J.-Y. Girard, Y. Lafont, and L. Regnier, editors. Advances in Linear Logic, Proceedings of the 1993 Workshop on Linear Logic, London Math. Soc. Lecture Note Series 222. Cambridge University Press, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....(i.e. syntax directed ) compilation from high level functional programs into a reversible model of computation. Our approach also has conceptual interest in that our constructions, while quite concrete, are based directly on ideas stemming from Linear Logic and Geometry of Interaction [18, 19, 20, 21], and developed in previous work by the present author and a number of colleagues [2, 3, 5, 6, 7, 9, 10] Our work here can be seen as a (relatively) concrete manifestation of these more abstract and foundational developments. However, no knowledge of Linear Logic or Geometry of Interaction is ....

....4.1 (I; f AS ; f AK ) is a combinatory algebra. This theorem is a minor variation on the results established in [5, 6, 9, 7, 10] see in particular [10] and the combinatory algebra of partial involutions studied in [7] The ideas on which this construction is based stem from Linear Logic [18, 21] and Geometry of Interaction [19, 20] in the form developed by the present author and a number of colleagues [2, 3, 5, 6, 9, 7, 10] We now want to de ne a subalgebra of I consisting of those partial injective maps realized or implemented by a biorthogonal automaton. The key result we need ....

J.-Y. Girard, Y. Lafont, L. Regnier, eds. Advances in Linear Logic, London Math. Soc. Series 222, Camb. Univ. Press.

....all favoured to some degree by di erent authors. Additive Multiplicative Conj Unit Disj Unit Conj Unit Disj Unit Here u t 1 0 Girard, 2] N 0 1 O Troelstra, 8] u t 1 0 Seely, 7] 1 0 I A nice survey of linear logic (as it stood in 1995) can be found in [3]. One of the novelties of linear logic is that formulas carry a duality ( For this we need to assume that the variables come in dual pairs P P i.e. the dual of P is P and the dual of this is P = P . When we have such a dual pairing we may generate the formal dual of ....

J.-Y. Girard, Y. Lafont, L. Regnier; `Advances in linear logic', London Math Soc lecture notes series 222, C.U.P., 1995.

....of the variables that are often present in such plataforms for computation, there is no Curry Howard Isomorphism here. Therefore, we are dealing with a model of computation that is more general than a purely mathematical one. In comparison with classical and intuitionistic logics, linear logic[26, 27], which is based on current states, can easily model actions on material resources, and it can also be used to model both parallel processing and mobility, if we do not want to consider details concerning the physical nature of computation. For instance, if A(X; t) stands for the attempt to ....

J.-Y. Girrard, Y. Lafont, and L. Regnier, editors. Advances in Linear Logic. Cambridge University Press, 1995.

....resemblance, but that were inspired by very different motivations: Interaction Nets and MONSTR. Interaction Nets (Lafont 1990, Lafont 1991) evolved from the multiplicative fragment of Linear Logic (From the vast literature on that subject, see the work by Girard (1987) Troelstra (1992) Girard et al. 1995). The basic idea is that a multiplicative proof object consists of inference steps. The object is represented by a graph, in which the individual inference steps, combining a number of hypotheses to form a conclusion, are represented by agent nodes for which the adjacent edges represent the ....

Girard, J-Y., Lafont, Y. and Regnier, L. (eds), (1995) Advances in Linear Logic. London Mathematical Society Lecture Notes Series 222, Cambridge University Press, Cambridge.

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J.-Y. Girard, Y. Lafont, and L. Regnier, editors. Advances in Linear Logic, Proceedings of the 1993 Workshop on Linear Logic, London Math. Soc. Lecture Note Series 222. Cambridge University Press, 1995.

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J.-Y. Girard, Y. Lafont, L. Regnier, eds. Advances in Linear Logic, London Math. Soc. Series 222, Camb. Univ. Press, 1995.

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Jean-Yves Girard, Yves Lafont, and Laurent Regnier, editors. Advances in Linear Logic,volume 222 of London Math. Soc. Lecture Notes. Cambridge Univ. Press, 1995. 12. COHERENCE SPACES 503

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