Alfieri functions as the chorus of the play, commenting on the action and the characters carrying out the action, but ultimately set apart and serving as a medium between the audience and the action of the play.
...it is Alfieri’s view that defines the action of the play and its unfolding.
Alfieri opens and closes the play with a poetic monologue that functions as a frame story. Within the context of the play, he narrates certain sections to show that time has moved on and also serves as a moral sounding board (almost like an oracle) when Eddie finds himself as a moral crossroads.
Though Alfieri is unable to change the course of Eddie's behavior, it is his role to explicate this behavior, communicating the meaning of the play's tragedy to the audience.
Alfieri serves as spokesperson for all as he delivers the final monologue, bringing the tragic tale to a close.
Without Alfieri, the play's thematic and formal connections to the plays of ancient Greece would not be clearly articulated. Alfieri then functions as a chorus, a narrator, and a formal link between Miller's inspiration and his own work.