| E. Goubault and C. L. Hankin. A lattice for the abstract interpretation of term graph rewriting systems. In M. R. Sleep, M. J. Plasmeijer, and M. C. J. D. van Eekelen, editors, Term Graph Rewriting - Theory and Practice, chapter 10. Wiley, Chichester, 1993. |
....directed graphs over the vertex set S # = ff # jf 2 Sg[f # ; # ; Union # g 2 where # and # are constants and Union # is of arbitrary arity. An expression Union # x 1 : xn will be written as hx 1 ; xn i. Detailed discussion of this domain can be found in [GH93] Because of the intended meaning of the Union # operator an ordering for this domain can only be given via a concretisation map fl. In line with the literature concerning abstract interpretation we define fl as a map from abstract values to sets of values in the standard interpretation. For ....
E. Goubault and C. L. Hankin. A lattice for the abstract interpretation of term graph rewriting systems. In M. R. Sleep, M. J. Plasmeijer, and M. C. J. D. van Eekelen, editors, Term Graph Rewriting - Theory and Practice, chapter 10. Wiley, Chichester, 1993.
....the set of directed graphs over the set S # = ff # jf 2 Sg[f # ; # ; Union # g where # and # are constants and Union # is of arbitrary arity. An expression Union # x 1 : x n will be written as hx 1 ; x n i. Detailed discussion of this domain can be found in [GH93] Because of the intended meaning of the Union # operator an ordering for this domain can only be given via a concretisation map fl. In line with the literature concerning abstract interpretation, we define fl as a map from abstract values to sets of values in the standard interpretation. For ....
E. Goubault and C. L. Hankin. A lattice for the abstract interpretation of term graph rewriting systems. In M. R. Sleep, M. J. Plasmeijer, and M. C. J. D. van Eekelen, editors, Term Graph Rewriting - Theory and Practice, chapter 10. Wiley, Chichester, 1993.
....the only additional symbols used are and . 1.2 Related Work There are a number of earlier papers which attempt to formalise the algorithm. We brie y review these. The rst and (hitherto) most complete formal account of the strictness analyser, is found in a pair of papers by Goubault et al. [12, 22], which show how to place the algorithm into an abstract interpretation framework. The rst of these papers [12] uses the syntax of abstract graphs to de ne a class of the lattices required by abstract interpretation: each abstract graph is unravelled to a set of regular trees and a standard ....
....to formalise the algorithm. We brie y review these. The rst and (hitherto) most complete formal account of the strictness analyser, is found in a pair of papers by Goubault et al. [12, 22] which show how to place the algorithm into an abstract interpretation framework. The rst of these papers [12] uses the syntax of abstract graphs to de ne a class of the lattices required by abstract interpretation: each abstract graph is unravelled to a set of regular trees and a standard ordering on trees is used to induce an ordering on abstract graphs. There are two drawbacks with this approach. ....
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E. Goubault and C. L. Hankin. A lattice for the abstract interpretation of term graph rewriting systems. In Term Graph Rewriting, theory and practice, pages 131-140. John Wiley and Sons Ltd., 1993.
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