Download Categorical Methods in Computer Science With Aspects from by Hartmut Ehrig (auth.), H. Ehrig, H. Herrlich, H. -J. PDF

By Hartmut Ehrig (auth.), H. Ehrig, H. Herrlich, H. -J. Kreowski, G. Preuß (eds.)

This quantity comprises chosen papers of the foreign Workshop on "Categorical equipment in machine technology - with features from Topology" and of the "6th overseas facts variety Workshop" held in August/September 1988 in Berlin. The 23 papers of this quantity are grouped into 3 elements: Part 1 comprises papers on specific foundations and primary strategies from class thought in machine technology. Part 2 provides purposes of specific tips on how to algebraic specification languages and strategies, information varieties, info bases, programming, and technique necessities. Part 3 contains papers on categorial points from topology which commonly pay attention to targeted adjoint occasions like cartesian closeness, Galois connections, reflections, and coreflections that are of growing to be curiosity in express topology and machine science.

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The following examples show how this can be done. 1 Example 1: Partial Orders. Suppose Prog( - - - , "lst", - - - ) is a program that takes as input a list "lst" of elements from a poset and retm'ns a list of maximal chains in "lst" as a list of lists. We want to determine a type for Prog. Clearly its type is of the form Vt e PO. [list of (t) ~ list of (list of (t))] where t ¢ PO means t is a suitable structure including a partial order. The problem is to describe a semantics for this kind of reslricted quantification.

M. E. EJ. Brouwer Centenary Symposium, A. S. Troelstra and D. , North-Holland, Amsterdam, 1982. [l-Iyland et a180] J. M. E. Hyland, P. T. Johnstone, A. M. Pitts, Tripos theory, Math. Proc. Cambridge Philos. Soe. 88 (1980), 205 - 232. [Hyland, Pills 89] J. M. E. Hyland and A. M. Pitts, The Theory of Constructions: Categorical Semantics and Topos-theoretic Models, in [CCSL], to appear. [Kelly 82a] G. M. Kelly, Structures defmed by finite limits in the enriched context, 1, Cahiers de Top. et G~om.

U n i o n t C O M P, : u n i o n --, bool ~ f o r i =. n are used: . Obviously, the specifications 2-union and, for example, 3 - u n i o n follow the same underlying scheme. But as parameterized specifications they are not closely related to each other. They are independent of each other, the underlying scheme is not supported by the concept of parameterized specifications. As such, edition and design of both specifications must be done twice in contradiction to our intuition. If we replace comp2 by 2u n i o n ( c o m p 2 + comp3) in 2 - u n i o n ( c o m p i + comp2) using the parameter passing morphism par with p a r ( c o m p l ) = compl and par(comp2) = union, we get at least an approximation of 3-union from 2-union.

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