Answer-Type Modification without Tears: Prompt-Passing Style Translation for Typed Delimited-Control Operators

The salient feature of delimited-control operators is their ability to modify answer types during computation. The feature, answer-type modification (ATM for short), allows one to express various interesting programs such as typed printf compactly and nicely, while it makes it difficult to embed these operators in standard functional languages. In this paper, we present a typed translation of delimited-control operators shift and reset with ATM into a familiar language with multi-prompt shift and reset without ATM, which lets us use ATM in standard languages without modifying the type system. Our translation generalizes Kiselyov's direct-style implementation of typed printf, which uses two prompts to emulate the modification of answer types, and passes them during computation. We prove that our translation preserves typing. As the naive prompt-passing style translation generates and passes many prompts even for pure terms, we show an optimized translation that generate prompts only when needed, which is also type-preserving. Finally, we give an implementation in the tagless-final style which respects typing by construction.Comment: In Proceedings WoC 2015, arXiv:1606.0583

Typeful Normalization by Evaluation

We present the first typeful implementation of Normalization by Evaluation for the simply typed lambda-calculus with sums and control operators: we guarantee type preservation and eta-long (modulo commuting conversions), beta-normal forms using only Generalized Algebraic Data Types in a general-purpose programming language, here OCaml; and we account for sums and control operators with Continuation-Passing Style. First, we implement the standard NbE algorithm for the implicational fragment in a typeful way that is correct by construction. We then derive its call-by-value continuation-passing counterpart, that maps a lambda-term with sums and call/cc into a CPS term in normal form, which we express in a typed dedicated syntax. Beyond showcasing the expressive power of GADTs, we emphasize that type inference gives a smooth way to re-derive the encodings of the syntax and typing of normal forms in Continuation-Passing Style

Implementing Explicit and Finding Implicit Sharing in Embedded DSLs

Aliasing, or sharing, is prominent in many domains, denoting that two differently-named objects are in fact identical: a change in one object (memory cell, circuit terminal, disk block) is instantly reflected in the other. Languages for modelling such domains should let the programmer explicitly define the sharing among objects or expressions. A DSL compiler may find other identical expressions and share them, implicitly. Such common subexpression elimination is crucial to the efficient implementation of DSLs. Sharing is tricky in embedded DSL, since host aliasing may correspond to copying of the underlying objects rather than their sharing. This tutorial summarizes discussions of implementing sharing in Haskell DSLs for automotive embedded systems and hardware description languages. The technique has since been used in a Haskell SAT solver and the DSL for music synthesis. We demonstrate the embedding in pure Haskell of a simple DSL with a language form for explicit sharing. The DSL also has implicit sharing, implemented via hash-consing. Explicit sharing greatly speeds up hash-consing. The seemingly imperative nature of hash-consing is hidden beneath a simple combinator language. The overall implementation remains pure functional and easy to reason about.Comment: In Proceedings DSL 2011, arXiv:1109.032