\subsection{Lexical maps}

We can easily generalize sharing to decorated tries. However,
substantial savings will result only if the information at a given node
is a function of the subtrie at that node, i.e. if such information is
defined as a {\sl trie morphism}. This will not be generally the case,
since this information is in general a function of the word stored at
that point, and thus of all the accessing path to that node. The way in which
the information is encoded is of course crucial. For instance, encoding
morphological derivation as an operation on the suffix of a inflected form
is likely to be amenable to sharing common suffixes in the inflected 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 initial
prefix of a word, we shall use the notion of {\sl differential word} above.

We may now store inverse maps of lexical relations (such as morphology
derivations) using the following structures 
(where the type parameter $\alpha$: codes the relation).