Abstract. Two general techniques for implementing a domain-specific language (DSL) with less overhead are the finally-tagless embedding of object programs and the direct-style representation of side effects. We use these techniques to build a DSL for probabilistic programming, for expressing countable probabilistic models and performing exact inference and importance sampling on them. Our language is embedded as an ordinary OCaml library and represents probability distributions as ordinary OCaml programs. We use delimited continuations to reify probabilistic programs as lazy search trees, which inference algorithms may traverse without imposing any interpretive overhead on deterministic parts of a model. We thus take advantage of the existing OCaml implementation to achieve competitive performance and ease of use. Inference algorithms can easily be embedded in probabilistic programs themselves.

Tony Hoare has always been a leader in writing down and proving properties of programs. To prove properties of programs automatically, the most widely used technology today is by far the ubiquitous type checker. Alas, static type systems inevitably exclude some good programs and allow some bad ones. Thus motivated, we describe some fun we have been having with Haskell, by making the type system more expressive without losing the benefits of automatic proof and compact expression. Specifically, we offer a programmer’s tour of so-called type families, a recent extension to Haskell that allows functions on types to be expressed as straightforwardly as functions on values. This facility makes it easier for programmers to effectively extend the compiler by writing functional programs that execute during type-checking. This paper gives a programmer’s tour of type families as they are supported in GHC. Source code for all the examples is available at

Many loops in probabilistic inference map almost every individual in their domain to the same result. Running such loops symbolically takes time sublinear in the domain size. Using normalization by evaluation with first-class delimited continuations, we lift inference procedures to reap this speed-up without interpretive overhead. To express nested loops, we use multiple control delimiters for metacircular interpretation. To express loops over a powerset domain, we convert nested loops over a subset to unnested loops. 1.

Abstract. Feldspar is a domain specific language, embedded in Haskell, for programming digital signal processing algorithms. The final aim of a Feldspar program is to generate low level code with good performance. Still, we chose to provide the user with a purely functional DSL. The language is implemented as a minimal, deeply embedded core language, with shallow extensions built upon it. This paper presents full details of the essential parts of the implementation. Our initial conclusion is that this approach works well in our domain, although much work remains. 1

We expound a view of type checking as evaluation with ‘abstract values’. Whereas dynamic semantics, evaluation, deals with (dynamic) values like 0, 1, etc., static semantics, type checking, deals with approximations like int. A type system is sound if it correctly approximates the dynamic behavior and predicts its outcome: if the static semantics predicts that a term has the type int, the dynamic evaluation of the term, if it terminates, will yield an integer. As object language, we use simply-typed and let-polymorphic lambda calculi with integers and integer operations as constants. We use Haskell as a metalanguage in which to write evaluators, type checkers, type reconstructors and inferencers for the object language. We explore the deep relation between parametric polymorphism and ‘inlining’. Polymorphic type checking then is an optimization allowing us to type check a polymorphic term at the place of its definition rather than at the places of its use. 1 Introduction: Untyped

Tony Hoare has always been a leader in writing down and proving properties of programs. To prove properties of programs automatically, the most widely used technology today is by far the ubiquitous type checker. Alas, static type systems inevitably exclude some good programs and allow some bad ones. This dilemma motivates us to describe some fun we’ve been having with Haskell, by making the type system more expressive without losing the benefits of automatic proof and compact expression. Haskell’s type system extends Hindley-Milner with two distinctive features: polymorphism over type constructors and overloading using type classes. These features have become integral to Haskell, and they are widely used and appreciated [29]. More recently, Haskell has been enriched with type families [6, 7, 43], which allows functions on types to be expressed as straightforwardly as functions on values. This facility makes it easier for programmers to effectively extend the compiler by writing functional programs that execute during type-checking. This paper gives a programmer’s tour of type families as they are supported in GHC today. This is the second major iteration of our paper. We warmly encourage feedback on this draft, prior to publication. Please add comments to the Wiki page

Code generation is the leading approach to making high-performance software reusable. Effects are indispensable in code generators, whether to report failures or to insert let-statements and ifguards. Extensive painful experience shows that unrestricted effects interact with generated binders in undesirable ways to produce unexpectedly unbound variables, or worse, unexpectedly bound ones. These subtleties prevent experts in the application domain, not in programming languages, from using and extending the generator. A pressing problem is thus to express the desired effects while regulating them so that the generated code is correct, or at least correctly scoped, by construction. In an imminently practical code-generation framework, we show how to express arbitrary effects, including mutable references and delimited control, that move open code across generated binders. The static types of our generator expressions not only ensure that a well-typed generator produces well-typed and well-scoped code, but also express the lexical scopes of generated binders and prevent mixing up variables with different scopes. This precise notion of lexical scope subsumes the complaints about intuitively wrong example generators in the literature. For the first time, we demonstrate statically safe let-insertion across an arbitrary number of binders. Our framework is implemented as a Haskell library that embeds an extensible typed higher-order domain-specific language. It may be regarded as ‘staged Haskell. ’ The library is convenient to use thanks to the maturity of Haskell, higher-order abstract syntax, and polymorphism over generated type environments.

Custom code generation is the leading approach to reconciling generality with performance. MetaOCaml, a dialect of OCaml, is the best-developed way today to write custom code generators and assure them type-safe across multiple stages of computation. Nevertheless, the continuing interest from the community has yet to result in a mature implementation of MetaOCaml that integrates cleanly with OCaml’s type checker and run-time system. Even in theory, it is unclear how staging interacts with effects, polymorphism, and user-defined data types. We report on the status of the ongoing MetaOCaml project, focusing on the gap between theory and practice and the difficulties that arise in a full-featured staged language rather than an idealized calculus. We highlight foundational problems in type soundness and cross-stage persistence that demand investigation. We also suggest a lightweight implementation of a two-stage dialect of OCaml, as syntactic sugar. 1.

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This millennium has seen a great deal of research into embedded domain-specific languages. Primarily, such languages are simplytyped. Focusing on System F, we demonstrate how to embed polymorphic domain specific languages in Haskell and OCaml. We exploit recent language extensions including kind polymorphism and first-class modules. Categories and Subject Descriptors D.3.1 [Programming Languages]: