Towards a typed geometry of interaction

Towards a typed geometry of interaction (2005)

by Esfandiar Haghverdi , Philip J. Scott

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Datum	Value	Source
TITLE	Towards a typed geometry of interaction	INFERENCE
AUTHOR NAME	Esfandiar Haghverdi	user correction
AUTHOR AFFIL	School of Informatics, Indiana University	user correction
AUTHOR ADDR	Bloomington, IN 47406, USA,	user correction
AUTHOR NAME	Philip J. Scott	user correction
AUTHOR AFFIL		user correction
AUTHOR ADDR		user correction
ABSTRACT	We introduce a typed version of Girard’s Geometry of Interaction, called Multiobject GoI (MGoI) semantics. We give an MGoI interpretation for multiplicative linear logic (MLL) without units which applies to new kinds of models, including finite dimensional vector spaces. For MGoI (i) we develop a version of partial traces and trace ideals (related to previous work of Abramsky, Blute, and Panangaden); (ii) we do not require the existence of a reflexive object for our interpretation (the original GoI 1 and 2 were untyped and hence involved a bureaucracy of domain equation isomorphisms); (iii) we introduce an abstract notion of orthogonality (related to work of Hyland and Schalk) and use this to develop a version of Girard’s theory of types, datum and algorithms in our setting, (iv) we prove appropriate Soundness and Completeness Theorems for our interpretations in partially traced categories with orthogonality; (v) we end with an application to completeness of (the original) untyped GoI in a unique decomposition category.	user correction
YEAR	2005	INFERENCE
PAGES	216--231	INFERENCE
CITATIONS	28 found	ParsCit 1.0