Type Theory in Ludics
Logic
2014-02-12 v1 Logic in Computer Science
Abstract
We present some first steps in the more general setting of the interpretation of dependent type theory in Ludics. The framework is the following: a (Martin-Lof) type A is represented by a behaviour (which corresponds to a formula) in such a way that canonical elements of A are interpreted in a set that is principal for the behaviour, where principal means in some way a minimal generator. We introduce some notions on Ludics and the interpretation of Martin-Lof rules. Then we propose a representation for simple types in Ludics, i.e., natural numbers, lists, the arrow construction and the usual constructors.
Keywords
Cite
@article{arxiv.1402.2511,
title = {Type Theory in Ludics},
author = {Eugenia Sironi},
journal= {arXiv preprint arXiv:1402.2511},
year = {2014}
}
Comments
arXiv admin note: text overlap with arXiv:1307.1028 by other authors