Categorical Models for Simply Typed Resource Calculi

Bucciarelli, Antonio; Ehrhard, Thomas; Manzonetto, Giulio

doi:10.1016/j.entcs.2010.08.013

Cited by 37 publications

(70 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The authors started from monoidal categories [5], then extended the notion to Cartesian ones [7]; a further generalization to Cartesian closed categories has been made in [4] to model differential and resource λ-calculi.…”

Section: Differential Categoriesmentioning

confidence: 99%

“…One way to do this is by studying calculi designed to capture resource usage, and their denotational models. Two such calculithe differential λ-calculus [1] of Ehrhard and Regnier and the resource calculus introduced by Tranquilli [2], inspired by the work of Boudol [3], are fundamentally related at the semantic level [4]: both may be interpreted using the notion of differential category introduced by Blute, Cockett and Seely [5]. In this paper, we study these concepts on both abstract and concrete levels.…”

Section: Introductionmentioning

confidence: 99%

“…Subsequently Bucciarelli, Ehrhard and Manzonetto proposed the notion of Cartesian closed differential category, proved that such categories are sound models of the simply typed resource calculus [4] and studied a concrete example. Other examples of such categories have been given by Blute, Ehrhard and Tasson in [14] and by Carraro, Ehrhard and Salibra in [15].…”

Section: Introductionmentioning

confidence: 99%

“…For example, applying it to the terminal (one object, one morphism) SMCC yields the key example of a differential category (and model of resource calculus [4]) based on the finite-multiset comonad on the category of sets and relations. We also show that our differential category of games embeds in one constructed from a simple symmetric monoidal category of games.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Constructing differential categories and deconstructing categories of games

Laird

Manzonetto

McCusker

2013

Information and Computation

Self Cite

View full text Add to dashboard Cite

Differential categories were introduced by Blute, Cockett and Seely to axiomatize categorically Ehrhard and Regnier's syntactic differential operator. We present an abstract construction that takes a symmetric monoidal category and yields a differential category, and show how this construction may be applied to categories of games. In one instance, we recover the category previously used to give a fully abstract model of a nondeterministic imperative language. The construction exposes the differential structure already present in this model, and shows how the differential combinator may be encoded in the imperative language. The second instance corresponds to a new Cartesian differential category of games. We give a model of a simply-typed resource calculus, Resource PCF, in this category and show that it possesses the finite definability property. Comparison with a semantics based on Bucciarelli, Ehrhard and Manzonetto's relational model reveals that the latter also possesses this property and is fully abstract.

show abstract

Section: Differential Categoriesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Constructing differential categories and deconstructing categories of games

Laird

Manzonetto

McCusker

2013

Information and Computation

Self Cite

View full text Add to dashboard Cite

show abstract

“…Regarding the semantics of these calculi, the first studies were conducted by Boudol et al [3] for the λ-calculus with multiplicities. In a forthcoming paper Bucciarelli et al [4] define categorical models for the differential λ-calculus.…”

Section: Introductionmentioning

confidence: 99%

Resource Combinatory Algebras

Carraro

Ehrhard

Salibra

2010

Mathematical Foundations of Computer Science 2010

Self Cite

View full text Add to dashboard Cite

Abstract. We initiate a purely algebraic study of Ehrhard and Regnier's resource λ-calculus, by introducing three equational classes of algebras: resource combinatory algebras, resource lambda-algebras and resource lambda-abstraction algebras. We establish the relations between them, laying down foundations for a model theory of resource λ-calculus. We also show that the ideal completion of a resource combinatory (resp. lambda-, lambda-abstraction) algebra induces a "classical" combinatory (resp. lambda-, lambda-abstraction) algebra, and that any model of the classical λ-calculus raising from a resource lambda-algebra determines a λ-theory which equates all terms having the same Böhm tree.

show abstract

Fixing Incremental Computation

Alvarez-Picallo

Eyers-Taylor²,

Jones³

et al. 2019

Programming Languages and Systems

View full text Add to dashboard Cite

Incremental computation has recently been studied using the concepts of change structures and derivatives of programs, where the derivative of a function allows updating the output of the function based on a change to its input. We generalise change structures to change actions, and study their algebraic properties. We develop change actions for common structures in computer science, including directed-complete partial orders and Boolean algebras. We then show how to compute derivatives of fixpoints. This allows us to perform incremental evaluation and maintenance of recursively defined functions with particular application generalised Datalog programs. Moreover, unlike previous results, our techniques are modular in that they are easy to apply both to variants of Datalog and to other programming languages.

show abstract

Categorical Models for Simply Typed Resource Calculi

Cited by 37 publications

References 9 publications

Constructing differential categories and deconstructing categories of games

Constructing differential categories and deconstructing categories of games

Resource Combinatory Algebras

Fixing Incremental Computation

Contact Info

Product

Resources

About