In order for grammars to be reversible, I argued in the beginning of this chapter, that operations on strings, which go beyond concatenation, may be helpful for the following two reasons.
Firstly, such non-concatenative grammars may allow analyses, which reflect more directly the way in which the semantic structures are built up. As a consequence, such grammars may be easier to handle for generation algorithms.
Secondly, I argued that the addition of expressive power, as compared with concatenative grammars, may be useful, in order to obtain grammars, which can effectively be parsed. In the case of concatenative grammars, one is often forced to `implement' certain discontinuous constituency constructions using the types of rule (empty rules, and non-branching rules) for which there is a danger that the resulting grammar is not effectively parsable anymore.
After a short excursion through a number of proposed extensions to concatenative grammars, I discussed a generalization of these extensions, and provided an example grammar, for a tiny fragment of Dutch.
I then showed that such non-concatenative grammars can be parsed, by a generalization of the left-corner parser: the head-corner parser. This parsing regime was motivated by the desire to use both bottom-up information (the information available in lexical entries), and top-down information (the constraints heads impose upon their arguments -- using head-feature percolations.)
A proper superset of Constraint-based Lexicalized Tree Adjoining Grammars can be parsed effectively, using the head corner parser.