Candidate and search space for given input sequence

Given a particular input sequence w, the candidate trees for this
sequence are

- all the trees that can be generated by the tree grammar
- which spell out w as their sequence of leaves (in left to right order)

How to find these trees/scores for given w is not your problem. There
is a standard device (called a tabulating tree parser) that can
compute the trees as well as the scores.

This device also applies the choice function specified with the
algebra at intermediate steps.

This means in ADP, after specifying algebra(s) and grammar, you have no
other code to add to obtain a running program.