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.

Since the summer of 1973, when I became a Burroughs Research Fellow, my life has been very different from what it had been before. The daily routine changed: instead of going to the University each day, where I used to spend most of my time in the company of others, I now went there only one day a week and was most of the time -that is, when not travelling!- alone in my study. In my solitude, mail and the written word in general became more and more important. The circumstance that my employer and I had the Atlantic Ocean between us was a further incentive to keep a fairly complete record of what I was doing. The public part of that output found its place in what became known as "the EWD series", which can be viewed as a form of scientific correspondence, possible since the advent of the copier. (That same copier makes it hard to estimate its actual distribution: I myself made about two dozen copies of my texts, but their recipients were welcome to act as further nodes of the distribution tree. ) The decision to publish a se1ection from the EWD series in book form was at first highly embarrassing, but as the months went by I got used to the idea. As soon as some guiding principles had been adopted -preferably not published elsewhere, as varied and as representative as possible, etc.

Since the summer of 1973, when I became a Burroughs Research Fellow, my life has been very different from what it had been before. The daily routine changed: instead of going to the University each day, where I used to spend most of my time in the company of others, I now went there only one day a week and was most of the time -that is, when not travelling!- alone in my study. In my solitude, mail and the written word in general became more and more important. The circumstance that my employer and I had the Atlantic Ocean between us was a further incentive to keep a fairly complete record of what I was doing. The public part of that output found its place in what became known as "the EWD series", which can be viewed as a form of scientific correspondence, possible since the advent of the copier. (That same copier makes it hard to estimate its actual distribution: I myself made about two dozen copies of my texts, but their recipients were welcome to act as further nodes of the distribution tree. ) The decision to publish a se1ection from the EWD series in book form was at first highly embarrassing, but as the months went by I got used to the idea. As soon as some guiding principles had been adopted -preferably not published elsewhere, as varied and as representative as possible, etc.

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.

Since the summer of 1973, when I became a Burroughs Research Fellow, my life has been very different from what it had been before. The daily routine changed: instead of going to the University each day, where I used to spend most of my time in the company of others, I now went there only one day a week and was most of the time -that is, when not travelling!- alone in my study. In my solitude, mail and the written word in general became more and more important. The circumstance that my employer and I had the Atlantic Ocean between us was a further incentive to keep a fairly complete record of what I was doing. The public part of that output found its place in what became known as "the EWD series", which can be viewed as a form of scientific correspondence, possible since the advent of the copier. (That same copier makes it hard to estimate its actual distribution: I myself made about two dozen copies of my texts, but their recipients were welcome to act as further nodes of the distribution tree. ) The decision to publish a se1ection from the EWD series in book form was at first highly embarrassing, but as the months went by I got used to the idea. As soon as some guiding principles had been adopted -preferably not published elsewhere, as varied and as representative as possible, etc.

Since the summer of 1973, when I became a Burroughs Research Fellow, my life has been very different from what it had been before. The daily routine changed: instead of going to the University each day, where I used to spend most of my time in the company of others, I now went there only one day a week and was most of the time -that is, when not travelling!- alone in my study. In my solitude, mail and the written word in general became more and more important. The circumstance that my employer and I had the Atlantic Ocean between us was a further incentive to keep a fairly complete record of what I was doing. The public part of that output found its place in what became known as "the EWD series", which can be viewed as a form of scientific correspondence, possible since the advent of the copier. (That same copier makes it hard to estimate its actual distribution: I myself made about two dozen copies of my texts, but their recipients were welcome to act as further nodes of the distribution tree. ) The decision to publish a se1ection from the EWD series in book form was at first highly embarrassing, but as the months went by I got used to the idea. As soon as some guiding principles had been adopted -preferably not published elsewhere, as varied and as representative as possible, etc.