Among some, for instance al-Izz ibn Abd al-Salam (one of the half-dozen or so great mujtahids of Islamic history), innovations fall under the five axiological headings of the Shari'a: the obligatory (wajib), the recommended (mandub), the permissible (mubah), the offensive (makruh), and the forbidden (haram).[6] Under the category of 'obligatory innovation', Ibn Abd al-Salam gives the following examples: recording the Qur'an and the laws of Islam in writing at a time when it was feared that they would be lost, studying Arabic grammar in order to resolve controversies over the Qur'an, and developing philosophical theology (kalam) to refute the claims of the Mu'tazilites.
Category two is 'recommended innovation'. Under this heading the ulema list such activities as building madrasas, writing books on beneficial Islamic subjects, and in-depth studies of Arabic linguistics.
Category three is 'permissible', or 'neutral innovation', including worldly activities such as sifting flour, and constructing houses in various styles not known in Medina.
Category four is the 'reprehensible innovation'. This includes such misdemeanours as overdecorating mosques or the Qur'an.
Category five is the 'forbidden innovation'. This includes unlawful taxes, giving judgeships to those unqualified to hold them, and sectarian beliefs and practices that explicitly contravene the known principles of the Qur'an and the Sunna.