Maddeningly...
Not long ago, my friend H sent me the following message:
‘You know the expression “I used to
In questions (and other constructions) that use ‘do-support’, tense is marked on do rather than the main verb.
(1)
a. Did you eat the cake?
b. *Do you ate the cake?
c. *Did you ate the cake?
This pattern points to did you use to as the answer, since did you used to has both did and used in the past tense.
Indeed, I quickly came across a ‘learn English’ website which states ‘You should use “use to” without a d in sentences when it follows “did” or “didn’t”.’ However, it also has the parenthetical caveat ‘don’t worry too much about this because lots of people get it wrong.’ This qualification suggests that many native English speakers do use did you used to. Thus, since linguists are concerned with describing actual usage rather than prescribing what is supposedly ‘right’ or ‘wrong’, H’s question clearly merited further consideration.
The expression used to is unusual in that, at least in declarative sentences, it is only used in the past tense. One cannot say (2), for instance, as a way of expressing a present habit.
(2) *He uses to eat cake every day.
While other verbs in English, such as seem and want, do take to-infinitive complements, they usually may take other types of complement as well, with no effect on the essential meaning of the verb.
(3)
a. He wants to eat cake.
b. He wants cake.
c. He seems to like cake.
d. He seems happy with his cake.
Perhaps a bit closer is have to, which, like used to, has a different sense from the form of the verb which does not take a to-infinitive complement.
(4)
a. He used to eat cake frequently.
b. He uses the knife to cut the cake.
c. He had to eat cake frequently.
d. He has cake and eats it, too.
As apparent from (4d), though, have in have to conjugates normally, as opposed to used in used to. Given that used to is always in the past tense in declarative sentences, then, it seems to be somewhat fixed, potentially making speakers disinclined to say use to, even in contexts where a verb would usually be in the present tense.
I ran the two options through a search engine in order to see if one shows up more frequently than the other. Since the internet comprises a vast amount of language data, produced by a variety of people, looking things up on Google can be a useful way to informally test hunches or look for usage trends. However, among its many limitations for research in linguistics, Google does not allow searchers to specify sentence structure. In this case, then, I got many instances of did you use to which had the utilisation sense of use:
(5) What did you use to teach yourself python?
It is also possible to have a similar construction with past tense used, as in:
(6) Here’s the book I used to learn python.
Of course, there is a clear semantic difference between to use in the sense of utilisation, and used to, which denotes either past actions, as in (7a), or being accustomed to something, as in (7b).
(7)
a. I used to eat lots of cake.
b. Now I am used to having crumpets instead.
It’s quite possible that all these meanings are etymologically related (see ‘use v.’ on this page). Regardless, the utilisation used to and the habitual used to are pronounced differently: in (8a) used has a z sound followed by a d sound; in (8b) it has an s sound and a t sound, though the latter is likely to not be present at all, since the following sound is also a t, and when two proximate sounds are identical one may get deleted.
(8)
a. That’s the fork I used to eat the cake.
b. I used to use a spoon instead.
This distinction in pronunciation may arise from the presence of a ‘trace’ (or at least some sort of gap) between used and to when they are adjacent for the utilisation sense (8b): the intervening element would block phonological processes which affect the pronunciation of used when it is adjacent to to in the habitual past sense (8a). This apparent interference mirrors the case of want to, which cannot be contracted to wanna in (9b) because there is an intervening trace. (The basic idea is that who starts out as the subject of the lower sentence, e.g. You want {who} to buy the cake, and then moves. Evidently, young children sometimes pronounce traces (second video).)
(9)
a. I wanna eat some cake.
b. *Who do you wanna bake the cake?
In conclusion, then, even if people intend to say did you used to (and Google actually comes up with more hits for people writing it this way than the other, though we can’t know how many are from non-native speakers, grammar guides, etc.), they are probably pronouncing it did you use to anyway. So, while both are acceptable, did you use to wins phonologically.
[NB: The BBC World Service agrees that both are grammatical. As does the OED, which states ‘In very frequent use from c 1400, but now only in pa. tense used to…and colloq. in did (not) use (or used) to’.]