Typed Exceptions and Continuations Cannot Macro-Express Each Other

Riecke, Jon G.; Thielecke, Hayo

doi:10.1007/3-540-48523-6_60

Cited by 19 publications

(27 citation statements)

References 15 publications

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“…The axiomatisation seems rather weak, and it would be good to test it, perhaps by attempting to determine whether it implies the soundness of operational semantics of continuations and effects such as those of [54,55]; Proposition 2 shows that some possible strengthenings are too strong as they imply that C is an isomorphism. In the following, we study both how our assumption and the assumption of invertibility propagate under the various combinations of algebraic effects and continuations.…”

Section: The Computational λ-Calculus Continuations and Algebraic Opmentioning

confidence: 97%

Combining algebraic effects with continuations

Hyland

Levy

Plotkin

et al. 2007

Theoretical Computer Science

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We consider the natural combinations of algebraic computational effects such as side-effects, exceptions, interactive input/output, and nondeterminism with continuations. Continuations are not an algebraic effect, but previously developed combinations of algebraic effects given by sum and tensor extend, with effort, to include commonly used combinations of the various algebraic effects with continuations. Continuations also give rise to a third sort of combination, that given by applying the continuations monad transformer to an algebraic effect. We investigate the extent to which sum and tensor extend from algebraic effects to arbitrary monads, and the extent to which Felleisen et al.'s C operator extends from continuations to its combination with algebraic effects. To do all this, we use Dubuc's characterisation of strong monads in terms of enriched large Lawvere theories.

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Section: The Computational λ-Calculus Continuations and Algebraic Opmentioning

confidence: 97%

Combining algebraic effects with continuations

Hyland

Levy

Plotkin

et al. 2007

Theoretical Computer Science

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“…Judgements Γ A; T are mapped to Γ * A * ∨ T * and have a similar interpretation. When writing such a translation in a general setting (Thielecke, 2001;Thielecke, 2000;Riecke and Thielecke, 1999), one is faced with a choice: should a use of a control operator capture the current exception handler or not? In our setting, the question is: if a continuation is captured under some #, and later invoked under another #, should calls to tp refer to the first # or the second?…”

Section: Understanding the Dynamic Annotationsmentioning

confidence: 99%

“…This final.tex; 11/04/2007; 15:30; p.2 seems to indicate that the understanding of the expressive power of such control operators must also include an understanding of the expressive power of other effects. Riecke and Thielecke (1999) and Thielecke (2000Thielecke ( , 2001 have formalised the expressive power of various combinations of continuations, exceptions and state but their results are not expressed using standard type systems and logics.…”

Section: Introductionmentioning

confidence: 99%

A type-theoretic foundation of delimited continuations

Ariola

Herbelin

Sabry

2007

Higher-Order Symb Comput

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Abstract. There is a correspondence between classical logic and programming language calculi with first-class continuations. With the addition of control delimiters, the continuations become composable and the calculi become more expressive. We present a fine-grained analysis of control delimiters and formalise that their addition corresponds to the addition of a single dynamically-scoped variable modelling the special top-level continuation. From a type perspective, the dynamically-scoped variable requires effect annotations. In the presence of control, the dynamically-scoped variable can be interpreted in a purely functional way by applying a store-passing style. At the type level, the effect annotations are mapped within standard classical logic extended with the dual of implication, namely subtraction. A continuation-passing-style transformation of lambda-calculus with control and subtraction is defined. Combining the translations provides a decomposition of standard CPS transformations for delimited continuations. Incidentally, we also give a direct normalisation proof of the simply-typed lambda-calculus with control and subtraction.

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“…The developments that we have been talking about-sophisticated error handling in high-level languages-were not a product of the AI community: Rather, they emerged because of perceived inadequacies of the previous method of error handling (namely the integer-valued return codes which one had in C and other similar languages), together with the hard mathematical work of developing a semantics for the new constructs (Riecke and Thielecke 1999;Landin 1965). The semantics for exceptions, when the concept of an exception finally emerged, came out of pre-existing theory (going back, at root, to the lambda calculus and the proof theory of classical logic), but the concept of an exception emerged, rather slowly and painfully, out of programming practice.…”

Section: The Language Designer's Viewpointmentioning

confidence: 97%

Bootstrapping Normativity

White

2010

Philos. Technol.

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We compare the role of Cartesian assumptions in the symbol grounding problem and in the Myth of the Given: We argue that the SellarsMcDowell critique of the Myth of the Given and, in particular, its use of the concept of normativity can provide useful resources for responding to the symbol grounding problem. We also describe the concepts of normativity at work in computer science and cognitive science: We argue that normative concepts are pervasive in the sciences and that, in particular, McDowell's dichotomy between the normative space of reasons and the realm of nature is somewhat problematic.

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Typed Exceptions and Continuations Cannot Macro-Express Each Other

Cited by 19 publications

References 15 publications

Combining algebraic effects with continuations

Combining algebraic effects with continuations

A type-theoretic foundation of delimited continuations

Bootstrapping Normativity

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