has no negative form. Also, will has an irregular negative won't instead of the expected *willn't and shall has an irregular negative shan't instead of the expected (and now archaic) *shalln't. Ellipsis In a typical case, an auxiliary verb takes a non-finite clause complement. But this can be elided, as in the example above. Lexical verbs taking a non-finite clause complement don't allow this kind of ellipsis. Rebuttal When two people are arguing, the second may deny a statement made by the first by using a stressed too or so. For example, having been told that they didn't do their homework, a child may reply I did too. This kind of rebuttal is impossible with lexical verbs. The case of to Various linguists, including Geoff Pullum, Paul Postal and Richard Hudson, and Robert Fiengohas have suggested that to in cases like I want to go (not the preposition to) is a special case of an auxiliary verb with a no tensed forms. Rodney Huddleston argues against this position in The Cambridge Grammar of the English Language, but Robert Levine counters these proposals. BetteLou Los calls Pullum's arguments that to is an auxiliary verb"compelling". In terms of the NICER properties, examples like it's fine to not go shows that it allows negation. Inversion, contraction of not, and rebuttal would only apply to tensed forms, and to is argued to have none. It does allows ellipsis though: I don't want to, but rebuttal is not possible. Auxiliaries as helping verbs An auxiliary is traditionally understood as a verb that "helps" another verb by adding (only) grammatical information to it. On this basis, English auxiliaries include: forms of the verb do (do, does, did) when used with another verb to form questions, negation, emphasis, etc. (see do-support); forms of the verb have (have, has, had) when used to express perfect aspect; forms of the verb be (am, are, is, was, were) when used to express progressive aspect or passive voice; the modal verbs, used in a variety of meanings, principally relating to modality. The following are examples of sentences containing the above types of auxiliary verbs: Do you want tea? – do is an auxiliary accompanying the verb want, used here to form a question. He had given his all. – had is an auxiliary accompanying the past participle given, expressing perfect aspect. We are singing. – are is an auxiliary accompanying the