It is possible to derive an instance of Ix automatically, using a deriving clause on a data declaration. Such derived instance declarations for the class Ix are only possible for enumerations (i.e. datatypes having only nullary constructors) and single-constructor datatypes, whose constituent types are instances of Ix. A Haskell implementation must provide Ix instances for tuples up to at least size 15.

For an enumeration, the nullary constructors are assumed to be numbered left-to-right with the indices being 0 to n-1 inclusive. This is the same numbering defined by the Enum class. For example, given the datatype:

 data Colour = Red | Orange | Yellow | Green | Blue | Indigo | Violet

we would have:

 range   (Yellow,Blue)        ==  [Yellow,Green,Blue]
 index   (Yellow,Blue) Green  ==  1
 inRange (Yellow,Blue) Red    ==  False

For single-constructor datatypes, the derived instance declarations are as shown for tuples:

 instance  (Ix a, Ix b)  => Ix (a,b) where
         range ((l,l'),(u,u'))
                 = [(i,i') | i <- range (l,u), i' <- range (l',u')]
         index ((l,l'),(u,u')) (i,i')
                 =  index (l,u) i * rangeSize (l',u') + index (l',u') i'
         inRange ((l,l'),(u,u')) (i,i')
                 = inRange (l,u) i && inRange (l',u') i'
 
 -- Instances for other tuples are obtained from this scheme:
 --
 --  instance  (Ix a1, Ix a2, ... , Ix ak) => Ix (a1,a2,...,ak)  where
 --      range ((l1,l2,...,lk),(u1,u2,...,uk)) =
 --          [(i1,i2,...,ik) | i1 <- range (l1,u1),
 --                            i2 <- range (l2,u2),
 --                            ...
 --                            ik <- range (lk,uk)]
 --
 --      index ((l1,l2,...,lk),(u1,u2,...,uk)) (i1,i2,...,ik) =
 --        index (lk,uk) ik + rangeSize (lk,uk) * (
 --         index (lk-1,uk-1) ik-1 + rangeSize (lk-1,uk-1) * (
 --          ...
 --           index (l1,u1)))
 --
 --      inRange ((l1,l2,...lk),(u1,u2,...,uk)) (i1,i2,...,ik) =
 --          inRange (l1,u1) i1 && inRange (l2,u2) i2 &&
 --              ... && inRange (lk,uk) ik