Your chance to submit to a Festschrift for David Turner.
- Joy of Coding, 17 June 2016, De Doelen, Rotterdam; keynote speaker.
- ACSD, 22—24 June 2016, Torun; keynote speaker.
- BETTY Summer School, 27 June—1 July 2016, Limassol, Cyprus; lecturer.
- International Summer School on Metaprogramming, 8—12 August 2016, Cambridge; lecturer.
- Lambda World, 1 October 2016, Cadiz; keynote speaker.
I've just released version 3.0.0, following on from jQuery 3.0.0 a few days ago. This release breaks compatibility with IE6-8, so if that's important to you, insert an upper bound on the package.
Philip Wadler: Papers We Love: John Reynolds, Definitional Interpreters for Higher-Order Programming Languages
I've added online links to the relevant papers (not behind paywalls), copied here.
Papers we love: John Reynolds, Definitional Interpreters for Higher-Order Programming Languages7 June 2016, Skills Matter, London.
Certain papers change your life. McCarthy's 'Recursive Functions of Symbolic Expressions and their Computation by Machine (Part I)' (1960) changed mine, and so did Landin's 'The Next 700 Programming Languages' (1966). And I remember the moment, halfway through my graduate career, when Guy Steele handed me Reynolds's 'Definitional Interpreters for Higher-Order Programming Languages' (1972).
It is now common to explicate the structure of a programming language by presenting an interpreter for that language. If the language interpreted is the same as the language doing the interpreting, the interpreter is called meta-circular.
Interpreters may be written at differing levels of detail, to explicate different implementation strategies. For instance, the interpreter may be written in a continuation-passing style; or some of the higher-order functions may be represented explicitly using data-structures, via defunctionalisation.
More elaborate interpreters may be derived from simpler versions, thus providing a methodology for discovering an implementation strategy and showing it correct. Each of these techniques has become a mainstay of the study of programming languages, and all of them were introduced in this single paper by Reynolds.
- John Reynolds, Definitional Interpreters for Higher-Order Programming Languages, 1972.
- John Reynolds, Definitional Interpreters for Higher-Order Programming Languages, 1998.
- John Reynolds, Definitional Interpreters Revisited, 1998.
- John Reynolds, The Discoveries of Continuations, 1993.
- John McCarthy, Recursive Functions of Symbolic Expressions and Their Computation by Machine, Part I, 1960.
- John McCarthy, Towards a Mathematical Science of Computation, 1962.
- Peter Landin, The Next 700 Programming Languages, 1966.
- Gordon Plotkin, Call-by-value, Call-by-name, and the Lambda Calculus, 1975.
- Robin Milner, A Theory of Type Polymorphism in Programming, 1978.
- Fermin Reig, ed, Reminiscences of Influential Papers, SIGPLAN Notices, 38(12):9—10, December 2003.
Set-Theoretic Types for Polymorphic Variants by Giuseppe Castagna, Tommaso Petrucciani, and Kim Nguyễn:
Polymorphic variants are a useful feature of the OCaml language whose current definition and implementation rely on kinding constraints to simulate a subtyping relation via unification. This yields an awkward formalization and results in a type system whose behaviour is in some cases unintuitive and/or unduly restrictive.
In this work, we present an alternative formalization of polymorphic variants, based on set-theoretic types and subtyping, that yields a cleaner and more streamlined system. Our formalization is more expressive than the current one (it types more programs while preserving type safety), it can internalize some meta-theoretic properties, and it removes some pathological cases of the current implementation resulting in a more intuitive and, thus, predictable type system. More generally, this work shows how to add full-fledged union types to functional languages of the ML family that usually rely on the Hindley-Milner type system. As an aside, our system also improves the theory of semantic subtyping, notably by proving completeness for the type reconstruction algorithm.
Looks like a nice result. They integrate union types and restricted intersection types for complete type inference, which prior work on CDuce could not do. The disadvantage is that it does not admit principal types, and so inference is non-deterministic (see section 5.3.2).
I have been pretty quiet on the blog in the past couple of months. One of the reasons for this is that I have spent most of my time learning Coq. I had my first contact with Coq well over a year ago when I started reading CPDT. Back then I only wanted to learn the basics of Coq to see how it works and what it has to offer compared to other languages with dependent types. This time I wanted to apply Coq to some ideas I had at work, so I was determined to be much more thorough in my learning. Coq is far from being a mainstream language but nevertheless it has some really good learning resources. Today I would like to present a brief overview of what I believe are the three most important books on Coq: “Interactive Theorem Proving and Program Development. Coq’Art: The Calculus of Inductive Constructions” (which I will briefly refer to as Coq’Art) by Yves Bertot and Pierre Castéran, “Certified Programming with Dependent Types” (CPDT) by Adam Chlipala and “Software Foundations” (SF for short) by Benjamin Pierce and over a dozen over contributors. All three books significantly differ in their scope and focus. CPDT and Coq’Art are standard, printed books. CPDT is also available online for free. Software Foundations is only available as an online book. Interestingly, there is also a version of SF that seems to be in the process of being revised.
I believe Coq’Art was the first book published on Coq. There are two editions – 2004 hardcover version and a 2010 paperback version – but as far as I know there are no differences between them. Too bad the 2010 edition was not updated for the newest versions of Coq – some of the code examples don’t work in the newest compiler. Coq’Art takes a theoretical approach, ie. it teaches Coq largely by explaining how the rules of Calculus of Constructions work. There are also practical elements like case studies and exercises but they do not dominate the book. Personally I found Coq’Art to be a very hard read. Not because it dives too much in theory – it doesn’t – but because the presentation seems to be chaotic. For example, description of a single tactic can be spread throughout deveral places in the book. In principle, I don’t object to extending earlier presentation with new details once the reader gets a hold of some new concepts, but I feel that Coq’Art definitely goes too far. Coq’Art also presents material in a very unusual order. Almost every introduction to Coq or any other functional language begins with defining data types. Coq’Art introduces them in chapter 6. On the other hand sorts and universes – something I would consider an advanced concept for anyone who is not familiar with type-level programming – are presented in the second chapter. (Note that first chapter is a very brief overview of the language.) By contrast, CPDT goes into detailed discussion of universes in chapter 12 and SF does not seem to cover them at all. Overall, Coq’Art is of limited usefulness to me. To tell the truth this is not because of its focus on theory rather than practice, but because of language style, which I find rather inaccessible. Many times I had problems understanding passages I was reading, forcing me to re-read them again and again, trying to figure out what is the message that the authors are trying to convey. I did not have such problems with CPDT, SF, nor any other book I have read in the past few years. At the moment I have given up on the idea of reading the book from cover to cover. Nevertheless I find Coq’Art a good supplementary reading for SF. Most importantly because of the sections that explain in detail the inner workings of various tactics.
As mentioned at the beginning, I already wrote a first impressions post about CPDT. Back then I said the book “is a great demonstration of what can be done in Coq but not a good explanation of how it can be done”. Having read all of it I sustain my claim. CPDT does not provide a thorough and systematic coverage of basics, but instead focuses on advanced topics. As such, it is not the best place to start for beginners but it is a priceless resource for Coq practitioners. The main focus of the book is proof automation with Ltac, Coq’s language for writing automated proof procedures. Reader is exposed to Ltac early on in the book, but detailed treatment of Ltac is delayed until chapter 14. Quite surprisingly, given that it is hard to understand earlier chapters without knowing Ltac. Luckily, the chapters are fairly independent of each other and can be read in any order the reader wishes. Definitely it is worth to dive into chapter 14 and fragments of apter 13 as early as possible – it makes understanding the book a whole lot easier. So far I have already read chapter 14 three times. As I learn Coq more and more I discover new bits of knowledge with each read. In fact, I expect to be going back regularly to CPDT.
Coq’Art and CPDT approach teaching Coq in totally different ways. It might then be surprising that Software Foundations uses yet another approach. Unlike Coq’Art it is focused on practice and unlike CPDT it places a very strong emphasis on learning the basics. I feel that SF makes Coq learning curve as flat as possible. The main focus of SF is applying Coq to formalizing programming languages semantics, especially their type systems. This should not come as a big surprise given that Benjamin Pierce, the author of SF, authored also “Types and Programming Languages” (TAPL), the best book on the topic of type systems and programming language semantics I have seen. It should not also be surprising that a huge chunk of material overlaps between TAPL and SF. I find this to be amongst the best things about SF. All the proofs that I read in TAPL make a lot more sense to me when I can convert them to a piece of code. This gives me a much deeper insight into the meaning of lemmas and theorems. Also, when I get stuck on an exercise I can take a look at TAPL to see what is the general idea behind the proof I am implementing.
SF is packed with material and thus it is a very long read. Three months after beginning the book and spending with it about two days a week I am halfway through. The main strength of SF is a plethora of exercises. (Coq’Art has some exercises, but not too many. CPDT has none). They can take a lot of time – and I really mean a lot – but I think this is the only way to learn a programming language. Besides, the exercises are very rewarding. One downside of the exercises is that the book provides no solutions, which is bad for self-studying. Moreover, the authors ask people not to publish the solutions on the internet, since “having solutions easily available makes [SF] much less useful for courses, which typically have graded homework assignments”. That being said, there are plenty of github repositories that contain the solved exercises (I also pledge guilty!). Although it goes against the authors’ will I consider it a really good thing for self-study: many times I have been stuck on exercises and was able to make progress only by peeking at someone else’s solution. This doesn’t mean I copied the solutions. I just used them to overcome difficulties and in some cases ended up with proofs more elegant than the ones I have found. As a side note I’ll add that I do not share the belief that publishing solutions on the web makes SF less useful for courses. Students who want to cheat will get the solutions from other students anyway. At least that has been my experience as an academic teacher.
To sum up, each of the books presents a different approach. Coq’Art focuses on learning Coq by understanding its theoretical foundations. SF focuses on learning Coq through practice. CPDT focuses on advanced techniques for proof automation. Personally, I feel I’ve learned the most from SF, with CPDT closely on the second place. YMMV