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It is common to hear people say "used to" to indicate that they did something in the past but no longer do; for example, "I used to play basketball." How would "used to," used in that context, fit into a sentence diagram? What part of speech is it?
If "used to" is a set idiomatic phrase (i.e. not a tense), then why would it change its form from "use to" to "used to" for the sentence as it does in the positive? I.e. why not say "I use to smoke". "Did you use to smoke?" "I didn't use to smoke".
Chambers's 1939 dictionary tells us that "use to" is an intransitive verb meaning "to be accostomed to" only used in the past tense and pronounced /ust/.
Also in Practical English Usage, (Oxford),Michael Swan says that the formal form of the question and negative of "use to" is "Used you to go to the opera?" and "I usedn't to play football" etc.
In Ireland we've have remained faithful to these concepts and often "Quazi-modalize" the question and negative by saying "Usen't you go...?" and "I usedn't play..." etc.
The problem I believe is that everybody argues the case in favour of what they themselves are, if you pardon the pun! "used to" saying themselves.
Unfortunately, English does not have an academy of experts that meet once a year, unlike Spanish.
This is more of a theoretical question, and so the answer depends a lot on what framework you prefer. "Used to" in this context is sometimes called a "quasi-modal" along with "want to", "ought to" and so on. Some linguists consider them the result of a historical process called grammaticalization, in which common collocations take on their own somewhat idiosyncratic grammatical properties.
I think there are tests you can use to demonstrate that quasi-modals don't behave the same way as infinitive structures (by making them questions, for instance), but this is not my specialty. However, I think a real infinitive use of "used to" would be as in:
(1) The saw was used to cut the wood.
I can't find a good article for this right now, unfortunately. Maybe someone else knows of one?
From snailboat on ELL SE: "This is one of the seven verbs Pullum playfully calls therapy verbs (want, prospective go, habitual used, obligation have, obligation got, ought, passive supposed) in which he analyzes -to not as a separate word (as in the so-called phrasal verbs) but as a suffix (forming wanna, gonna, usta, hafta, gotta, oughta, sposta), leaving the stem as a morphological head (just as under- in undergo leaves go as the head, giving us under[gone] and under[went] rather than [undergo]ed)." (full source)
In this case, I'd say that the verb use is selecting the infinitive as its complement, making the to infinitive the direct object. The verb is tensed, ending up "used to". Another example would be "hope to blah". Here is an interesting paper on the distribution and semantic correlations between verbs that select for infinitives.
I'm not certain about the terminology, but I'm pretty sure "used to" is a set idiomatic phrase that marks verbs as being in the imperfect (past continuous) tense.
How would you explain "didn't use to" then?
I don't think I'm familiar with "didn't use to" or "didn't used to", but I would think it would be used to contrast with the present progressive: "I didn't use(d) to play basketball" would imply that I play now, but that it is a relatively new thing.
The negative is tricky, as is the question form. Didn't use to or Usen't to? Used you to or Did you use to?
@TRIG, the negative and question forms are indeed tricky. I was surprised when you wrote didn't use to and did you use to. I'm quite sure I've never had occasion to write it or to think about it much, but I'm pretty sure I've had conversations where I thought I was saying something like, "Didn't you used to play little league?"