Question

The following code

{-# LANGUAGE TypeSynonymInstances, FlexibleInstances  #-}

module Function where

import qualified Data.Vector.Unboxed as V
import Control.Monad

type Function = V.Vector Double

instance Num Function where
  (+) = liftM2 (+)
  (*) = liftM2 (*)
  negate = fmap negate

returns errors like

No instance for (Monad V.Vector)
  arising from a use of `liftM2'

though it is said in the documentation that Vector is an instance of Monad.

Answer 1

Unboxed Vector is not an instance of Monad. Notice the vector package exports many different types that are all called Vector. Data.Vector.Unboxed.Vector /= Data.Vector.Vector /= Data.Vector.Storable.Vector.