Predicate Calculus and Program Semantics

1. Front Matter

   Pages i-xi

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2. On structures

   • Edsger W. Dijkstra, Carel S. Schotten

   Pages 1-9

3. On substitution and replacement

   • Edsger W. Dijkstra, Carel S. Scholten

   Pages 11-16

4. On functions and equality

   • Edsger W. Dijkstra, Carel S. Schotten

   Pages 17-20

5. On our proof format

   • Edsger W. Dijkstra, Carel S. Scholten

   Pages 21-29

6. The calculus of boolean structures

   • Edsger W. Dijkstra, Carel S. Schölten

   Pages 30-80

7. Some properties of predicate transformers

   • Edsger W. Dijkstra, Carel S. Scholten

   Pages 81-120

8. Semantics of straight-line programs

   • Edsger W. Dijkstra, Carel S. Schölten

   Pages 121-146

9. Equations in predicates and their extreme solutions

   • Edsger W. Dijkstra, Carel S. Schölten

   Pages 147-170

10. Semantics of repetitions

    • Edsger W. Dijkstra, Carel S. Schölten

    Pages 170-189

11. Operational considerations

    • Edsger W. Dijkstra, Carel S. Schölten

    Pages 190-200

12. Converse predicate transformers

    • Edsger W. Dijkstra, Carel S. Schölten

    Pages 201-208

13. The strongest postcondition

    • Edsger W. Dijkstra, Carel S. Schölten

    Pages 209-215

14. Back Matter

    Pages 216-222

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This booklet presents a reasonably self-contained theory of predicate trans­ former semantics. Predicate transformers were introduced by one of us (EWD) as a means for defining programming language semantics in a way that would directly support the systematic development of programs from their formal specifications. They met their original goal, but as time went on and program derivation became a more and more formal activity, their informal introduction and the fact that many of their properties had never been proved became more and more unsatisfactory. And so did the original exclusion of unbounded nondeterminacy. In 1982 we started to remedy these shortcomings. This little monograph is a result of that work. A possible -and even likely- criticism is that anyone sufficiently versed in lattice theory can easily derive all of our results himself. That criticism would be correct but somewhat beside the point. The first remark is that the average book on lattice theory is several times fatter (and probably less self­ contained) than this booklet. The second remark is that the predicate transformer semantics provided only one of the reasons for going through the pains of publication.

• formal specification
• program semantics
• programming language
• semantics

• University of Texas at Austin, Austin, USA

  Edsger W. Dijkstra

• Beekbergen, The Netherlands

  Carel S. Scholten

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