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A unified category-theoretic formulation of typed binding signatures


Reference:

Tanaka, M. and Power, J., 2005. A unified category-theoretic formulation of typed binding signatures. In: MERLIN '05 Proceedings of the 3rd ACM SIGPLAN workshop on Mechanized reasoning about languages with variable binding. New York: ACM, pp. 13-24.

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Official URL:

http://dx.doi.org/10.1145/1088454.1088457

Abstract

We generalise Fiore et al's account of variable binding for untyped cartesian contexts and Tanaka's account of variable binding for untyped linear contexts to give an account of variable binding for simply typed axiomatically defined contexts. In line with earlier work by us, we axiomatise the notion of context by means of a pseudo-monad S on Cat: Fiore et al implicitly used the pseudo-monad Tfp for small categories with finite products, and Tanaka implicitly used the pseudo-monad Tsm for small symmetric monoidal categories. But here we also extend from untyped variable binding to typed variable binding. Given a set A of types, this involves generalising from Fiore et al's use of [F,Set] to [(SA)op,SetA]. We define a substitution monoidal structure on [(SA)op,SetA], give a definition of binding signature at this level of generality, and extend initial algebra semantics to this typed, axiomatic setting. This generalises and axiomatises previous work by Fiore et al and later authors in particular cases. In particular, it includes the Logic of Bunched Implications and variants, and it yields an improved axiomatic definition of binding signature even in the case of untyped binders.

Details

Item Type Book Sections
CreatorsTanaka, M.and Power, J.
DOI10.1145/1088454.1088457
DepartmentsFaculty of Science > Computer Science
StatusPublished
ID Code26509

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