diff --git a/src/Data/Comp/Param/Multi/Equality.hs b/src/Data/Comp/Param/Multi/Equality.hs
index 8884e64..4bcd3a6 100644
--- a/src/Data/Comp/Param/Multi/Equality.hs
+++ b/src/Data/Comp/Param/Multi/Equality.hs
@@ -24,12 +24,22 @@ import Data.Comp.Param.Multi.Sum
 import Data.Comp.Param.Multi.Ops
 import Data.Comp.Param.Multi.HDifunctor
 import Data.Comp.Param.Multi.FreshM
+import Data.Functor.Product
+import Data.Functor.Sum
+import Control.Applicative
 
 -- |Equality on parametric values. The equality test is performed inside the
 -- 'FreshM' monad for generating fresh identifiers.
 class PEq a where
     peq :: a i -> a j -> FreshM Bool
 
+instance (PEq a, PEq b) => PEq (Product a b) where peq (Pair u x) (Pair v y) = liftA2 (&&) (peq u v) (peq x y)
+
+instance (PEq a, PEq b) => PEq (Sum a b) where
+    peq (InL x) (InL y) = peq x y
+    peq (InR x) (InR y) = peq x y
+    peq _       _       = pure False
+
 instance Eq a => PEq (K a) where
     peq (K x) (K y) = return $ x == y