## Relating Graph and Term Rewriting via Böhm Models (1993)

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Venue: | in Engineering, Communication and Computing 7 |

Citations: | 8 - 4 self |

### BibTeX

@INPROCEEDINGS{Ariola93relatinggraph,

author = {Zena M. Ariola},

title = {Relating Graph and Term Rewriting via Böhm Models},

booktitle = {in Engineering, Communication and Computing 7},

year = {1993},

pages = {401--426}

}

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### Abstract

. Dealing properly with sharing is important for expressing some of the common compiler optimizations, such as common subexpressions elimination, lifting of free expressions and removal of invariants from a loop, as source-to-source transformations. Graph rewriting is a suitable vehicle to accommodate these concerns. In [4] we have presented a term model for graph rewriting systems (GRSs) without interfering rules, and shown the partial correctness of the aforementioned optimizations. In this paper we define a different model for GRSs, which allows us to prove total correctness of those optimizations. Differently from [4] we will discard sharing from our observations and introduce more restrictions on the rules. We will introduce the notion of Bohm tree for GRSs, and show that in a system without interfering and non-left linear rules (orthogonal GRSs), Bohm tree equivalence defines a congruence. Total correctness then follows in a straightforward way from showing that if a program M co...