id * id, F * id, T * id, T * F, T, E
which form the rotos of the subtrees in Fig 4.25.
By definition, a reduction is the reverse of a step in a derivatiion (recall that in a derivation, a nonterminal in a sentential form is replaced by the body of one of its productions). The goals of bottom-up parsing is to construct a derivation in revese order. The following derivation corresponds to the parse in Fig. 4.25.
E ⇒ T ⇒ T * F ⇒ T * id ⇒ F * id ⇒ id * id
Fig 4.26 Handles during a parse of id1 * id2
Formally, if S ⇒rm* βAω ⇒rm αβω, as in Fig 4.27, then production A → β in the position following α is a handle of αβω. Alternatively ....