diff --git a/Data/SortedList.hs b/Data/SortedList.hs
--- a/Data/SortedList.hs
+++ b/Data/SortedList.hs
@@ -29,13 +29,14 @@
   , null
   , elemOrd
     -- * Others
+  , map
   , nub
   ) where
 
 import Prelude hiding
   ( take, drop, splitAt, filter
   , repeat, replicate, iterate
-  , null
+  , null, map
 #if !MIN_VERSION_base(4,8,0)
   , foldr
 #endif
@@ -179,3 +180,21 @@
       [] -> error "SortedList.maximum: empty list"
       _ -> last xs
 #endif
+
+-- | Map a function over all the elements of a sorted list.
+--   Note that 'map' will hang if the argument is an infinite list.
+--
+--   Even though 'SortedList' can't be made an instance of 'Functor',
+--   'map' /does/ hold the 'Functor' laws. The problem to write the
+--   the instance is the 'Ord' instance requirement on the type of
+--   the elements of the result list. Therefore, while 'SortedList'
+--   is not a functor type in general, it is when restricted to elements of
+--   orderable types.
+map :: Ord b => (a -> b) -> SortedList a -> SortedList b
+{-# INLINE[1] map #-}
+map f = foldr (insert . f) mempty
+
+{-# RULES
+"SortedList:map/map" forall f g xs. map f (map g xs) = map (f . g) xs
+"SortedList:map/id"  forall xs.     map id xs = xs
+  #-}
diff --git a/sorted-list.cabal b/sorted-list.cabal
--- a/sorted-list.cabal
+++ b/sorted-list.cabal
@@ -1,5 +1,5 @@
 name:                sorted-list
-version:             0.1.1.0
+version:             0.1.2.0
 synopsis:            Type-enforced sorted lists and related functions.
 description:         Type-enforced sorted lists and related functions.
                      .