Categorical Models for Intuitionistic and Linear Type Theory (2000)
| Venue: | In Foundations of Software Science and Computation Structure (FoSSaCS 2000), Springer Lecture Notes in Comput. Sci. 1784 |
| Citations: | 3 - 1 self |
BibTeX
@INPROCEEDINGS{Maietti00categoricalmodels,
author = {Maria Emilia Maietti and Valeria De Paiva and Eike Ritter},
title = {Categorical Models for Intuitionistic and Linear Type Theory},
booktitle = {In Foundations of Software Science and Computation Structure (FoSSaCS 2000), Springer Lecture Notes in Comput. Sci. 1784},
year = {2000},
pages = {22--3},
publisher = {Springer}
}
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Abstract
This paper describes the categorical semantics of a system of mixed intuitionistic and linear type theory (ILT). ILT was proposed by G. Plotkin and also independently by P. Wadler. The logic associated with ILT is obtained as a combination of intuitionistic logic with intuitionistic linear logic, and can be embedded in Barber and Plotkin's Dual Intuitionistic Linear Logic (DILL). However, unlike DILL, the logic for ILT lacks an explicit modality ! that translates intuitionistic proofs into linear ones. So while the semantics of DILL can be given in terms of monoidal adjunctions between symmetric monoidal closed categories and cartesian closed categories, the semantics of ILT is better presented via fibrations. These interpret double contexts, which cannot be reduced to linear ones. In order to interpret the intuitionistic and linear identity axioms acting on the same type we need fibrations satisfying the comprehension axiom.
Citations
| 170 | The logic of bunched implications - O’Hearn, Pym - 1999 |
| 122 | Linear types can change the world - Wadler - 1990 |
| 92 | What is a Categorical Model of Intuitionistic Linear Logic - Bierman - 1995 |
| 88 | A mixed linear and non-linear logic: Proofs, terms and models - Benton - 1995 |
| 79 | Dual intuitionistic linear logic - Barber - 1996 |
| 53 | Equality in hyperdoctrines and comprehension schema as an adjoint functor, Applications of Categorical Algebra (Proc - Lawvere - 1968 |
| 35 | Categorical Logic and Type Theory, volume 141 - Jacobs - 1999 |
| 15 | A categorical semantics of constructions - Ehrhard - 1988 |
| 11 | Linear explicit substitutions - Ghani, Paiva, et al. - 1998 |
| 5 | Type theory and recursion - Plotkin - 1993 |
| 1 | Categorical models of explicit subsitutions - Ghani, Paiva, et al. - 1999 |
