The verb do can be used optionally as an auxiliary even in simple declarative sentences, usually as a means of adding emphasis (e.g. "I did shut the fridge.").
However, in negated and inverted clauses, do is usually used in today's Modern English.
For example, the sentence I am not with the copula be is fully idiomatic, but I know not with the finite lexical verb know, while grammatical, is archaic.
The presence of an auxiliary (or copular) verb allows subject–auxiliary inversion to take place,[1][2] as is required in most interrogative sentences in English.
[1][2][3][4] In the second sentence, do-support is required because idiomatic Modern English does not allow forms like *She laughs not.
The auxiliary generally appears for purposes of emphasis, for instance to establish a contrast or to express a correction: As before, the main verb following the auxiliary becomes a bare infinitive, which is not inflected (one cannot say *did ate or *does sings in the above examples).
That applies whether or not do-support is used: Emphatic do can also be used with imperatives, including with the copula be: The auxiliary do is also used in various types of elliptical sentences, where the main verb is omitted (it can be said to be "understood", usually because it would be the same verb as was used in a preceding sentence or clause).
That includes the following types: Such uses include cases that do-support would have been used in a complete clause (questions, negatives, inversion) but also cases that (as in the last example) the complete clause would normally have been constructed without do (I fell asleep too).
In Early Modern English, the semantic value was lost, and the usage of forms with do began to approximate that found today.
[8]: 23 Examples of auxiliary "do" in Old English writing appear to be limited to its use in a causative sense, which is parallel to the earliest uses in other West Germanic languages.
[8]: 24 Some scholars, such as linguist John McWhorter, argue that the construction arose via the influence of Celtic speakers;[9] for instance Welsh uses the verb gwneud "to do" to optionally form periphrastic alternatives to inflected verbs (with no difference in meaning).
[citation needed] Others contend that the construction arose as a form of creolization when native speakers addressed foreigners and children.