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Jean-Yves Girard. Geometry of interaction II: Deadlock free algorithms. In Martin-Lof & Mints, editor, Proceedings of COLOG'88, volume 417 of Lecture Notes in Computer Science, pages 76--93. Springer-Verlag, 1988.

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Reversible, Irreversible and Optimal ...-machines - Danos, Regnier   (Correct)

.... ij 2 A, such that a coefficient e ij ( S) S 0 ) iff there is a successful run starting in the i th conclusion with the initial pair ( S) and ending in the j th conclusion with the final pair ( S 0 ) This is Girard s execution formula rephrased as appropriate in our framework; see [8, 9, 10] for the original presentation. This may seem a formidable thing to compute, but remember that all actions are finitely representable, and then it is easy to come up with a finitary formulation of this ex(R) Note also that by bi determinicity ex(R) is a self dual action matrix. Now, take note, ....

Jean-Yves Girard. Geometry of interaction II: Deadlock free algorithms. In Martin-Lof & Mints, editor, Proceedings of COLOG'88, volume 417 of Lecture Notes in Computer Science, pages 76--93. Springer-Verlag, 1988.


The Geometry of Optimal Lambda Reduction - Gonthier, Abadi, Lévy (1992)   (73 citations)  (Correct)

.... This paper develops for the third time a semantics of computation free from the twin drawbacks of reductionism (which leads to static modelisation) and subjectivism (which leads to syntactical abuses, in other terms bureaucracy) Such a semantics was developed previously by Jean Yves Girard [Gir89, Gira] and by John Lamping [Lam90] Girard is a logician INRIA Rocquencourt. y Digital Equipment Corporation, Systems Research Center. 0 and Lamping is an autodidactic engineer. It is no surprise that they never read one another although they were working on the same problem from different ....

Jean-Yves Girard. Geometry of interaction II: Deadlock-free algorithms.


Proof-nets and the Hilbert space - Danos, Regnier (1995)   (19 citations)  (Correct)

.... basis X = e n ) The big model of L R is the set of bounded operators on H, denoted by B(H) The interest of this new model is that we are going to use our remark about the linearity of the commutation relation by superposing small solutions; another interest may be understood by reading [Gir88b] or [MR91] The basic structure. B(H) is clearly an involutive monoid (w.r.t. composition and adjunction) wherein there is a zero and a one. It even is a C algebra. The shift morphism. Take : H Omega H Gamma H to be the isomorphism defined by (e i Omega e j ) e di;je , where H Omega ....

Jean-Yves Girard. Geometry of interaction II: Deadlock free algorithm. In Martin-Lof & Mints, editor, Proceedings of COLOG'88, volume 417 of Lecture Notes in Computer Science, pages 76--93. Springer-Verlag, 1988.

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