Ian Mackie. The Geometry of Interaction Machine. In Proc. of the 22nd Symposium on Principles of Programming Languages, pages 198-208, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....analysis of sharing and garbage collection. More concretely, some of the overhead involved in the environment based approach could be avoided by detecting linear usage of variables and directly performing substitutions for such variables. These ideas have led to several abstract machines [16, 17, 18], but all run into diculties with correctly exploiting linearity information. In particular, Wadler [22] and Chirimar et al. 7] tried to give an operational semantics where terms of linear type have exactly one pointer to them. However, their attempts failed mainly because the linearity inherent ....

Ian Mackie. The Geometry of Interaction Machine. In Proc. of the 22nd Symposium on Principles of Programming Languages, pages 198-208, 1995.

....degree of parallelism. The other way in which GoI has been used for implementation was by turning graphs into bideterministic automata, attaching an action to each edge. Actions act on contexts (which play the role of words) as given by the context semantics of [8] The rst GoI implementation [10] was in fact obtained in this way, for the PCF language: the Geometry of Interaction Machine compiles terms into assembly code of a generic register machine, which runs an automaton. Our Approach. In this paper we apply the execution formula directly. Our approach resembles VR in that it is ....

....Ex(t) Ex(t 0 ) The unique conclusion (or root) of the corresponding proofnet will by convention have the highest index in the matrices. Ex(t) is a square matrix of dimension N containing 0 everywhere except Ex(t) N;N , which is the weight of the execution path of t. The following result from [10] is the last ingredient required for using the execution formula as an evaluation device: Proposition 2. If t has ground type and reduces to a constant c, and is the weight of its execution path, then L = c. 3 Basic Computation Tasks As far as the design of an abstract machine is ....

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Ian Mackie. The geometry of interaction machine. In Proceedings of the 22nd ACM Symposium on Principles of Programming Languages (POPL'95), pages 198-208. ACM Press, January 1995.

....degree of parallelism. The other way in which GoI has been used for implementation was by turning graphs into bideterministic automata, attaching an action to each edge. Actions act on contexts (which play the role of words) as given by the context semantics of [8] The rst GoI implementation [10] was in fact obtained in this way, for the PCF language: the Geometry of Interaction Machine compiles terms into assembly code of a generic register machine. Executing this code corresponds to running the automaton with the empty context. In this paper we follow a di erent approach which consists ....

....= Ex(t 0 ) The unique conclusion (or root) of the corresponding proof net will by convention have the highest index in the matrices. Ex(t) is a square matrix of dimension N containing 0 everywhere except Ex(t) N;N , which is the weight of the execution path of t. The following result from [10] is the last ingredient required for using the execution formula as an evaluation device: Proposition 2. If t has ground type and reduces to a constant c, and is the weight of its execution path, then L = c. 3 Basic Computation Tasks Since the execution path is unique, it has to be ....

Ian Mackie. The geometry of interaction machine. In Proceedings of the 22nd ACM Symposium on Principles of Programming Languages (POPL'95), pages 198-208. ACM Press, January 1995.

....analysis of sharing and garbage collection. More concretely, some of the overhead involved in the environment based approach could be avoided by detecting linear usage of variables and directly performing substitutions for such variables. These ideas have led to several abstract machines [16, 17, 18], but all run into difficulties with correctly exploiting linearity information. In particular, Wadler [22] and Chirimar et al. 7] tried to give an operational semantics where terms of linear type have exactly one pointer to them. However, their attempts failed mainly because the linearity ....

Ian Mackie. The Geometry of Interaction Machine. In Proc. of the 22nd Symposium on Principles of Programming Languages, pages 198--208, 1995.

....garbage collection. More concretely, some of the overheads involved in the environment based approach could be avoided by detecting linear usage of variables and directly performing substitutions for such variables. Several abstract machines for linear logic have been proposed based on these ideas [14, 15, 16], but all run into difficulties with correctly exploiting linearity information. In particular, Wadler [20] and Chirimar et al. 5] tried to give an operational semantics where terms of linear type have exactly one pointer to them. However, their attempts failed mainly because the linearity ....

Ian Mackie. The Geometry of Interaction Machine. In Proc. of the 22nd Symposium on Principles of Programming Languages, pages 198--208, 1995.

....each time it is used. The implementation of classical linear logic given here dioeers from the CHAM in not being parallel, but resembles it in being call by name. Although parallelism does not seem to be an inherent characteristic of classical linear logic, call by name evaluation may be. Mackie [Mac95] has investigated implementation techniques based on the Geometry of Interaction, aiming for eOEcient implementations of a simple functional language. In contrast, our notion of implementation is on a more abstract level. Seely s model of linear logic requires that multiplicatives (ffl, 1) ....

Ian Mackie. The Geometry of Interaction Machine. In Proceedings 22th ACM Symposium on Principles of Programming Languages, pages 198 208, 1995.

....of Interaction, which has been used successfully for interaction nets before, can be used. The final part of this programme will be the study of the implementation of interaction nets, both directly (net rewriting) and also via the semantics (as done with the Geometry of interaction Machine [26]) This would give, as for the semantics, a uniform implementation of term rewriting, which can be extended to combinations of term rewriting and calculus. The study of the correspondences between term rewriting and interaction nets offers a new perspective on both formalisms; we hope that these ....

I. Mackie. The Geometry of Interaction Machine. In Proceedings, 22nd ACM Symposium on Principles of Programming Languages, pages 198--208, 1995.

....have been many successful attempts to give implementations of functional programming languages by looking at models of the calculus. To highlight just two, we mention categorical combinators, coming from categorical models of the calculus; and SKI combinators coming from combinatory logic. In [9] the second author gave a different kind of compilation of a simple calculus based functional programming language coming directly from Girard s Geometry of Interaction semantics [7, 6] a semantics of computation capturing the actual reduction process. One way of understanding the Geometry of ....

....into fixed code (which behaves as the network) The runtime system is then realized as a token traversing this network, following the code generated from the root of the graph, thus giving a sequential data flow model of computation. This is the method given for the Geometry of Interaction Machine [9], which we believe is the simplest method of compilation for this idea. Second author funded by a British Royal Society Research Fellowship. 1 One of the main novelties of this approach to compilation is that the basic instructions (or combinators) are very simple. More precisely, they are ....

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Ian Mackie. The Geometry of Interaction Machine. In Proceedings, 22nd ACM Symposium on Principles of Programming Languages, pages 198--208, January 1995.

....etc. so that the resulting system can be compared with other implementations of the functional languages. Finally, we remark that the path semantics for the interaction combinators [5] may provide alternative methods of implementation in the spirit of the Geometry of Interaction Machine [7]. ....

Ian Mackie. The Geometry of Interaction Machine. In Proceedings of the 22nd ACM Symposium on Principles of Programming Languages (POPL'95), pages 198--208, January 1995.

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Ian Mackie. The geometry of interaction machine. In Proceedings of the 22nd ACM Symposium on Principles of Programming Languages (POPL'95), pages 198--208, San Francisco, Jan 1995. IEEE.

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