Tutorial by Examples

Given data Empty a we have data Free Empty a = Pure a -- the Free constructor is impossible! which is isomorphic to data Identity a = Identity a

Given data Identity a = Identity a we have data Free Identity a = Pure a | Free (Identity (Free Identity a)) which is isomorphic to data Deferred a = Now a | Later (Deferred a) or equivalently (if you promise to evaluate the fst element first) (Nat, a), aka Writer...

Given data Maybe a = Just a | Nothing we have data Free Maybe a = Pure a | Free (Just (Free Maybe a)) | Free Nothing which is equivalent to data Hopes a = Confirmed a | Possible (Hopes a) | Failed or equivalently (if you promise to evalua...

Given data Writer w a = Writer w a we have data Free (Writer w) a = Pure a | Free (Writer w (Free (Writer w) a)) which is isomorphic to data ProgLog w a = Done a | After w (ProgLog w a) or, equivalently, (if you promise to evaluate the log first), Writer [w] a. ...

Given data Const c a = Const c we have data Free (Const c) a = Pure a | Free (Const c) which is isomorphic to data Either c a = Right a | Left c

Given data Reader x a = Reader (x -> a) we have data Free (Reader x) a = Pure a | Free (x -> Free (Reader x) a) which is isomorphic to data Demand x a = Satisfied a | Hungry (x -> Demand x a) or equivalently Stream x -> a with data Stream x = Stream x...