Common use of Afterwards Clause in Contracts

Afterwards. I wanted to change the direction of my own research towards the investigation of the foundations of separation logic (while continuing collaboration with Xxxxxxx Xxxx on verifying Java libraries, continuing work on the Reowolf project, and continuing teaching Concepts of Programming Languages and Program Correctness). There were several reasons for considering this change of direction: firstly, we received numerous anonymous reviews in response to our earlier articles about Java program verification that mentioned separation logic as related work. Secondly, on several occasions Xxxxx indicated he was a contrarian in this subfield, of separation logic, so I was inclined to become a meta-contrarian1. Lastly, I had many interesting discussions about separation logic during the PhD Day organized by the VvL. Although at that time I had only superficial knowledge, I started to wonder: what the hell is separation logic, really? Already, I had done several years of work of a practical nature, in actual Java program verification, and in the mean time I had learned more about higher-order logic, set theory, model theory, proof theory, and foundational issues in mathematics. Now I wanted to do more work of a theoretical nature in mathematical logic, and continue my work on formalizing Xxxxx’x logic. So I convinced Xxxxx that it was a good idea to investigate separation logic. Our approach would be from a foundational point of view, and my goal was to understand what were the issues in separation logic that Xxxxx refrained from articulating in the past twenty years or so. What emerged was a symbiotic relationship between me and my promotor: I gladly took Xxxxx as a confident oracle, and saw myself as a skeptical verifier. In this period we worked together intensively, often spending many hours a day discussing next to a whiteboard. Also I used the Coq proof assistant to meticulously check my work. But at other times, the roles reversed, and I saw myself as the oracle while Xxxxx was verifying my ‘nonsense’, critically and skeptically questioning my position until we obtained something reasonable. The benefit of our symbiosis was that we discovered many of our own mistakes, that we were able to repair ourselves. As such, I was deeply involved in the discovery, the refinement, the verification, and the presentation of the subject matter that is presented in this thesis. Xxxxx and I collaborated on a 1Thanks to Xxxxxxxx for explaining to me why I am an ‘intellectual hipster’: whereas Xxxxx is a contrarian (i.e. opposing separation logic), I took an opposite position in Frank’s contrariness (thus opposing Frank’s opposition, in defense of separation logic). paper until no longer there would be any ground to oppose each other, and then we involved my first co-promotor, Xxxxx, to check the intermediate paper—whether what we did made sense. Finally, after this thesis was written, also my second co-promotor, Xxxxxx Xxxxxxx, was involved to check whether the thesis as a whole made sense. I found this way of working to be very productive. <rant> Whereas the collaboration between me and my promotor and co-pro- motors was very productive, I found that there was also a source of counter- productivity: the anonymous reviewers of our articles about separation logic. As mentioned earlier, we had structured our collaboration by means of writing articles that were submitted for presentation at several conferences. However, that last part, submission to conferences and subjecting our articles to objective anonymous reviewers, was severely frustrating our productivity. Contrary to the positive symbiotic relation between me and my promotor, I had experienced the relation between me and my anonymous reviewers as negative, even alienating. It felt I was in a toxic burn pit that slowly burned me out. The epitome of toxicity was when a reviewer was rejecting, insistingly, our article on the basis of a counter-example to our result, that was also a counter-example to G¨odel’s completeness theorem! Communication with anonymous reviewers was very limited and the reviewers did not respond to requests to discuss the matter further.</rant> In an attempt to prevent any confusion about what the background material is, I spent several months writing the appendix. In the end, I am deeply indebted to Xxxxx for his encouragement: to continue to defend these new foundations for separation logic, and to regard less of negative and discouraging comments by anonymous reviewers. I am also delighted by the fact that Xxxxx and Xxxxxx were always able to give useful and constructive feedback on papers or this thesis. I am grateful to all the members of the PhD committee for reading a preliminary version of this thesis and giving valuable feedback that has lead to an improved and final version. x

Afterwards. I wanted to change the direction of my own research towards the investigation of the foundations of separation logic (while continuing collaboration with Xxxxxxx Xxxx on verifying Java libraries, continuing work on the Reowolf project, and continuing teaching Concepts of Programming Languages and Program Correctness). There were several reasons for considering this change of direction: firstly, we received numerous anonymous reviews in response to our earlier articles about Java program verification that mentioned separation logic as related work. Secondly, on several occasions Xxxxx indicated he was a contrarian in this subfield, of separation logic, so I was inclined to become a meta-contrarian1. Lastly, I had many interesting discussions about separation logic during the PhD Day organized by the VvL. Although at that time I had only superficial knowledge, I started to wonder: what the hell is separation logic, really? Already, I had done several years of work of a practical nature, in actual Java program verification, and in the mean time I had learned more about higher-order logic, set theory, model theory, proof theory, and foundational issues in mathematics. Now I wanted to do more work of a theoretical nature in mathematical logic, and continue my work on formalizing Xxxxx’x logic. So I convinced Xxxxx that it was a good idea to investigate separation logic. Our approach would be from a foundational point of view, and my goal was to understand what were the issues in separation logic that Xxxxx refrained from articulating in the past twenty years or so. What emerged was a symbiotic relationship between me and my promotor: I gladly took Xxxxx as a confident oracle, and saw myself as a skeptical verifier. In this period we worked together intensively, often spending many hours a day discussing next to a whiteboard. Also I used the Coq proof assistant to meticulously check my work. But at other times, the roles reversed, and I saw myself as the oracle while Xxxxx was verifying my ‘nonsense’, critically and skeptically questioning my position until we obtained something reasonable. The benefit of our symbiosis was that we discovered many of our own mistakes, that we were able to repair ourselves. As such, I was deeply involved in the discovery, the refinement, the verification, and the presentation of the subject matter that is presented in this thesis. Xxxxx and I collaborated on a 1Thanks to Xxxxxxxx for explaining to me why I am an ‘intellectual hipster’: whereas Xxxxx is a contrarian (i.e. opposing separation logic), I took an opposite position in Frank’s contrariness (thus opposing Frank’s opposition, in defense of separation logic). paper until no longer there would be any ground to oppose each other, and then we involved my first co-promotor, Xxxxx, to check the intermediate paper—whether what we did made sense. Finally, after this thesis was written, also my second co-promotor, Xxxxxx Xxxxxxx, was involved to check whether the thesis as a whole made sense. I found this way of working to be very productive. <rant> Whereas the collaboration between me and my promotor and co-pro- motors was very productive, I found that there was also a source of counter- productivity: the anonymous reviewers of our articles about separation logic. As mentioned earlier, we had structured our collaboration by means of writing articles that were submitted for presentation at several conferences. However, that last part, submission to conferences and subjecting our articles to objective anonymous reviewers, was severely frustrating our productivity. Contrary to the positive symbiotic relation between me and my promotor, I had experienced the relation between me and my anonymous reviewers as negative, even alienating. It felt I was in a toxic burn pit that slowly burned me out. The epitome of toxicity was when a reviewer was rejecting, insistingly, our article on the basis of a counter-example to our result, that was also a counter-example to G¨odel’s completeness theorem! Communication with anonymous reviewers was very limited and the reviewers did not respond to requests to discuss the matter further.</rant> In an attempt to prevent any confusion about what the background material is, I spent several months writing the appendix. In the end, I am deeply indebted to Xxxxx for his encouragement: to continue to defend these new foundations for separation logic, and to regard less of negative and discouraging comments by anonymous reviewers. I am also delighted by the fact that Xxxxx and Xxxxxx were always able to give useful and constructive feedback on papers or this thesis. I am grateful to all the members of the PhD committee for reading a preliminary version of this thesis and giving valuable feedback that has lead to an improved and final version. x.

Afterwards. I wanted to change the direction of my own research towards the investigation of the foundations of separation logic (while continuing collaboration with Xxxxxxx Xxxx on verifying Java libraries, continuing work on the Reowolf project, and continuing teaching Concepts of Programming Languages and Program Correctness). There were several reasons for considering this change of direction: firstly, we received numerous anonymous reviews in response to our earlier articles about Java program verification that mentioned separation logic as related work. Secondly, on several occasions Xxxxx indicated he was a contrarian in this subfield, of separation logic, so I was inclined to become a meta-contrarian1. Lastly, I had many interesting discussions about separation logic during the PhD Day organized by the VvL. Although at that time I had only superficial knowledge, I started to wonder: what the hell is separation logic, really? Already, I had done several years of work of a practical nature, in actual Java program verification, and in the mean time I had learned more about higher-order logic, set theory, model theory, proof theory, and foundational issues in mathematics. Now I wanted to do more work of a theoretical nature in mathematical logic, and continue my work on formalizing Xxxxx’x logic. So I convinced Xxxxx that it was a good idea to investigate separation logic. Our approach would be from a foundational point of view, and my goal was to understand what were the issues in separation logic that Xxxxx refrained from articulating in the past twenty years or so. What emerged was a symbiotic relationship between me and my promotor: I gladly took Xxxxx as a confident oracle, and saw myself as a skeptical verifier. In this period we worked together intensively, often spending many hours a day discussing next to a whiteboard. Also I used the Coq proof assistant to meticulously check my work. But at other times, the roles reversed, and I saw myself as the oracle while Xxxxx was verifying my ‘nonsense’, critically and skeptically questioning my position until we obtained something reasonable. The benefit of our symbiosis was that we discovered many of our own mistakes, that we were able to repair ourselves. As such, I was deeply involved in the discovery, the refinement, the verification, and the presentation of the subject matter that is presented in this thesis. Xxxxx and I collaborated on a 1Thanks to Xxxxxxxx for explaining to me why I am an ‘intellectual hipster’: whereas Xxxxx is a contrarian (i.e. opposing separation logic), I took an opposite position in Frank’s Xxxxx’x contrariness (thus opposing Frank’s Xxxxx’x opposition, in defense of separation logic). paper until no longer there would be any ground to oppose each other, and then we involved my first co-promotor, Xxxxx, to check the intermediate paper—whether what we did made sense. Finally, after this thesis was written, also my second co-promotor, Xxxxxx Xxxxxxx, was involved to check whether the thesis as a whole made sense. I found this way of working to be very productive. <rant> Whereas the collaboration between me and my promotor and co-pro- motors was very productive, I found that there was also a source of counter- productivity: the anonymous reviewers of our articles about separation logic. As mentioned earlier, we had structured our collaboration by means of writing articles that were submitted for presentation at several conferences. However, that last part, submission to conferences and subjecting our articles to objective anonymous reviewers, was severely frustrating our productivity. Contrary to the positive symbiotic relation between me and my promotor, I had experienced the relation between me and my anonymous reviewers as negative, even alienating. It felt I was in a toxic burn pit that slowly burned me out. The epitome of toxicity was when a reviewer was rejecting, insistingly, our article on the basis of a counter-example to our result, that was also a counter-example to G¨odel’s completeness theorem! Communication with anonymous reviewers was very limited and the reviewers did not respond to requests to discuss the matter further.</rant> In an attempt to prevent any confusion about what the background material is, I spent several months writing the appendix. In the end, I am deeply indebted to Xxxxx for his encouragement: to continue to defend these new foundations for separation logic, and to regard less of negative and discouraging comments by anonymous reviewers. I am also delighted by the fact that Xxxxx and Xxxxxx were always able to give useful and constructive feedback on papers or this thesis. I am grateful to all the members of the PhD committee for reading a preliminary version of this thesis and giving valuable feedback that has lead to an improved and final version. x.