\subsection{Lexical maps}We can easily generalize sharing to decorated tries. However,substantial savings will result only if the information at a given nodeis a function of the subtrie at that node, i.e. if such information isdefined as a {\sl trie morphism}. This will not be generally the case,since this information is in general a function of the word stored atthat point, and thus of all the accessing path to that node. The way in whichthe information is encoded is of course crucial. For instance, encodingmorphological derivation as an operation on the suffix of a flexed formis likely to be amenable to sharing common suffixes in the flexed trie,whereas encoding it as an operation on the whole stem will prevent any such sharing. In order to facilitate the sharing of mappings which preserve an initialprefix of a word, we shall use the notion of {\sl differential word} above.We may now store inverse maps of lexical relations (such as morphologyderivations) using the following structures (where the type parameter $\alpha$: codes the relation).
