The Free type is isomorphic to:

data Free f r = Pure r | Wrap (f (Free f r))

... except that if you want to pattern match against those constructors, you must first use runFree to unwrap the value first.

Similarly, you don't use the raw constructors to build a value of type Free. You instead use the smart constructors pure (from Control.Applicative) and wrap.

A free monad transformer alternates nesting the base functor f and the base monad m.

• f - The functor that generates the free monad
• m - The base monad
• r - The type of the return value

This type commonly arises in coroutine/iteratee libraries under various names.