Formalizing Implementation Strategies for First-Class Continuations

We present the first formalization of implementation strategies for first-class continuations. The formalization hinges on abstractmachines for continuation-passing style (CPS) programs with a specialtreatment for the current continuation, accounting for the essence offirst-class continuations. These abstract machines are proven equivalentto a standard, substitution-based abstract machine. The proof techniqueswork uniformly for various representations of continuations. As a byproduct, we also present a formal proof of the two folklore theorems that onecontinuation identifier is enough for second-class continuations and thatsecond-class continuations are stackable.A large body of work exists on implementing continuations, but it is predominantly empirical and implementation-oriented. In contrast, our formalization abstracts the essence of first-class continuations and providesa uniform setting for specifying and formalizing their representation

Combining and Relating Control Effects and their Semantics

Combining local exceptions and first class continuations leads to programs with complex control flow, as well as the possibility of expressing powerful constructs such as resumable exceptions. We describe and compare games models for a programming language which includes these features, as well as higher-order references. They are obtained by contrasting methodologies: by annotating sequences of moves with "control pointers" indicating where exceptions are thrown and caught, and by composing the exceptions and continuations monads. The former approach allows an explicit representation of control flow in games for exceptions, and hence a straightforward proof of definability (full abstraction) by factorization, as well as offering the possibility of a semantic approach to control flow analysis of exception-handling. However, establishing soundness of such a concrete and complex model is a non-trivial problem. It may be resolved by establishing a correspondence with the monad semantics, based on erasing explicit exception moves and replacing them with control pointers.Comment: In Proceedings COS 2013, arXiv:1309.092

A Dynamic Continuation-Passing Style for Dynamic Delimited Continuations (Preliminary Version)

We present a new abstract machine that accounts for dynamic delimited continuations. We prove the correctness of this new abstract machine with respect to a definitional abstract machine. Unlike this definitional abstract machine, the new abstract machine is in defunctionalized form, which makes it possible to state the corresponding higher-order evaluator. This evaluator is in continuation+state passing style, and threads a trail of delimited continuations and a meta-continuation. Since this style accounts for dynamic delimited continuations, we refer to it as `dynamic continuation-passing style.' We illustrate that the new machine is more efficient than the definitional one, and we show that the notion of computation induced by the corresponding evaluator takes the form of a monad

A Dynamic Continuation-Passing Style for Dynamic Delimited Continuations

We present a new abstract machine that accounts for dynamic delimited continuations. We prove the correctness of this new abstract machine with respect to a pre-existing, definitional abstract machine. Unlike this definitional abstract machine, the new abstract machine is in defunctionalized form, which makes it possible to state the corresponding higher-order evaluator. This evaluator is in continuation+state passing style and threads a trail of delimited continuations and a meta-continuation. Since this style accounts for dynamic delimited continuations, we refer to it as `dynamic continuation-passing style.' We show that the new machine operates more efficiently than the definitional one and that the notion of computation induced by the corresponding evaluator takes the form of a monad. We also present new examples and a new simulation of dynamic delimited continuations in terms of static ones

Towards Compatible and Interderivable Semantic Specifications for the Scheme Programming Language, Part I: Denotational Semantics, Natural Semantics, and Abstract Machines

We derive two big-step abstract machines, a natural semantics, and the valuation function of a denotational semantics based on the small-step abstract machine for Core Scheme presented by Clinger at PLDI'98. Starting from a functional implementation of this small-step abstract machine, (1) we fuse its transition function with its driver loop, obtaining the functional implementation of a big-step abstract machine; (2) we adjust this big-step abstract machine so that it is in defunctionalized form, obtaining the functional implementation of a second big-step abstract machine; (3) we refunctionalize this adjusted abstract machine, obtaining the functional implementation of a natural semantics in continuation style; and (4) we closure-unconvert this natural semantics, obtaining a compositional continuation-passing evaluation function which we identify as the functional implementation of a denotational semantics in continuation style. We then compare this valuation function with that of Clinger's original denotational semantics of Scheme

Wasm/k: Delimited Continuations for WebAssembly

WebAssembly is designed to be an alternative to JavaScript that is a safe, portable, and efficient compilation target for a variety of languages. The performance of high-level languages depends not only on the underlying performance of WebAssembly, but also on the quality of the generated WebAssembly code. In this paper, we identify several features of high-level languages that current approaches can only compile to WebAssembly by generating complex and inefficient code. We argue that these problems could be addressed if WebAssembly natively supported first-class continuations. We then present Wasm/k, which extends WebAssembly with delimited continuations. Wasm/k introduces no new value types, and thus does not require significant changes to the WebAssembly type system (validation). Wasm/k is safe, even in the presence of foreign function calls (e.g., to and from JavaScript). Finally, Wasm/k is amenable to efficient implementation: we implement Wasm/k as a local change to Wasmtime, an existing WebAssembly JIT. We evaluate Wasm/k by implementing C/k, which adds delimited continuations to C/C++. C/k uses Emscripten and its implementation serves as a case study on how to use Wasm/k in a compiler that targets WebAssembly. We present several case studies using C/k, and show that on implementing green threads, it can outperform the state-of-the-art approach Asyncify with an 18% improvement in performance and a 30% improvement in code size

Status report: specifying JavaScript with ML

The Ecma TC39-TG1 working group is using ML as the specification language for the next generation of JavaScript, the popular programming language for browser-based web applications. This “definitional interpreter ” serves many purposes: a high-level and readable specification language, an executable and testable specification, a reference implementation, and an aid in driving the design process. We describe the design and specification of JavaScript and our experience so far using Standard ML for this purpose. Categories and Subject Descriptors D.2.1 [Software Engineering]: Requirements/Specifications—Languages; D.3.1 [Programmin

A First-Order One-Pass CPS Transformation

We present a new transformation of call-by-value lambda-terms into continuation-passing style (CPS). This transformation operates in one pass and is both compositional and first-order. Because it operates in one pass, it directly yields compact CPS programs that are comparable to what one would write by hand. Because it is compositional, it allows proofs by structural induction. Because it is first-order, reasoning about it does not require the use of a logical relation. This new CPS transformation connects two separate lines of research. It has already been used to state a new and simpler correctness proof of a direct-style transformation, and to develop a new and simpler CPS transformation of control-flow information

Query Evaluation in Deductive Databases

It is desirable to answer queries posed to deductive databases by computing fixpoints because such computations are directly amenable to set-oriented fact processing. However, the classical fixpoint procedures based on bottom-up processing — the naive and semi-naive methods — are rather primitive and often inefficient. In this article, we rely on bottom-up meta-interpretation for formalizing a new fixpoint procedure that performs a different kind of reasoning: We specify a top-down query answering method, which we call the Backward Fixpoint Procedure. Then, we reconsider query evaluation methods for recursive databases. First, we show that the methods based on rewriting on the one hand, and the methods based on resolution on the other hand, implement the Backward Fixpoint Procedure. Second, we interpret the rewritings of the Alexander and Magic Set methods as specializations of the Backward Fixpoint Procedure. Finally, we argue that such a rewriting is also needed in a database context for implementing efficiently the resolution-based methods. Thus, the methods based on rewriting and the methods based on resolution implement the same top-down evaluation of the original database rules by means of auxiliary rules processed bottom-up