An exclamation of praise or encouragement, an enthusiastic 'that's great!' or 'way to go!'
Informal American English, possibly from 'that's a baby' or 'attaboy' variant, emerging in early 20th-century colloquial speech. The exact origin is debated but likely developed from slang compression of encouragement phrases.
Attababy is linguistic shorthand—it's what happens when people say the same encouraging phrases so fast and so often that they get squished into one word. It's a living example of how speech gets lazy and efficient at the same time.
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