Geometry of Interaction and linear combinatory algebras
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- 1 April 2002
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Structures in Computer Science
- Vol. 12 (5) , 625-665
- https://doi.org/10.1017/s0960129502003730
Abstract
We present an axiomatic framework for Girard's Geometry of Interaction based on the notion of linear combinatory algebra. We give a general construction on traced monoidal categories, with certain additional structure, that is sufficient to capture the exponentials of Linear Logic, which produces such algebras (and hence also ordinary combinatory algebras). We illustrate the construction on six standard examples, representing both the ‘particle-style’ as well as the ‘wave-style’ Geometry of Interaction.Keywords
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