Haskell Language Common monads as free monads Free Identity ~~ (Nat,) ~~ Writer Nat
Example
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 Nat a, with
data Nat = Z | S Nat
data Writer Nat a = Writer Nat a
