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Programs are Predicates [and Discussion]
C. A. R. Hoare and F. K. Hanna
Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
Vol. 312, No. 1522, Mathematical Logic and Programming Languages [Displayed chronologically; published out of order] (Oct. 1, 1984), pp. 475-489
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/37446
Page Count: 15
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A computer program is identified with the strongest predicate describing every relevant observation that can be made of the behaviour of a computer executing that program. A programming language is a subset of logical and mathematical notations, which is so restricted that products described in the language can be automatically implemented on a computer. The notations enjoy a number of elegant algebraic properties, which can be used for optimizing program efficiency. A specification is a predicate describing all permitted observations of a program, and it may be expressed with greatest clarity by taking advantage of the whole language of logic and mathematics. A program P meets its specification S iff [Note: Equation omitted. See the image of page 475 for this equation.]. The proof of this implication may use all the classical methods of mathematics and logic. These points are illustrated by design of a small language that includes assignments, conditionals, non-determinism, recursion, input, output, and concurrency.
Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences © 1984 Royal Society