Consider the following Haskell datatypes representing sugared and unsugared calculus terms. data PureLC = Lambda String PureLC | App PureLC PureLC | Var String deriving Show data SugaredLC = Lambdas [String] SugaredLC | Apps [SugaredLC] | Vars String deriving Show Write fv:: PurelC [ String ] desugar :: SugaredLC PurelC which finds a list of the free variables in a pure calculus term, and de-sugars a sugared calculus term, respectively. So for example Prelude> desugar (LambdaS ["f", "x"] (Apps [(Vars "f"), Apps [Vars "t", Vars "g", Vars "g"]])) Lambda "f" (Lambda "x" (App (Var "f") (App (App (Var "t") (Var "g")) (Var "g")))) Prelude> fv (Lambda "f" (Lambda "x" (App (Var "f") (App (App (Var "t") (Var "g")) (Var "g"))))) ["t", "g"]