutiz463b.pdf

Monitors: an operating system structuring concept

In recent years there has been an increasing interest in the art of computer programming, the conceptual tools available for the design of programs, and the prevention of programming oversights and error. The initial outstanding contribution to our understanding of this subject was made by E. W. Dijkstra, whose Notes on Structured Programming form the first and major section of this book. They clearly expound the reflections of a brilliant programmer on the methods which he has hitherto unconsciously applied; there can be no programmer of the present day who could not increase his skills by a study and conscious application of these principles.

In the second monograph I have tried to describe how similar principles can be applied in the design of data structures. I have suggested that in analysing a problem and groping towards a solution, a programmer should take advantage of abstract concepts such as sets, sequences, and mappings; and judiciously postpone decisions on representation until he is constructing the more detailed code of the program. The monograph also describes a range of useful ideas for data representation, and suggests the criteria relevant for their selection.

The third monograph provides a synthesis of the previous two, and expounds the close theoretical and practical connections between the design of data and the design of programs. It introduces useful additional methods for program and data structuring which may be unfamiliar to many programmers. The examples show that structured programming principles can be equally applied in "bottom-up" as in "top-down" program design. The original inspiration, insight, and all the examples were contributed by O.-J. Dahl; I have only assembled the material, and added some additional explanations where I found it difficult to understand.

Structured Programming

A mathematical model for communicating sequential processes is given, and a number of its interesting and useful properties are stated and proved. The possibilities of nondetermimsm are fully taken into account.

/pdf/a-theory-of-communicating-sequential-processes-4d19h3zocs.pdf

C. A. R. Hoare

Papers

Communicating sequential processes

An axiomatic basis for computer programming

Monitors: an operating system structuring concept

Structured Programming

A Theory of Communicating Sequential Processes