Direct Models of the Computational Lambda-calculus

Führmann, Carsten

doi:10.1016/s1571-0661(04)80078-1

Cited by 32 publications

(40 citation statements)

References 12 publications

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“…As Führmann has shown, the converse is true iff C satisfies Moggi's equalizing requirement (Moggi 1988;Führmann 1999). We say that an object A ∈ |C| satisfies the equalizing requirement if the canonical morphism ∂ A : A → R R A is an equalizer in the following diagram:…”

Section: The Center Of a Category Of Continuationsmentioning

confidence: 99%

Control categories and duality: on the categorical semantics of the lambda-mu calculus

Selinger¹

2001

Math. Struct. Comp. Sci.

125

174

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We give a categorical semantics to the call-by-name and call-by-value versions of Parigot's λµ-calculus with disjunction types. We introduce the class of control categories, which combine a cartesian-closed structure with a premonoidal structure in the sense of Power and Robinson. We prove, via a categorical structure theorem, that the categorical semantics is equivalent to a CPS semantics in the style of Hofmann and Streicher. We show that the call-by-name λµ-calculus forms an internal language for control categories, and that the call-by-value λµ-calculus forms an internal language for the dual co-control categories. As a corollary, we obtain a syntactic duality result: there exist syntactic translations between call-by-name and call-by-value which are mutually inverse and which preserve the operational semantics. This answers a question of Streicher and Reus.

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Section: The Center Of a Category Of Continuationsmentioning

confidence: 99%

Control categories and duality: on the categorical semantics of the lambda-mu calculus

Selinger¹

2001

Math. Struct. Comp. Sci.

125

174

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“…Dealing with the same duality, Hasegawa and Kakutani pointed out a fundamental relationship between central expressions and rigid functionals [5], which play a key rôle in Filinski's recursion-from-iteration construction [2]. It was soon pointed out that those sets of expressions are interesting for arbitrary computational effects, not only continuations [3,4]. Recently, it was discovered that typical models of partiality (i.e.…”

Section: Introductionmentioning

confidence: 99%

Varieties of Effects

Führmann

2002

Lecture Notes in Computer Science

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“…In connection to the model theory, direct algebraic descriptions of our calculi are to be obtained in terms of the duploids arising from the effect adjunctions. These direct models are to be put in reflection with the enriched adjunction models, to generalise Führmann's direct characterisation of -models [21], in the continuity of [39]. In fact, we conjecture that the calculi form initial models, not only for direct duploid models, but also for the adjunction models, provided that the data of values and stacks is appropriately preserved.…”

Section: Completenessmentioning

confidence: 74%

A theory of effects and resources: adjunction models and polarised calculi

CurienPierre-Louis

FioreMarcelo

Munch-MaccagnoniGuillaume

2016

SIGPLAN Not.

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We consider the Curry-Howard-Lambek correspondence for effectful computation and resource management, specifically proposing polarised calculi together with presheaf-enriched adjunction models as the starting point for a comprehensive semantic theory relating logical systems, typed calculi, and categorical models in this context.Our thesis is that the combination of effects and resources should be considered orthogonally. Model theoretically, this leads to an understanding of our categorical models from two complementary perspectives: (i) as a linearisation of CBPV (Call-by-Push-Value) adjunction models, and (ii) as an extension of linear/non-linear adjunction models with an adjoint resolution of computational effects. When the linear structure is cartesian and the resource structure is trivial we recover Levy's notion of CBPV adjunction model, while when the effect structure is trivial we have Benton's linear/nonlinear adjunction models. Further instances of our model theory include the dialogue categories with a resource modality of Melliès and Tabareau, and the [E]EC ([Enriched] Effect Calculus) models of Egger, Møgelberg and Simpson. Our development substantiates the approach by providing a lifting theorem of linear models into cartesian ones.To each of our categorical models we systematically associate a typed term calculus, each of which corresponds to a variant of the sequent calculi LJ (Intuitionistic Logic) or ILL (Intuitionistic Linear Logic). The adjoint resolution of effects corresponds to polarisation whereby, syntactically, types locally determine a strict or lazy evaluation order and, semantically, the associativity of cuts is relaxed. In particular, our results show that polarisation provides a computational interpretation of CBPV in direct style. Further, we characterise depolarised models: those where the cut is associative, and where the evaluation order is unimportant. We explain possible advantages of this style of calculi for the operational semantics of effects.

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Direct Models of the Computational Lambda-calculus

Cited by 32 publications

References 12 publications

Control categories and duality: on the categorical semantics of the lambda-mu calculus

Control categories and duality: on the categorical semantics of the lambda-mu calculus

Varieties of Effects

A theory of effects and resources: adjunction models and polarised calculi

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