WoW API: UIHANDLER OnTabPressed

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EditBox:OnTabPressed()

EditBox:SetScript("OnTabPressed", function(self)
    self:Insert("    "); -- (4 spaces)
end;

This will insert 4 spaces at your cursor's position. A tab character or \t will not work, therefore spaces are used.

Warning: Default sort key "OnTabPressed" overrides earlier default sort key "UIHANDLER OnTabPressed".