K. Bruce, A.R. Meyer, and J.C. Mitchell, The semantics of 2nd order - calculus, Information and Computation 85 (1990), p.76-134.  Home/Search   Document Not in Database   Summary   Related Articles

....complete for F: This choice is not at all costly: one just nds here retraction pairs where one would nd pairs of inverse isomorphisms in the extensional case. Very general de nitions of models of F have already been proposed in the literature 10 , mainly: the de nition of Bruce Meyer Mitchell [11], and various categorical de nitions (see e.g. 3] and [23] Because of the strong reactions of one referee it seems we have to be still more explicit about the reasons why we do not start from one of these de nitions. 9 In fact it only covers the universal retraction models which are based on ....

....why we do not start from a categorical de nition, whether well known or possibly adapted for our paper, is that such de nitions are hermetic to the nonspecialist, and that their high level of abstraction is of no use here. The reason why we do not start from the (well established) de nition of [11] is di erent. This de nition describes in a rather natural way what a second order structure is and what the interpretations of types and terms in it should be, but then it only de nes a model as a second order structure such that these interpretations are well de ned. Such a statement gives ....

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K. Bruce, A.R. Meyer, and J.C. Mitchell, The semantics of 2nd order - calculus, Information and Computation 85 (1990), p.76-134.

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