Summary: Relating Graph and Term Rewriting via B¨ohm
Models
Zena M. Ariola
Computer & Information Science Department, University of Oregon
Eugene, OR 97403­1202
Abstract. Dealing properly with sharing is important for expressing
some of the common compiler optimizations, such as common subex­
pressions elimination, lifting of free expressions and removal of invariants
from a loop, as source­to­source 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 optimiza­
tions. 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 restric­
tions on the rules. We will introduce the notion of B¨ohm tree for GRSs,
and show that in a system without interfering and non­left linear rules
(orthogonal GRSs), B¨ohm tree equivalence defines a congruence. Total
correctness then follows in a straightforward way from showing that if a
program M contains less sharing than a program N , then both M and

Source: Ariola, Zena M. - Department of Computer and Information Science, University of Oregon

Collections: Computer Technologies and Information Sciences