-dir — written-register copula and modal of inference
-dir (with harmony variants -dır, -dur, -dür, and -tir/-tır/-tur/-tür after voiceless consonants) is the formal written copula meaning 'is' or 'are'. O bir öğrencidir. = 'He/she is a student' — like English 'he is a student' but more formal, the way you'd see it in a textbook or news report. In speech you'd usually drop it: O bir öğrenci. -dir also expresses probability or inference on past or evidential forms: Şimdi evdedir. = 'He must be at home now / He's surely at home'. Gelmiştir. = 'He must have come / He's come (it's been established).'
The eight harmony shapes
After a, ı: -dır (after voiceless -tır). After e, i: -dir (after voiceless -tir). After o, u: -dur (after voiceless -tur). After ö, ü: -dür (after voiceless -tür). So: öğrencidir ('is a student'), kapıdır ('it's a door'), doktordur ('is a doctor'), müdürdür ('is a manager'), kitaptır ('is a book' — voiceless p triggers t), çiçektir ('is a flower'), dosttur ('is a friend'), gençtir ('is young').
Spoken vs. written
In conversation, -dir is rare for plain statements. You'd say O bir öğrenci. ('She's a student') with a bare predicate — Turkish copula-zero is the default. -dir comes back in: textbooks (Türkiye, başkenti Ankara olan bir ülkedir.), encyclopedias, news (Cumhurbaşkanı bugün Ankara'dadır.), official signs (Sigara içmek yasaktır. = 'Smoking is forbidden'), and probability (see below).
Probability and inference
Stack -dir onto a tense form to mean 'must / surely / probably'. Şimdi uyuyordur. = 'He must be sleeping now.' Yorgundur. = 'She's surely tired.' Trafikte kalmıştır. = 'He must have got stuck in traffic.' (lit. 'has-stayed-must'). Gelmiştir vs. gelmiş: the bare gelmiş says 'apparently he came' (hearsay). Gelmiştir strengthens it to 'he has indeed come / he must have come' — a confident inference. This is one of the most common live uses of -dir in modern speech.
Var and yok with -dir
var ('there is') and yok ('there is not') can also take -dir: Bu kitapta üç bölüm vardır. = 'There are three chapters in this book' (formal/written). Hiçbir umut yoktur. = 'There is no hope.' Add a 3rd-person plural and you get vardırlar / yokturlar but those are very heavy — reserve -dir + -lar for the most formal contexts. In ordinary speech: var, yok with no suffix is fine.
Person endings vs. -dir
-dir is only the 3rd person. For other persons you use the regular personal endings you already know: öğrenciyim (I am a student), öğrencisin (you are), öğrencidir (he/she is — formal), öğrenciyiz (we are), öğrencisiniz (you all are), öğrenciler / öğrencidirler (they are). Probability -dir can attach to other persons too: Geç kalmışımdır. = 'I must have been late.' But this is rare — usually -dir sits on the 3rd person.
