R. M. Burstall, An Algebraic Description of Programs with Assertions, Verification and Simulation, in Proc. ACM Conference on Proving Assertions about Programs, SIGPLAN Notices 7, 1, ACM 72.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....pullback. As an application of the theory, Section 7 introduces a simple parallel language which is given a categorical interpretation in Section 8. We conclude in Section 9. 2 Flowcharts as functors We begin with an example of a category of systems which provides intuition for later sections. In [9] Rod Burstall describes how a flow chart can be represented by a functor from a free category to the category of sets and partial functions, or more generally, sets and relations. A program is a system (G; F (G) S Rel) where G is a graph and F (G) is the free category. Figure 1 illustrates this ....

Rod Burstall. An algebraic description of programs with assertions, verification and simulation. In J. Mack Adams, John Johnston, and Richard Stark, editors, Conference on Proving Assertions about Programs, pages 7--14. ACM, 1972.

....2, and the assignment X : X Gamma 1 corresponds to the partial function sending X to X Gamma 1 when X 0. The semantics of P with input node n and output node n 0 is then given by the formula P (n; n 0 ) S fP (p) j p : n n 0 2 Pa(G)g. This approach originated in Burstall [5]. Techniques that allow programs to have syntax as well as semantics are described in [19] 2 : A program scheme is a functor P : G T into a theory T enriched with a partial order structure on its morphism sets T (A; B) the reader familiar with 2 categories should note that this makes T a ....

....or sketches) and to the more general data representations studied in the abstract data type literature (e.g. 33, 9] 3.4 Program Homomorphisms. Because Example 2.7 defines programs as functors, we expect program homomorphisms to be natural transformations between programs. Indeed, Burstall [5] shows that a weak form of Milner s program simulations [53] arises in just this way. In [19] this is generalised to programs that may have different shapes, and to maps from edges to paths, by defining a homomorphism from P 0 : G 0 C to P 1 : G 1 C to consist of a functor F : G 0 Pa(G 1 ) ....

Rod Burstall. An algebraic description of programs with assertions, verification, and simulation. In J. Mack Adams, John Johnston, and Richard Stark, editors, Proceedings, Conference on Proving Assertions about Programs, pages 7--14. Association for Computing Machinery, 1972.

No context found.

R. M. Burstall, An Algebraic Description of Programs with Assertions, Verification and Simulation, in Proc. ACM Conference on Proving Assertions about Programs, SIGPLAN Notices 7, 1, ACM 72.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC