§ The smallest implementation of reverse mode AD (autograd) ever:

{-# LANGUAGE GeneralizedNewtypeDeriving #-}
import qualified Data.Map.Strict as M

-- | This file can be copy-pasted and will run!

-- | Symbols
type Sym = String
-- | Environments
type E a = M.Map Sym a
-- | Newtype to represent deriative values
type F = Float
newtype Der = Der { under :: F } deriving(Show, Num)

infixl 7 !#
-- | We are indexing the map at a "hash" (Sym)
(!#) :: E a -> Sym -> a
(!#) = (M.!)

-- | A node in the computation graph
data Node =
  Node { name :: Sym -- ^ Name of the node
       , ins :: [Node] -- ^ inputs to the node
       , out :: E F -> F -- ^ output of the node
       , der :: (E F, E (Sym -> Der))
                  -> Sym -> Der -- ^ derivative wrt to a name
       }

-- | @ looks like a "circle", which is a node. So we are indexing the map
-- at a node.
(!@) :: E a -> Node -> a
(!@) e node = e M.! (name node)

-- | Given the current environments of values and derivatives, compute
-- | The new value and derivative for a node.
run_ :: (E F, E (Sym -> Der)) -> Node -> (E F, E (Sym -> Der))
run_ ein (Node name ins out der) =
  let (e', ed') = foldl run_ ein ins -- run all the inputs
      v = out e' -- compute the output
      dv = der (e', ed') -- and the derivative
  in (M.insert name v e', M.insert name dv ed')  -- and insert them

-- | Run the program given a node
run :: E F -> Node -> (E F, E (Sym -> Der))
run e n = run_ (e, mempty) n

-- | Let's build nodes
nconst :: Sym -> F -> Node
nconst n f = Node n [] (\_ -> f) (\_ _ -> 0)

-- | Variable
nvar :: Sym -> Node
nvar n = Node n [] (!# n) (\_ n' -> if n == n' then 1 else 0)

-- | binary operation
nbinop :: (F -> F -> F)  -- ^ output computation from inputs
 -> (F -> Der -> F -> Der -> Der) -- ^ derivative computation from outputs
 -> Sym -- ^ Name
 -> (Node, Node) -- ^ input nodes
 -> Node
nbinop f df n (in1, in2) =
  Node { name = n
       , ins = [in1, in2]
       , out = \e -> f (e !# name in1) (e !# name in2)
       , der = \(e, ed) n' ->
                 let (name1, name2) = (name in1, name in2)
                     (v1, v2) = (e !# name1, e !# name2)
                     (dv1, dv2) = (ed !# name1 $ n', ed !# name2 $ n')
                     in df v1 dv1 v2 dv2
       }

nadd :: Sym -> (Node, Node) -> Node
nadd = nbinop (+) (\v dv v' dv' -> dv + dv')

nmul :: Sym -> (Node, Node) -> Node
nmul = nbinop (*) (\v (Der dv) v' (Der dv') -> Der $ (v*dv') + (v'*dv))

main :: IO ()
main = do
  let x = nvar "x" :: Node
  let y = nvar "y"
  let xsq = nmul "xsq" (x, x)
  let ten = nconst "10" 10
  let xsq_plus_10 = nadd "xsq_plus_10" (xsq, ten)
  let xsq_plus_10_plus_y = nadd "xsq_plus_10_plus_y"  (xsq_plus_10, y)
  let (e, de) = run (M.fromList $ [("x", 2.0), ("y", 3.0)]) xsq_plus_10_plus_y
  putStrLn $ show e
  putStrLn $ show $ de !@ xsq_plus_10_plus_y $ "x"
  putStrLn $ show $ de !@ xsq_plus_10_plus_y $ "y"

Yeah, in ~80 lines of code, you can basically build an autograd engine. Isn't haskell so rad?