Alison Bechdel’s 2006 graphic memoir, subtitled “A Family Tragicomic,” made many top ten lists and became something of a cult classic. In it, Bechdel describes growing up in small-town Pennsylvania in a repressed family led by a difficult father with a passion for house restoration. The “fun home” of the title is the family’s affectionate shorthand for “funeral home,” the family business that supplements the parents’ schoolteacher salaries. Alison and her father had a complicated relationship -- their common interest in literature was the closest thing to a bond. Shortly after Alison came out as a lesbian, her father died, perhaps a suicide. Jeanine Tesori (Caroline, or Change) and Lisa Kron (Well) have bravely adapted Bechdel’s memoir for the musical stage, in a production now in previews at the Public Theater. Tesori’s music and Kron’s lyrics have produced several fine songs, but some of the best have little to do with Bechdel’s material. Alison is played by three actors -- Alison as a child (Sydney Lucas), college-age Alison (Alexandra Socha) and 43-year-old Alison (Beth Malone). Lucas and Socha are very engaging, but Malone is a bit of a stick (not helped by the fact that she is frightfully thin). Michael Cerveris as the father and Judy Kuhn as the mother do not get enough to work with to develop complex characters. Griffin Birney and Noah Hinsdale play Alison’s younger brothers, Roberta Colindrez is Joan, her first lover, and Joel Perez plays Ron, the sexy handyman. Musicals must inevitably simplify, but oversimplification is sometimes a hazard. The book’s many literary allusions disappear. David Zinn’s set and costumes are good, but do not compare favorably with Bechtel’s wonderful line drawings. I think the play needs further work, particularly on the opening and the final scene. Sam Gold directed. The audience was clearly made up of fans. It was obvious even before the play began that, whatever transpired, the reaction would be an enthusiastic one. Running time: 1 hour, 40 minutes; no intermission.