Head wrapping

[67] proposes a grammatical formalism called Head Grammar (HG). HG is a slightly more powerful formalism than context-free grammar. The extra power is available through head wrapping operations. A head wrapping operation manipulates strings which contain a distinguished element (its head). Such headed strings are a pair of an ordinary string, and an index (the pointer to the head), for example $\langle$w₁w₂w₃w₄, 3$\rangle$ is the string w₁w₂w₃w₄ of which the head is w₃. Grammar rules define operations on such strings. Such an operation takes n headed strings as its arguments and returns a headed string. A simple example is the operation which takes two headed strings and concatenates the first one to the left of the second one, and where the head of the first one is the head of the result (this shows that the operations subsume ordinary concatenation). The rule is labelled LC1 by Pollard:

$$LC1( \langle\sigma,i\rangle, \langle\tau,j\rangle ) := \langle\sigma\tau,i\rangle$$
The following example shows that head-wrapping operations are in general more powerful than concatenation. In this example the second argument is `wrapped' around the first argument:

$$RL2(\langle\sigma,j\rangle,\langle t_1\dots t_n,i\rangle) := \langle t_1 \dots t_i \sigma t_{i+1}\dots t_n,i\rangle$$
As an example, Pollard presents a rule for English auxiliary inversion:

$$S[+INV] \rightarrow RL2(NP, VP[+AUX])$$
which may combine the noun phrase `Kim' and the verb phrase `must go' to yield `Must Kim go', with head `must'.

The motivation Pollard presents for extending context-free grammars (in fact, GPSG), is of a linguistic nature. Especially so-called discontinuous constituencies can be handled by HG whereas they constitute typical puzzles for GPSG. Apart from the above mentioned subject-auxiliary inversion he discusses the analysis of `transitive verb phrases' based on [8]. The idea is that in sentences such as

`persuaded' + `to leave' form a (VP) constituent, which then combines with the NP object ('Kim') by a wrapping operation.

Yet another example of the use of head-wrapping in English are the analyses of the following sentences.

where in the first two cases `taller than Sandy' is a constituent, and in the latter examples `easy to please' is a constituent.

Breton and Irish are VSO languages, for which it has been claimed that the V and the O form a constituent. Such an analysis is readily available using head wrapping, thus providing a non-transformational alternative for the analysis of [56].

Finally, Pollard also provides a wrapping analysis of Dutch cross-serial dependencies.