In all cases there was demanded the presentation of a libellus, or form of abjuration, in which the convert renounced and anathematized his former tenets. After declaring his abjuration to be free from compulsion, fear, or other unworthy motive, he proceeded to anathematize all heresies in general and in particular that sect to which he had belonged, together with its heresiarchs, past, present, and future. He then enumerated the tenets accepted by said sect, and, having repudiated them singly and generally, he ended with a profession of his belief in the true Faith. Sometimes there was added, under pain of punishment, a promise to remain in the Church. Accidental differences only are found in the ancient formulas of abjuration extant. Later, in the countries especially where the Inquisition was established, three sorts of abjuration were practised:

•Abjuration de formali (of formal heresy), made by a notorious heretic or apostate;
•de vehementi (of strong suspicion of heresy), made by a Catholic strongly suspected of heresy;
•de levi (of slight suspicion of heresy), made by a Catholic slightly suspected of heresy.

Source: Catholic Encyclopedia