Cut-n-paste from material I'm not using in the book anymore (edit later to make sense): Now, how are we going to test these tree patterns against every subtree in our original tree? In what order should we visit nodes? For this application, it turns out we need a simple ``apply once'' rule application strategy and a ``down then up'' tree traversal strategy. Let's look at rule application first. As we visit each node, we need to see if any of our patterns match. If a pattern matches, we execute the associated tree rewrite and move on to the next node. In other words, we only look for a single rule application opportunity (we'll see below that we sometimes need to repeatedly apply rules). The following method applies a rule in a @cl TreeParser (derived from a tree grammar) to a tree: here is where weReferenced code/walking/patterns/TreePatternMatcher.java It uses reflection to lookup the appropriate rule within the generated tree parser class (@cl Simplify in this case). Most of the time, the rule will not match the tree. To avoid issuing syntax errors and attempting error recovery, it bumps up the backtracking level. Upon failure, the invoked rule immediately returns. If you don't plan on using this technique in your own ANTLR-based application, don't sweat the details. This method boils down to ``call a rule to match a tree, executing any embedded actions and rewrite rules.'' At this point, we know how to define tree grammar rules and how to apply them to a particular subtree. The final piece of the tree pattern matcher is the actual tree traversal. We have to get the correct node visitation order. In particular, we need to perform the scalar-vector multiply transformation on the way down (preorder) and we need to reduce multiply-by-zero subtrees on the way up (postorder). To implement a top-down visitor, we do a depth first walk of the tree, executing an action in the preorder position. To get a bottom-up visitor, we execute an action in the postorder position. ANTLR provides a standard @cl TreeVisitor class with a depth first search @v visit method. That method executes either a @m pre or @m post method or both. In our case, we need to call @m applyOnce in both. On the way down, we'll look for @r vmult patterns. On the way up, we'll look for @r mult0 patterns.