diff --git a/CHANGELOG.md b/CHANGELOG.md
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,5 +1,9 @@
 # Revision history for futhark-data
 
+## 1.1.4.0
+
+* `GetValue` and `PutValue` now has instances for all primitive types.
+
 ## 1.1.3.0
 
 * `GetValue` instances for `Int` and `Integer` as a convenience.
diff --git a/futhark-data.cabal b/futhark-data.cabal
--- a/futhark-data.cabal
+++ b/futhark-data.cabal
@@ -1,6 +1,6 @@
 cabal-version:      2.4
 name:               futhark-data
-version:            1.1.3.0
+version:            1.1.4.0
 synopsis:           An implementation of the Futhark data format.
 
 description: The Futhark compiler and its tools uses a simple external
diff --git a/src/Futhark/Data.hs b/src/Futhark/Data.hs
--- a/src/Futhark/Data.hs
+++ b/src/Futhark/Data.hs
@@ -422,12 +422,33 @@
 instance GetValue Int where
   getValue v = fmap fromInteger (getValue v :: Maybe Integer)
 
+instance GetValue Half where
+  getValue (F16Value shape vs)
+    | [] <- SVec.toList shape =
+        Just $ vs SVec.! 0
+  getValue _ = Nothing
+
+instance GetValue Float where
+  getValue (F32Value shape vs)
+    | [] <- SVec.toList shape =
+        Just $ vs SVec.! 0
+  getValue _ = Nothing
+
+instance GetValue Double where
+  getValue (F64Value shape vs)
+    | [] <- SVec.toList shape =
+        Just $ vs SVec.! 0
+  getValue _ = Nothing
+
 -- | A class for Haskell values that can be converted to 'Value'.
 -- This is a convenience facility - don't expect it to be fast.
 class PutValue t where
   -- | This may fail for cases such as irregular arrays.
   putValue :: t -> Maybe Value
 
+instance PutValue Bool where
+  putValue = Just . putValue1
+
 instance PutValue Int8 where
   putValue = Just . putValue1
 
@@ -452,6 +473,15 @@
 instance PutValue Word64 where
   putValue = Just . putValue1
 
+instance PutValue Half where
+  putValue = Just . putValue1
+
+instance PutValue Float where
+  putValue = Just . putValue1
+
+instance PutValue Double where
+  putValue = Just . putValue1
+
 instance PutValue [Value] where
   putValue [] = Nothing
   putValue (x : xs) = do
@@ -501,6 +531,9 @@
 class PutValue1 t where
   putValue1 :: t -> Value
 
+instance PutValue1 Bool where
+  putValue1 = BoolValue mempty . SVec.singleton
+
 instance PutValue1 Int8 where
   putValue1 = I8Value mempty . SVec.singleton
 
@@ -524,6 +557,15 @@
 
 instance PutValue1 Word64 where
   putValue1 = U64Value mempty . SVec.singleton
+
+instance PutValue1 Half where
+  putValue1 = F16Value mempty . SVec.singleton
+
+instance PutValue1 Float where
+  putValue1 = F32Value mempty . SVec.singleton
+
+instance PutValue1 Double where
+  putValue1 = F64Value mempty . SVec.singleton
 
 instance PutValue1 T.Text where
   putValue1 = putValue1 . T.encodeUtf8