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The Geometry of Optimal Lambda Reduction
, 1992
"... Lamping discovered an optimal graphreduction implementation of the calculus. Simultaneously, Girard invented the geometry of interaction, a mathematical foundation for operational semantics. In this paper, we connect and explain the geometry of interaction and Lamping's graphs. The geometry o ..."
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Cited by 122 (2 self)
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Lamping discovered an optimal graphreduction implementation of the calculus. Simultaneously, Girard invented the geometry of interaction, a mathematical foundation for operational semantics. In this paper, we connect and explain the geometry of interaction and Lamping's graphs. The geometry of interaction provides a suitable semantic basis for explaining and improving Lamping's system. On the other hand, graphs similar to Lamping's provide a concrete representation of the geometry of interaction. Together, they offer a new understanding of computation, as well as ideas for efficient and correct implementations.
An implementation model of the typed lambdacalculus based on Linear Chemical Abstract Machine
, 2001
"... Machine Shinya Sato 1 , Toru Sugimoto 2 , and Shinichi Yamada 1 1 Department of Information Sciences, Science University of Tokyo, 2641 Yamazaki, Noda, Chiba 2788510, JAPAN shinya@sy.is.noda.sut.ac.jp, yamada@is.noda.sut.ac.jp 2 RIKEN Brain Science Institute 21 Hirosawa, Wako, Saitama 35 ..."
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Machine Shinya Sato 1 , Toru Sugimoto 2 , and Shinichi Yamada 1 1 Department of Information Sciences, Science University of Tokyo, 2641 Yamazaki, Noda, Chiba 2788510, JAPAN shinya@sy.is.noda.sut.ac.jp, yamada@is.noda.sut.ac.jp 2 RIKEN Brain Science Institute 21 Hirosawa, Wako, Saitama 3510198, JAPAN sugimoto@brain.riken.go.jp Abstract. Abramsky's Linear Chemical Abstract Machine is a term calculus which corresponds to Linear Logic, via the CurryHoward isomorphism. We show that the typed calculus is embedded into Linear Chemical Abstract Machine by Girard's embedding of Intuitionistic Logic into Linear Logic. Then we extend our result to a simple functional programming language obtained from the typed calculus by adding constants from PCF. We show that the callbyvalue evaluation of terms of ground types (Booleans and Natural numbers) are preserved and reflected by this translation. Finally, we discuss an operational perspective of our result. We give a sequential execution model of Linear CHAM based on Abramsky's idea of a stack of coequations and a name queue, and then we consider a concurrent multithread implementation of the model. 1
Two Papers Concerning Categories in Concurrency Theory
, 1994
"... This paper presents a metamodel of observation in concurrency theory; it allows us to unify notions of observation in many different behavioural settings. We treat traces, process trees and event structures, and show how observations of them fit into a common framework. Behaviour and observation wi ..."
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This paper presents a metamodel of observation in concurrency theory; it allows us to unify notions of observation in many different behavioural settings. We treat traces, process trees and event structures, and show how observations of them fit into a common framework. Behaviour and observation will both be modeled as categories and linked using the notions of `functor' and `adjunction'. Timing will be our chief example of observation; we present a timed traces model, and show how it generalises to timed process trees (branching time) and timed `true concurrency.' Our general framework sees timing as a way of embedding observations into time. Stable categories of embeddings are then natural metamodels of timed observation. I always console myself with the thought that whatever can be known of me is by definition not me, is hetronomous to my authentic being, since the subject cannot be captured in an objective representation. Terry Eagleton x1. Introduction Concurrency theory is n...