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- Ian Mackie
- POPL
- 1995

We investigate implementation techniques arising directly from Girard's Geometry of Interaction semantics for Linear Logic, specifically for a simple functional programming language (PCF). This gives rise to a very simple, compact, compilation schema and run-time system. We analyse various properties of this kind of computation that suggest substantial… (More)

Interaction nets are graphical rewriting systems which can be used as either a high-level programming paradigm or a low-level implementation language. However, an operational semantics together with notions of strategy and normal form which are essential to reason about implementations, are not easy to formalize in this graphical framework. The purpose of… (More)

We present a generalisation of first-order rewriting which allows us to deal with terms involving binding operations in an elegant and practical way. We use a nominal approach to binding, in which bound entities are explicitly named (rather than using a nameless syntax such as de Bruijn indices), yet we get a rewriting formalism which respects… (More)

- Ian Mackie
- RTA
- 2004

- Ian Mackie
- ICFP
- 1998

Interaction nets provide a graphical paradigm of computation based on net rewriting. They have proved most successful in understanding the dynamics of reduction in the &lambda;-calculus, where the prime example is the implementation of optimal reduction for the &lambda;-calculus (Lamping's algorithm), given by Gonthier, Abadi and L&eacute;vy.… (More)

In this paper we present a system of interaction that gener-alises Lafont's interaction nets by allowing computation in several nets in parallel and communication through a state. This framework allows us to represent large classes of term rewriting systems, genuine parallel functions, non-determinism, communication, sharing, and hence can be used to code… (More)

Term rewriting systems provide a framework in which it is possible to specify and program in a traditional syntax (oriented equations). Interaction nets, on the other hand, provide a graphical syntax for the same purpose, but can be regarded as being closer to an implementation since the reduction process is local and asynchronous, and all the operations… (More)