what was the function of the Roman cavalry?

[Matthew]

For instance in the 17th century, John Cruso in his "Militarie Instructions for the Cavallerie", the standard manual used for cavalry in the English Civil War, wrote how to train a horse "to ride him against a compleat armour, so set upon a steak, that he may overthrow it, and trample it under his feet: that so (and by such other means) your horse (finding that he receiveth no harm) may become bold to approach any object"
In that period there are plenty of battles in which infantry was charged and routed by cavalry.

That's not quite the same thing as training a horse to charge a compact body of Infantry, though; that's training a horse to fight and cope with individual combatants.

As I recall, the last time this discussion was had, it was shown that Cavalry could be (and were at some point) trained to charge compact Infantry bodies, but that it was not a commonly used tactic. Much more common (overwhelmingly so) was for Cavalry to be used against Infantry when the latter was vulnerable to such attacks. The relative vulnerability of any given Infantry body is likely the difference between a failed and successful Cavalry charge.

Matthew James Stanham