New Foundations for the Geometry of Interaction

New Foundations for the Geometry of Interaction (1993)

Cached

Download Links

[web.comlab.ox.ac.uk]
[www.math.luc.edu]

Other Repositories/Bibliography

DBLP

by Samson Abramsky , Radha Jagadeesan

Venue:	Information and Computation
Citations:	69 - 20 self

Versions

Version History

Metadata Version 3

User correction supplied by SystemCorrections

Datum	Value	Source
TITLE	New Foundations for the Geometry of Interaction	user correction - Legacy Corrections
AUTHOR NAME	Samson Abramsky	user correction - Legacy Corrections
AUTHOR AFFIL	Dept. of Computing Dept. of Computing; Imperial College Imperial College; London London.	user correction - Legacy Corrections
AUTHOR NAME	Radha Jagadeesan	user correction - Legacy Corrections
AUTHOR AFFIL	Dept. of Computing Dept. of Computing; Imperial College Imperial College; London London.	user correction - Legacy Corrections
ABSTRACT	this paper, we present a new formal embodiment of Girard's programme, with the following salient features. 1. Our formalisation is based on elementary Domain Theory rather than C --algebras. It exposes precisely what structure is required of the ambient category in order to carry out the interpretation. Furthermore, we show how the interpretation arises from the construction of a categorical model of Linear Logic; this provides the basis for a rational reconstruction which makes the structure of the interpretation much easier to understand. 2. The key definitions in our interpretation differ from Girard's. Most notably, we replace the "execution formula" by a least fixpoint, essentially a generalisation of Kahn's semantics for feedback in dataflow networks [Kah77, KM77]. This, coupled with the use of the other distinctive construct of Domain theory, the lifting monad, enables us to interpret the whole of Linear Logic, and to prove soundness in full generality. 3. Our general notion of interpretation has simple examples, providing a suitable basis for concrete implementations. In fact, we sketch a computational interpretation of the Geometry of Interaction in terms of dataflow networks. Recall that computation in dataflow networks is asynchronous, i.e. "no global time", and proceeds by purely local "firing rules" that manipulate tokens. The further structure of this paper is as follows. In Section 2, we review the syntax of Linear Logic, and present the basic, and quite simple intuitions underlying the interpretation. In Section 3, we use these ideas to construct models of Linear Logic. In Section 4 we define the Geometry of Interaction interpretations, and how that they arise from the model constructed previously in a natural fashion. In Section 5, we give a computati...	user correction - Legacy Corrections
YEAR	1993	user correction - Legacy Corrections
VENUE	Information and Computation	INFERENCE
VENUE TYPE	JOURNAL	INFERENCE
PAGES	53--119	INFERENCE
VOLUME	111	INFERENCE
CITATIONS	9 found	ParsCit 1.0