Categorical Models for Simply Typed Resource Calculi

Authors:
Antonio Bucciarelli;Thomas Ehrhard;Giulio Manzonetto
Affiliations:
Laboratoire PPS, Université Paris-Diderot, CNRS UMR 7126, 2, place Jussieu (case 7014), 75251 Paris Cedex 05, France;Laboratoire PPS, Université Paris-Diderot, CNRS UMR 7126, 2, place Jussieu (case 7014), 75251 Paris Cedex 05, France;Laboratoire LIPN, Université Paris Nord, CNRS UMR 7030, 99, avenue Jean-Baptiste Clément 93430 Villetaneuse, France
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2010

Citing 10
Cited 4

Categories, types, and structures: an introduction to category theory for the working computer scientist

Categories, types, and structures: an introduction to category theory for the working computer scientist
The Lambda-Calculus with Multiplicities (Abstract)

CONCUR '93 Proceedings of the 4th International Conference on Concurrency Theory
The differential Lambda-calculus

Theoretical Computer Science
Finiteness spaces

Mathematical Structures in Computer Science
Differential categories

Mathematical Structures in Computer Science
Differential interaction nets

Theoretical Computer Science - Logic, language, information and computation
Uniformity and the Taylor expansion of ordinary lambda-terms

Theoretical Computer Science
Parallel Reduction in Resource Lambda-Calculus

APLAS '09 Proceedings of the 7th Asian Symposium on Programming Languages and Systems
Böhm trees, krivine's machine and the taylor expansion of lambda-terms

CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Not enough points is enough

CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic

Complexity of strongly normalising λ-terms via non-idempotent intersection types

FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
Constructing differential categories and deconstructing categories of games

ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
A Simply Typed λ-Calculus of Forward Automatic Differentiation

Electronic Notes in Theoretical Computer Science (ENTCS)
Constructing differential categories and deconstructing categories of games

Information and Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

We introduce the notion of differential @l-category as an extension of Blute-Cockett-Seely's differential Cartesian categories. We prove that differential @l-categories can be used to model the simply typed versions of: (i) the differential @l-calculus, a @l-calculus extended with a syntactic derivative operator; (ii) the resource calculus, a non-lazy axiomatisation of Boudol's @l-calculus with multiplicities. Finally, we provide two concrete examples of differential @l-categories, namely, the category MRel of sets and relations, and the category MFin of finiteness spaces and finitary relations.