Categorical models for simply typed resource calculi
by
Antonio Bucciarelli
,
Thomas Ehrhard
,
Giulio Manzonetto
| Venue: | ENTCS |
| Citations: | 3 - 1 self |
BibTeX
@ARTICLE{Bucciarelli_categoricalmodels,
author = {Antonio Bucciarelli and Thomas Ehrhard and Giulio Manzonetto},
title = {Categorical models for simply typed resource calculi},
journal = {ENTCS},
year = {},
pages = {2010}
}
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Abstract
We introduce the notion of differential λ-category as an extension of Blute-Cockett-Seely’s differential Cartesian categories. We prove that differential λ-categories can be used to model the simply typed versions of: (i) the differential λ-calculus, a λ-calculus extended with a syntactic derivative operator; (ii) the resource calculus, a non-lazy axiomatisation of Boudol’s λ-calculus with multiplicities. Finally, we provide two
Citations
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| 30 | The differential lambda calculus - Ehrhard, Regnier |
| 25 | Differential interaction nets - Ehrhard, Regnier - 2004 |
| 11 | Böhm Trees, Krivine’s Machine and the Taylor Expansion of Lambda-Terms - Ehrhard, Regnier - 2006 |
| 9 | Normal functors, power series and λ-calculus - Girard - 1988 |
| 3 | Categories, types and structures. Category theory for the working computer scientist - Asperti, Longo - 1991 |
| 2 | Cartesian differential categories - Blute, Cockett, et al. - 2008 |
| 2 | The lambda-calculus with multiplicities. CONCUR’93 - Boudol |
| 2 | Parallel reduction in resource λ-calculus. APLAS’09 - Pagani, Tranquilli |
| 1 | Not enough points is enough. CSL’07 - Bucciarelli, Ehrhard, et al. - 2007 |
| 1 | Uniformity and the Taylor expansion of ordinary λ-terms - Ehrhard, Regnier - 2008 |
