Tutorial by Examples: cofree

Given data Empty a we have data Cofree Empty a -- = a :< ... not possible!

Given data Const c a = Const c we have data Cofree (Const c) a = a :< Const c which is isomorphic to data Writer c a = Writer c a

Given data Identity a = Identity a we have data Cofree Identity a = a :< Identity (Cofree Identity a) which is isomorphic to data Stream a = Stream a (Stream a)

Given data Maybe a = Just a | Nothing we have data Cofree Maybe a = a :< Just (Cofree Maybe a) | a :< Nothing which is isomorphic to data NonEmpty a = NECons a (NonEmpty a) | NESingle a

Given data Writer w a = Writer w a we have data Cofree (Writer w) a = a :< (w, Cofree (Writer w) a) which is equivalent to data Stream (w,a) = Stream (w,a) (Stream (w,a)) which can properly be written as WriterT w Stream with data WriterT w m a = WriterT (m (w,a))

Given data Either e a = Left e | Right a we have data Cofree (Either e) a = a :< Left e | a :< Right (Cofree (Either e) a) which is isomorphic to data Hospitable e a = Sorry_AllIHaveIsThis_Here'sWhy a e | EatThis a (Hospitable e a) or, if yo...

Given data Reader x a = Reader (x -> a) we have data Cofree (Reader x) a = a :< (x -> Cofree (Reader x) a) which is isomorphic to data Plant x a = Plant a (x -> Plant x a) aka Moore machine.