diff --git a/Data/Primitive/Array.hs b/Data/Primitive/Array.hs
index f35d2236..4130caad 100644
--- a/Data/Primitive/Array.hs
+++ b/Data/Primitive/Array.hs
@@ -23,6 +23,7 @@ module Data.Primitive.Array (
   cloneArray, cloneMutableArray,
   sizeofArray, sizeofMutableArray,
   fromListN, fromList,
+  mapArray',
   unsafeTraverseArray
 ) where
 
@@ -559,6 +560,21 @@ unsafeTraverseArray f = \ !ary ->
     go 0 mary
 {-# INLINE unsafeTraverseArray #-}
 
+-- | Strict map over the elements of the array.
+mapArray' :: (a -> b) -> Array a -> Array b
+mapArray' f a =
+  createArray (sizeofArray a) (die "mapArray'" "impossible") $ \mb ->
+    let go i | i == sizeofArray a
+             = return ()
+             | otherwise
+             = do x <- indexArrayM a i
+                  -- We use indexArrayM here so that we will perform the
+                  -- indexing eagerly even if f is lazy.
+                  let !y = f x
+                  writeArray mb i y >> go (i+1)
+     in go 0
+{-# INLINE mapArray' #-}
+
 arrayFromListN :: Int -> [a] -> Array a
 arrayFromListN n l =
   createArray n (die "fromListN" "uninitialized element") $ \sma ->
diff --git a/Data/Primitive/SmallArray.hs b/Data/Primitive/SmallArray.hs
index b0cd77e0..262a70d2 100644
--- a/Data/Primitive/SmallArray.hs
+++ b/Data/Primitive/SmallArray.hs
@@ -57,6 +57,7 @@ module Data.Primitive.SmallArray
   , sizeofSmallMutableArray
   , smallArrayFromList
   , smallArrayFromListN
+  , mapSmallArray'
   , unsafeTraverseSmallArray
   ) where
 
@@ -436,6 +437,20 @@ unsafeTraverseSmallArray f (SmallArray ar) = SmallArray `liftM` unsafeTraverseAr
 #endif
 {-# INLINE unsafeTraverseSmallArray #-}
 
+-- | Strict map over the elements of the array.
+mapSmallArray' :: (a -> b) -> SmallArray a -> SmallArray b
+#if HAVE_SMALL_ARRAY
+mapSmallArray' f sa = createSmallArray (length sa) (die "mapSmallArray'" "impossible") $ \smb ->
+  fix ? 0 $ \go i ->
+    when (i < length sa) $ do
+      x <- indexSmallArrayM sa i
+      let !y = f x
+      writeSmallArray smb i y *> go (i+1)
+#else
+mapSmallArray' f (SmallArray ar) = SmallArray (mapArray' f ar)
+#endif
+{-# INLINE mapSmallArray' #-}
+
 #ifndef HAVE_SMALL_ARRAY
 runSmallArray
   :: (forall s. ST s (SmallMutableArray s a))
diff --git a/test/main.hs b/test/main.hs
index 44552d27..197e3c80 100644
--- a/test/main.hs
+++ b/test/main.hs
@@ -45,15 +45,16 @@ main = do
       , lawsToTest (QCC.ordLaws (Proxy :: Proxy (Array Int)))
       , lawsToTest (QCC.monoidLaws (Proxy :: Proxy (Array Int)))
       , lawsToTest (QCC.showReadLaws (Proxy :: Proxy (Array Int)))
-#if MIN_VERSION_base(4,7,0)
-      , lawsToTest (QCC.isListLaws (Proxy :: Proxy (Array Int)))
-#endif
 #if MIN_VERSION_base(4,9,0) || MIN_VERSION_transformers(0,4,0)
       , lawsToTest (QCC.functorLaws (Proxy1 :: Proxy1 Array))
       , lawsToTest (QCC.applicativeLaws (Proxy1 :: Proxy1 Array))
       , lawsToTest (QCC.monadLaws (Proxy1 :: Proxy1 Array))
       , lawsToTest (QCC.foldableLaws (Proxy1 :: Proxy1 Array))
       , lawsToTest (QCC.traversableLaws (Proxy1 :: Proxy1 Array))
+#endif
+#if MIN_VERSION_base(4,7,0)
+      , lawsToTest (QCC.isListLaws (Proxy :: Proxy (Array Int)))
+      , TQC.testProperty "mapArray'" (QCCL.mapProp int16 int32 mapArray')
 #endif
       ]
     , testGroup "SmallArray"
@@ -61,15 +62,16 @@ main = do
       , lawsToTest (QCC.ordLaws (Proxy :: Proxy (SmallArray Int)))
       , lawsToTest (QCC.monoidLaws (Proxy :: Proxy (SmallArray Int)))
       , lawsToTest (QCC.showReadLaws (Proxy :: Proxy (Array Int)))
-#if MIN_VERSION_base(4,7,0)
-      , lawsToTest (QCC.isListLaws (Proxy :: Proxy (SmallArray Int)))
-#endif
 #if MIN_VERSION_base(4,9,0) || MIN_VERSION_transformers(0,4,0)
       , lawsToTest (QCC.functorLaws (Proxy1 :: Proxy1 SmallArray))
       , lawsToTest (QCC.applicativeLaws (Proxy1 :: Proxy1 SmallArray))
       , lawsToTest (QCC.monadLaws (Proxy1 :: Proxy1 SmallArray))
       , lawsToTest (QCC.foldableLaws (Proxy1 :: Proxy1 SmallArray))
       , lawsToTest (QCC.traversableLaws (Proxy1 :: Proxy1 SmallArray))
+#endif
+#if MIN_VERSION_base(4,7,0)
+      , lawsToTest (QCC.isListLaws (Proxy :: Proxy (SmallArray Int)))
+      , TQC.testProperty "mapSmallArray'" (QCCL.mapProp int16 int32 mapSmallArray')
 #endif
       ]
     , testGroup "ByteArray"