We show how the binary encoding and decoding of typed data and typed programs can be understood, programmed and verified with the help of question–answer games. The encoding of a value is determined by the yes/no answers to a sequence of questions about that value; conversely, decoding is the interpretation of binary data as answers to the same question scheme. We introduce a general framework for writing and verifying game-based codecs. We present games in Haskell for structured, recursive, polymorphic and indexed types, building up to a representation of well-typed terms in the simply-typed λ-calculus with polymorphic constants. The framework makes novel use of isomorphisms between types in the definition of games. The definition of isomorphisms together with additional simple properties make it easy to prove that codecs derived from games never encode two distinct values using the same code, never decode two codes to the same value and interpret any bit sequence as a valid code for a value or as a prefix of a valid code. Formal properties of the framework have been proved using the Coq proof assistant.

My main reason for wanting to read this book was to find out what a well-known publicist from the world of OO would have to say about the state of the art of domain specific languages (DSLs), in particular when it comes to type error feedback, functional programming, and the combination. As most readers will be aware, languages like Scheme and Haskell are very well suited to embed DSLs in: Scheme can be considered a core language to which new language facilities can be easily added by means of hygienic syntax macro's (Abelson et al. 1998), and there are so many papers on embedded DSLs in Haskell (Hudak, 1998), that any realistic selection would aggravate more people than I would please. Great was my disappointment when I read on page XXV that these topics were not discussed at all in the book. Although I can imagine that Fowler does not feel comfortable writing about subjects he is not sufficiently at home with, the question does arise whether the title of this book is sufficiently covered by its contents.

A new version of a special-purpose processor for running lazy functional programs is presented. This processor – the Reduceron – exploits parallel memories and dynamic analyses to increase evaluation speed, and is implemented using reconfigurable hardware. Compared to a more conventional functional language implementation targeting a standard RISC processor running on the same reconfigurable hardware, the Reduceron offers a significant improvement in run-time performance.

Atoms and de Bruijn indices are two well-known representation techniques for data structures that involve names and binders. However, using either technique, it is all too easy to make a programming error that causes one name to be used where another was intended. We propose an abstract interface to names and binders that rules out many of these errors. This interface is implemented as a library in Agda. It allows defining and manipulating term representations in nominal style and in de Bruijn style. The programmer is not forced to choose between these styles: on the contrary, the library allows using both styles in the same program, if desired. Whereas indexing the types of names and terms with a natural number is a well-known technique to better control the use of de Bruijn indices, we index types with worlds. Worlds are at the same time more precise and more abstract than natural numbers. Via logical relations and parametricity, we are able to demonstrate in what sense our library is safe, and to obtain theorems for free about world-polymorphic functions. For instance, we prove that a world-polymorphic term transformation function must commute with any renaming of the free variables. The proof is entirely carried out in Agda.

We describe a derivational approach to abstract interpretation that yields novel and transparently sound static analyses when applied to well-established abstract machines for higher-order and imperative programming languages. To demonstrate the technique and support our claim, we transform the CEK machine of Felleisen and Friedman (Proc. of the 14th ACM SIGACT-SIGPLAN Symp. Prin. Program. Langs, 1987, pp. 314–325), a lazy variant of Krivine's machine (Higher-Order Symb. Comput. Vol 20, 2007, pp. 199–207), and the stack-inspecting CM machine of Clements and Felleisen (ACM Trans. Program. Lang. Syst. Vol 26, 2004, pp. 1029–1052) into abstract interpretations of themselves. The resulting analyses bound temporal ordering of program events; predict return-flow and stack-inspection behavior; and approximate the flow and evaluation of by-need parameters. For all of these machines, we find that a series of well-known concrete machine refactorings, plus a technique of store-allocated continuations, leads to machines that abstract into static analyses simply by bounding their stores. These machines are parameterized by allocation functions that tune performance and precision and substantially expand the space of analyses that this framework can represent. We demonstrate that the technique scales up uniformly to allow static analysis of realistic language features, including tail calls, conditionals, mutation, exceptions, first-class continuations, and even garbage collection. In order to close the gap between formalism and implementation, we provide translations of the mathematics as running Haskell code for the initial development of our method.