| Jean-Yves Girard. Linear logic and parallelism. In Mathematical Models for the Semantics of Parallelism, LNCS 280, Springer Verlag, 1987. |
....model of Linear CHAM based on Abramsky s idea of a stack of coequations and a name queue, and then we consider a concurrent multi thread implementation of the model. 1 Introduction Girard s Classical Linear Logic (CLL) 6] is expected to give new theoretical foundations of parallel computation [7]. Abramsky [1] gave a computational interpretation of CLL using the framework of Berry and Boudol s Chemical Abstract Machine (CHAM) 3] In this computational system which is called Linear Chemical Abstract Machine (Linear CHAM) proof expressions are assigned to proof trees in CLL, and they are ....
Jean-Yves Girard. Linear logic and parallelism. In Mathematical Models for the Semantics of Parallelism, LNCS 280, Springer Verlag, 1987.
....some of his nodes. The nodes are those presented in the introduction: T root void i croissant i bracket i fan 3.2 Reduction The rules for reduction are particularly simple, since we want not to be ridiculous. To our knowledge, Girard was the first to write on the desire not to be ridiculous [Girb]; we continue his work in this respect too. In the rules, given in Figure 1, it is assumed that 0 i j. Because of the form of these rules, we are dealing with interaction nets. An immediate consequence is that the system is Church Rosser, as there are no critical pairs. Interaction nets have ....
Jean-Yves Girard. Linear logic and parallelism.
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