Comedy: It's not necessarily funny

When my friends tell me about a new comedy show that they want me to watch, I always ask, "Is it really that funny?" For me before this class, the purpose of comedy was to amuse me and make me laugh. Comedy plays were plays that made me laugh, like A Very Potter Musical. In my mind, comedy was something that made me laugh. If not funny, it was not comedy.
However, this is not the actual definition of comedy (even though it might be the popular one.) To be comedic, a play must have a relatively resolved happy ending aka not be a tragedy. Perhaps it has jokes, and perhaps it is funny, but it doesn't have to be.
The play that cemented this new definition of comedy for me was The Contrast. The plot is not even in the least bit amusing. There is some irony in the play, the 'use of theater against it' or making fun of plays in a play, but it just evoked a 'heh' from me rather than any sort of actual amusement. The point of the play is to show the characteristics of a 'true' American. This I am able to see easily from reading the play. It was difficult for me to grasp at first that something that did not make me laugh or even make me feel happy or amused could be a comedy. And while The Contrast was certainly not funny, it was a comedy.
The progress I made in refining my definition of comedy was significant after reading this play. The final events of the play, finding out Dimple was a player and the union of Maria and Manly were instrumental for this progress. Dimple, the bad character, did not receive a happy ending and the two chaste characters did. Everything was tied up in an appropriate manner given the behaviour of their respective characters. This ending is an example of comedy for me now. Good is rewarded and bad is not, humour is optional.
While this new perspective is far from finished (I'm still trying to comprehend the finale of The Beaver Coat), it is deeper than my previous understanding.