Haskell Language Common monads as free monads Free Maybe ~~ MaybeT (Writer Nat)
Example
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 evaluate the fst element first) (Nat, Maybe a), aka MaybeT (Writer Nat) a with
data Nat = Z | S Nat
data Writer Nat a = Writer Nat a
data MaybeT (Writer Nat) a = MaybeT (Nat, Maybe a)
