P.J. Freyd, E.P. Robinson, and G. Rosolini. Dinaturality for free. In M.P. Fourman, P.T. Johnstone, and A.M. Pitts, eds., Applications of Categories in Computer Science, pages 107--118. London Math. Soc. Lecture Note Series, vol. 177, Cambridge Univ. Press, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....relationship between polymorphism on one hand and functional languages on the other. Perhaps even more fascinating is the question of parametricity where one s goal is to find models in which the interpretations of the encodings are initial among the models of the corresponding structures. See [5, 12, 18, 6] for some results on the topic. There has also been attempt to carry out the similar construction in dependent calculi [3, 17] But so far there has been no good result. We are not sure to what extent this is due to our ignorance of the free structures of generalized algebras [2] From another ....

P. Freyd, E. Robinson, and G. Rosolini. Dinaturality for free, 1992.

....bi [A ThetaB] ha 0 ; b 0 i iff a[A]a 0 b[B]b 0 ; m [A)B]n iff 8a; a 0 . a[A]a 0 implies (m Delta a) B] n Delta a 0 ) Again we will ignore recursion in this semantics. It could be incorporated using one of the PER categories that possess domain theoretic structure (Amadio, 1989; Freyd et al. 1990; Phoa, 1990) 10.1 Store Shapes Oles s construction of the category of store shapes can be carried out starting from any category C with finite products, by expressing the equational constraints on morphisms as commutative diagrams. The resulting category Sigma(C) is as follows. The proof ....

Freyd, P. J., Robinson, E. P., and Rosolini, G. (1992a). Dinaturality for free. In Fourman, M. P., Johnstone, P. T., and Pitts, A. M., editors, Applications of Categories in Computer Science, volume 177 of London Mathematical Society Lecture Note Series, pages 107--118, Cambridge, England. Cambridge University Press.

....bi [A ThetaB] ha 0 ; b 0 i iff a[A]a 0 b[B]b 0 ; m [A)B]n iff 8a; a 0 . a[A]a 0 implies (m Delta a) B] n Delta a 0 ) Again we will ignore recursion in this semantics. It could be incorporated using one of the PER categories that possess domain theoretic structure (Amadio, 1989; Freyd et al. 1990; Phoa, 1990) 10.1 Store Shapes Oles s construction of the category of store shapes can be carried out starting from any category C with finite products, by expressing the equational constraints on morphisms as commutative diagrams. The resulting category Sigma(C) is as follows. The proof ....

Freyd, P. J., Robinson, E. P., and Rosolini, G. (1992a). Dinaturality for free. In Fourman, M. P., Johnstone, P. T., and Pitts, A. M., editors, Applications of Categories in Computer Science, volume 177 of London Mathematical Society Lecture Note Series, pages 107--118, Cambridge, England. Cambridge University Press.

....free exact categories. These exact categories have some better categorical properties than the corresponding category of PER s but we need a better understanding of how this may be applied to for example programming language semantics. Thus I plan to investigate the following questions: in [21], where it was shown that under certain conditions, satisfied in the case of Kleene realizability, the above shown type does give an initial algebra. These results can possibly be generalized to other PCA s. 1. To what extent may we use the corresponding exact category instead of the category of ....

P.J. Freyd, E.P. Robinson, and G. Rosolini. Dinaturality for free. In M. P. Fourman, P.T. Johnstone, and A. M. Pitts, editors, Applications of Categories in Computer Science. Proceedings of the LMS Symposium, Durham 1991, volume 177 of London Mathematical Society Lecture Note Series, pages 107--118. Cambridge University Press, 1991.

....( Furthermore the forgetful functor to RT VEC preserves the autonomous structure. 7 Functorial Polymorphism We shall give a further development of the theory of Functorial Polymorphism applied to linear logic, following [5, 9, 22] For other developments of the general theory, cf [16, 17]. Recall that in functorial polymorphism, the types of a calculus are interpreted directly as certain multivariant functors, while terms are an appropriate multivariant version of natural transformation known as a dinatural transformation: Definition 7.1 Let C be a category, and F; G : C op ....

P. J. Freyd, E.P. Robinson, and G. Rosolini, Dinaturality for Free, in: Applications of Categories in Computer Science, ed. by M.P. Fourman, P. Johnstone, and A. M. Pitts, Cambridge University Press, (1992), pp.107-118.

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P.J. Freyd, E.P. Robinson, and G. Rosolini. Dinaturality for free. In M.P. Fourman, P.T. Johnstone, and A.M. Pitts, eds., Applications of Categories in Computer Science, pages 107--118. London Math. Soc. Lecture Note Series, vol. 177, Cambridge Univ. Press, 1992.

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