New foundations for the geometry of interaction

Abramsky, Samson; Jagadeesan, Radha

doi:10.1109/lics.1992.185534

Cited by 33 publications

(45 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We shall provide substantial answers to questions (2)- (4) above in the present paper. These results also suggest that the Brandenburger-Keisler 'paradox' does offer a good point of entry for considering the more general question (1).…”

Section: Introductionmentioning

confidence: 86%

See 1 more Smart Citation

From Lawvere to Brandenburger-Keisler: Interactive Forms of Diagonalization and Self-reference

Abramsky

Zvesper

2012

Coalgebraic Methods in Computer Science

View full text Add to dashboard Cite

Section: Introductionmentioning

confidence: 86%

“…In fact, having isomorphisms α : , and similarly for T b and P(U a ). 4 However, we shall emphasize the situation where we do have isomorphisms, where we can really speak of canonical solutions.…”

Section: Functorial Constructions Of Assumption-complete Modelsmentioning

confidence: 99%

From Lawvere to Brandenburger-Keisler: Interactive Forms of Diagonalization and Self-reference

Abramsky

Zvesper

2012

Coalgebraic Methods in Computer Science

View full text Add to dashboard Cite

“…effective) and denotational (i.e. inductive on the language syntax) [AJ92]. These ideas have already been exploited in devising optimal compilation strategies for the lambda calculus, a technique called Geometry of Implementation [Mac94,Mac95].…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Geometry of synthesis iv

Ghica¹,

Smith²,

Singh³

2011

Proceedings of the 16th ACM SIGPLAN International Conference on Functional Programming

View full text Add to dashboard Cite

Abramsky's Geometry of Interaction interpretation (GoI) is a logical-directed way to reconcile the process and functional views of computation, and can lead to a dataflow-style semantics of programming languages that is both operational (i.e. effective) and denotational (i.e. inductive on the language syntax). The key idea of Ghica's Geometry of Synthesis (GoS) approach is that for certain programming languages (namely Reynolds's affine Syntactic Control of Interference-SCI) the GoI processes-like interpretation of the language can be given a finitary representation, for both internal state and tokens. A physical realisation of this representation becomes a semantics-directed compiler for SCI into hardware. In this paper we examine the issue of compiling affine recursive programs into hardware using the GoS method. We give syntax and compilation techniques for unfolding recursive computation in space or in time and we illustrate it with simple benchmark-style examples. We examine the performance of the benchmarks against conventional CPU-based execution models.

show abstract

“…[13]. What is "reversible" is the evaluation of the partial involutions interpreting the combinators, but this is surprisingly enough to achieve a reversible model of computation 1 . The crucial notion is that of application between automata, or between partial involutions.…”

Section: Introductionmentioning

confidence: 99%

“…57), pp. 254-270The Involutions-as-Principal Types/Application-as-Unification Ciaffaglione, Honsell, Lenisa and Scagnetto stems from Girard's Execution Formula, or Abramsky's symmetric feedback [1]. The former was introduced by J. Y. Girard [17,18] in the context of "Geometry of Interaction" (GoI) to model, in a language-independent way, the fine semantics of Linear Logic.Constructions similar to the Combinatory Algebra of partial involutions, introduced in [3], appear in various papers by S. Abramsky, e.g.…”

mentioning

confidence: 99%

The involutions-as-principal types/application-as-unification Analogy

Ciaffaglione

Honsell

Lenisa

et al.

EPiC Series in Computing

View full text Add to dashboard Cite

In 2005, S. Abramsky introduced various universal models of computation based on Affine Combinatory Logic, consisting of partial involutions over a suitable formal language of moves, in order to discuss reversible computation in a game-theoretic setting. We investigate Abramsky’s models from the point of view of the model theory of λ-calculus, focusing on the purely linear and affine fragments of Abramsky’s Combinatory Algebras.Our approach stems from realizing a structural analogy, which had not been hitherto pointed out in the literature, between the partial involution interpreting a combinator and the principal type of that term, with respect to a simple types discipline for λ-calculus. This analogy allows for explaining as unification between principal types the somewhat awkward linear application of involutions arising from Geometry of Interaction (GoI).Our approach provides immediately an answer to the open problem, raised by Abram- sky, of characterising those finitely describable partial involutions which are denotations of combinators, in the purely affine fragment. We prove also that the (purely) linear combinatory algebra of partial involutions is a (purely) linear λ-algebra, albeit not a combinatory model, while the (purely) affine combinatory algebra is not. In order to check the complex equations involved in the definition of affine λ-algebra, we implement in Erlang the compilation of λ-terms as involutions, and their execution.

show abstract

New foundations for the geometry of interaction

Cited by 33 publications

References 10 publications

From Lawvere to Brandenburger-Keisler: Interactive Forms of Diagonalization and Self-reference

From Lawvere to Brandenburger-Keisler: Interactive Forms of Diagonalization and Self-reference

Geometry of synthesis iv

The involutions-as-principal types/application-as-unification Analogy

Contact Info

Product

Resources

About