@MISC{Schroeter01datarefinement, author = {Gunnar Schroeter and Gunnar Schroeter Tu-berlin}, title = {Data Refinement as Reduction Steps}, year = {2001} }

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Abstract

this paper this is done for data re nement as de ned in [1], i.e., program re nement, data type re nement and L-simulation and L simulation of data types are reconstructed as development steps of transformation systems. Then these reconstructions are extended up to arbitrary transformation systems. The adequacy is shown by proofs of the equivalence of the original and the reconstructed re nement relations. Finally by the reconstruction of the re nement operation of transformation systems within the relational framework of [1] the open question of constructing compatible data types could be answered. But we will start with a short introduction into the transformation system famework of [2], i.e., the de nition of transformation systems and the de nitions of development steps of transformation systems. 2 Transformation Sytems and Development Steps A transition system is a two layer structure with a transition graph, called control graph, as the representation of the control ow, a transition graph, called data space, as the space of all possible labels and a labeling maping from the control graph into the data space. A transition graph includes the following parts: a set CS of (control) states, a family T = T (c; d) c;d2CS of sets of transitions from an arbitrary (control) state c to an arbitrary (control) state d, a special initialization respectively nalization state in 2 CS and a function id : CS ! T that assigns an idle transition id(c) 2 T (c; c) for each (control) state c 2 CS