In “Functional Unparsing ” (JFP 8(6): 621–625, 1998), Danvy presented a type-safe printf function using continuations and an accumulator to achieve the effect of dependent types. The key technique employed in Danvy’s solution is the non-standard use of continuations: not all of its calls are tail calls, i.e., it uses delimited continuations. Against this backdrop, we present three new solutions to the printf problem: a simpler one that also uses delimited continuations but that does not use an accumulator, and the corresponding two in direct style with the delimited-control operators, shift and reset. These two solutions are the direct-style counterparts of the two continuation-based ones. The last solution pinpoints the essence of Danvy’s solution: shift is used to change the answer type of delimited continuations. Besides providing a new application of shift and reset, the solutions in direct style raise a key issue in the typing of first-class delimited continuations and require Danvy and Filinski’s original type system. The resulting types precisely account for the behavior of printf. This is the extended version of the previous technical report OCHA-IS 07-1. It contains an introduction to continuation-passing style and delimited-control operators, shift and reset.

It is often hard to write programs that are efficient yet reusable. For example, an efficient implementation of Gaussian elimination should be specialized to the structure and known static properties of the input matrix. The most profitable optimizations, such as choosing the best pivoting or memoization, cannot be expected of even an advanced compiler because they are specific to the domain, but expressing these optimizations directly makes for ungainly source code. Instead, a promising and popular way to reconcile efficiency with reusability is for a domain expert to write code generators. Two pillars of this approach are types and effects. Typed multilevel languages such as MetaOCaml ensure safety: a well-typed code generator neither goes wrong nor generates code that goes wrong. Side effects such as state and control ease correctness: an effectful generator can resemble the textbook presentation of an algorithm, as is familiar to domain experts, yet insert let for memoization and if for bounds-checking, as is necessary for efficiency. However, adding effects blindly renders multilevel types unsound. We introduce the first two-level calculus with control effects and a sound type system. We give small-step operational semantics as well as a continuation-passing style (CPS) translation. For soundness, our calculus restricts the code generator’s effects to the scope of generated binders. Even with this restriction, we can finally write efficient code generators for dynamic programming and numerical methods in direct style, like in algorithm textbooks, rather than in CPS or monadic style.

Abstract. We study the dynamic control operators for delimited continuations, control and prompt. Based on recent developments on purely functional CPS translations for them, we introduce a polymorphically typed calculus for these control operators which allows answer-type modification. We show that our calculus enjoys type soundness and is compatible with the CPS translation. We also show that the typed dynamic control operators can macro-express the typed static ones (shift and reset), while the converse direction is not possible, which exhibits a sharp contrast with the type-free case.

We propose a typed call-by-name λ-calculus with shift, reset and strict functions and describe its linguistic applications, improving on the previous continuation-based analyses of quantification, binding, raised and in-situ wh-questions, binding in wh-questions, and superiority. The evaluation order is not fixed left-to-right: rather, it is determined by the demand for values exerted by reset and strict functions. Since functions can take general, effectful terms, our analyses need no thunks and similar type raising. The main improvement of the present analyses is in typing: assigning types both to terms and contexts and building types using connectives with clear logical interpretation. Types abstractly interpret operational semantics, and thus concisely describe all the effects that could occur in the evaluation of a term. Our main result is that both typing and call-by-name are necessary to correctly predict superiority and binding in wh-questions with topicalization, without resorting to thunking or type raising and thus maintaining the uniformity of the analyses. We have implemented the calculus including the type checking and mechanically verified all the analyses. 1.

Abstract. The notion of delimited continuations has been proved useful in various areas of computer programming such as partial evaluation, mobile computing, and web transaction. In our previous work, we proposed polymorphic calculi with control operators for delimited continuations. This paper presents a proof of strong normalization (SN) of these calculi based on a refined (i.e. administrative redex-free) CPS translation.

It is often hard to write programs that are efficient yet reusable. For example, an efficient implementation of Gaussian elimination should be specialized to the structure and known static properties of the input matrix. The most profitable optimizations, such as choosing the best pivoting or memoization, cannot be expected of even an advanced compiler because they are specific to the domain, but expressing these optimizations directly makes for ungainly source code. Instead, a promising and popular way to reconcile efficiency with reusability is for a domain expert to write code generators. Two pillars of this approach are types and effects. Typed multilevel languages such as MetaOCaml ensure safety: a well-typed code generator neither goes wrong nor generates code that goes wrong. Side effects such as state and control ease correctness: an effectful generator can resemble the textbook presentation of an algorithm, as is familiar to domain experts, yet insert let for memoization and if for bounds-checking, as is necessary for efficiency. However, adding effects blindly renders multilevel types unsound. We introduce the first two-level calculus with control effects and a sound type system. We give small-step operational semantics as well as a continuation-passing style (CPS) translation. For soundness, our calculus restricts the code generator’s effects to the scope of generated binders. Even with this restriction, we can finally write efficient code generators for dynamic programming and numerical methods in direct style, like in algorithm textbooks, rather than in CPS or monadic style.

We describe the implementation of first-class polymorphic delimited continuations in the programming language Scala. We use Scala’s pluggable typing architecture to implement a simple type and effect system, which discriminates expressions with control effects from those without and accurately tracks answer type modification incurred by control effects. To tackle the problem of implementing first-class continuations under the adverse conditions brought upon by the Java VM, we employ a selective CPS transform, which is driven entirely by effect-annotated types and leaves pure code in direct style. Benchmarks indicate that this high-level approach performs competitively.

We propose an extension of minimal intuitionistic predicate logic, based on delimited control operators, that can derive the predicate-logic version of the Double-negation Shift schema, while preserving the disjunction and existence properties. Keywords: delimited control operators, Double-negation Shift, disjunction property, existence property, intermediate logic 2000 MSC: 03B20, 03B40, 68N18, 03F55, 03F50, 03B55 1.