Henry George Liddell, Robert Scott, A Greek-English Lexicon

A.real appearance seen in a state of waking, waking vision, opp. ὄναρ (a dream), οὐκ ὄναρ, ἀλλ᾽ ὕ. no illusive dream, but a (vision of) reality, Od.19.547, 20.90; “ἐξ ὀνείρου δ᾽ αὐτίκα ἦν ὕ.” Pi.O.13.67; “ἵνα ὕ. ἀντ᾽ ὀνείρατος γίγνηται” Pl. Plt.278e.

II. acc. abs. is used as Adv., in a waking state, awake, “ὕ. ἀλλήλοις διαλεγόμεθα” Id.Tht.158c, cf. IG42(1).122.133, al. (Epid., iv B. C.); opp. ὄναρ, ἀμφισβήτημα . . περὶ τοῦ ὄναρ τε καὶ ὕ. a question . . about sleeping and waking, Pl.Tht. l. c.; οἷον ὄναρ εἰδὼς . . πάλιν ὥσπερ ὕ. ἀγνοεῖν knowing things in a dream . . not to know them when one awakes, Id.Plt.277d; ὄναρ ἢ ὕ. ζῆν to pass life asleep or awake, Id.R. 476c, cf. Ti.71e; καὶ ὄναρ καὶ ὕ. both sleeping and waking, i.e. both by day and night, always, Hp.Lex4, cf. Democr.174; οὔτε ὄναρ οὔθ᾽ ὕ. neither sleeping nor waking, i.e. not at all, Pl.Phlb.36e; οὔθ᾽ ὕ. οὔτ᾽ ὄναρ ib.65e, cf. R.382e; καθ᾽ ὕπνον . . , ἢ καὶ ὕ. ἐγρηγορώς wide awake, Id.Lg.800a; opp.ἐν τοῖς ὕπνοις, Arist.Pr.957a18; ὕ. καὶ μεθ᾽ ἡμέραν, opp. κατὰ τὸν ὕπνον, Plb.10.5.5.

2. ὕπαρ in reality, actually, “ἔκρινα πρῶτος ἐξ ὀνειράτων ἃ χρὴ ὕ. γενέσθαι” A.Pr.486; “ὕ. ἡ πόλις οἰκήσεται ἀλλ᾽ οὐκ ὄναρ” Pl.R.520c, cf. 574e, 576b, al.—The phrase καθ᾽ ὕπαρ is censured by Phryn.395, and is f.l. for καθ᾽ ὕπνους in Apollod.3.12.5.