Ad extirpanda ("To eradicate"; named for its Latin incipit) was a papal bull promulgated on Wednesday, May 15, 1252 by Pope Innocent IV which authorized under defined circumstances the use of torture by the Inquisition as a tool for interrogation.

[1][2] The bull was issued in the wake of the murder of the papal inquisitor of Lombardy, St. Peter of Verona, who was killed by a conspiracy of Cathar sympathizers on 6 April 1252.

[2] The bull argued that as heretics are "murderers of souls as well as robbers of God’s sacraments and of the Christian faith", they are "to be coerced—as are thieves and bandits—into confessing their errors and accusing others, although one must stop short of danger to life or limb.

[6][1] The relevant portion of the bull read: "Those convicted of heresy by the aforesaid Diocesan Bishop, surrogate or inquisitors, shall be taken in shackles to the head of state or ruler or his special representative, instantly, or at least within five days, and the latter shall apply the regulations promulgated against such persons.

"[1] The 1199 bull Vergentis in senium by Innocent III already declared heresy a crime of lèse-majesté, so deserving the death penalty.