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Title:A Dependent Type Theory with Names and Binding
Authors: Ulrich Schoepp ; Ian Stark
Date:Sep 2004
Publication Title:Proceedings of CSL 2004 (Conference for Computer Science Logic)
Publication Type:Conference Paper Publication Status:Published
Volume No:3210 Page Nos:235-249
We consider the problem of providing formal support for working with abstract syntax involving variable binders. Gabbay and Pitts have shown in their work on Fraenkel-Mostowski (FM) set theory how to address this through first-class names: in this paper we present a dependent type theory for programming and reasoning with such names. Our development is based on a categorical axiomatisation of names, with freshness as its central notion. An associated adjunction captures constructions known from FM theory: the freshness quantifier И, name-binding, and unique choice of fresh names. The Schanuel topos the category underlying FM set theory is an instance of this axiomatisation. Working from the categorical structure, we define a dependent type theory which it models. This uses bunches to integrate the monoidal structure corresponding to freshness, from which we define novel multiplicative dependent products Π* and sums Σ* as well as a propositions-as-types generalisation H of the freshness quantifier.
Springer-Verlag Berlin Heidelberg 2004
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author = { Ulrich Schoepp and Ian Stark },
title = {A Dependent Type Theory with Names and Binding},
book title = {Proceedings of CSL 2004 (Conference for Computer Science Logic)},
publisher = {Springer},
year = 2004,
month = {Sep},
volume = {3210},
pages = {235-249},
doi = {10.1007/b100120},
url = {},

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