Shaw was such a respected playwright that the critics gave him his very own adjective: Shavian. The word is still used today to compare other pieces of literature to Shaw's work. Saint Joan bears all of Shaw's trademarks. Many of the characters are hyper articulate. They're able to understand complex concepts and enjoy debating them passionately, sometimes at great length and detail. You get plenty of this in Saint Joan. In Joan's trial, it's Joan's beliefs vs. Church doctrine. Another good example is Warwick and Cauchon's discussions of Nationalism and Protestantism.
If a play is described as Shavian it usually means that it turns the stage into a forum for ideas. Another hallmark of Shavian style is wittiness. Shaw punctuated his intellectual discussions with a sharp sense of humor. As soon as the play is in danger of getting bogged down, he keeps us engaged with some witty observation. Once again, Joan's trial is a good example. All the long debates are peppered with sassy comebacks from our heroine.