ضَرَبْتُهُ لِلتَّأْدِيبِ
Translation: I struck him for discipline.
ضَرَبْتُهُ: past verb, subject suffix, and object pronoun.
لِـ: causal preposition.
التَّأْدِيبِ: genitive noun governed by the expressed lām.
This teaching expansion makes the book’s “ay li-t-taʾdīb” explicit. With a pronounced lām, the noun is genitive, not accusative.