Shaw's Man and Superman is a comedy of purpose in that it is a vehicle for Shaw's evolving philosophy that emphasized evolution, eugenics, and the so-called "Life Force." This philosophy, heavily influenced by thinkers ranging from Jean-Baptiste Lamarck to Friedrich Nietzsche and Henri Bergson, claimed that men and women were driven by the so-called "Life Force" to bring about the elevation of the species to what he called, following Nietzsche, "supermen." The play revolves around this concept, particularly the romance between Ann Whitefield and John Tanner. Conventional morality and all the ritualistic aspects of courtship are in many ways "window dressing" for this will to improve the species through finding a mate with superior qualities.
Act III, in particular, makes for very difficult viewing (and staging) and is fairly blatantly intended to be an exposition of Shaw's views. It features Don Juan, Ann, and the Devil in an extended conversation about the subject, with the Devil specifically referencing Nietzsche, whose works have become "the latest in fashion among Life Force fanatics." But perhaps the most telling evidence that the play was intended as a comedy of purpose comes in the dedicatory epistle written by Shaw to his friend Arthur Bingham Walkley. In it, he expressly says that he has no illusions that the play will be popular with the masses, and that he would rather it appealed to intelligent, educated people:
It will take my books as read and my genius for granted, trusting me to put forth work of such quality as shall bear out its verdict...what I have always wanted is a pit of philosophers; and this is a play for such a pit.
So Shaw is far more concerned with the purpose of expressing his philosophic convictions than writing a comedy that will appeal to theater-goers.