diff --git a/src/Language/Futhark/TypeChecker/Constraints.hs b/src/Language/Futhark/TypeChecker/Constraints.hs
index 1ad98997ad..b6d186b195 100644
--- a/src/Language/Futhark/TypeChecker/Constraints.hs
+++ b/src/Language/Futhark/TypeChecker/Constraints.hs
@@ -110,8 +110,6 @@ data TyVarInfo
     TyVarRecord Loc (M.Map Name Type)
   | -- | Must be a sum type with these fields.
     TyVarSum Loc (M.Map Name [Type])
-  | -- | Must be a type that supports equality.
-    TyVarEql Loc
   deriving (Show, Eq)
 
 instance Pretty TyVarInfo where
@@ -119,14 +117,12 @@ instance Pretty TyVarInfo where
   pretty (TyVarPrim _ pts) = "∈" <+> pretty pts
   pretty (TyVarRecord _ fs) = pretty $ Scalar $ Record fs
   pretty (TyVarSum _ cs) = pretty $ Scalar $ Sum cs
-  pretty (TyVarEql _) = "equality"
 
 instance Located TyVarInfo where
   locOf (TyVarFree loc _) = loc
   locOf (TyVarPrim loc _) = loc
   locOf (TyVarRecord loc _) = loc
   locOf (TyVarSum loc _) = loc
-  locOf (TyVarEql loc) = loc
 
 type TyVar = VName
 
@@ -285,9 +281,6 @@ unifySharedFields reason bcs fs1 fs2 =
   forM_ (M.toList $ M.intersectionWith (,) fs1 fs2) $ \(f, (ts1, ts2)) ->
     solveEq reason (matchingField f <> bcs) ts1 ts2
 
-mustSupportEql :: Reason -> Type -> SolveM ()
-mustSupportEql _reason _t = pure ()
-
 scopeViolation :: Reason -> VName -> Type -> VName -> SolveM ()
 scopeViolation reason v1 ty v2 =
   typeError (locOf reason) mempty $
@@ -440,8 +433,6 @@ subTyVar reason bcs v t = do
             </> indent 2 (pretty (Record fs1))
             </> "with type"
             </> indent 2 (pretty t)
-    (Just (Right (TyVarUnsol (TyVarEql _))), _) ->
-      mustSupportEql reason t
     --
     -- Internal error cases
     (Just (Right TyVarSol {}), _) ->
@@ -481,10 +472,6 @@ unionTyVars reason bcs v t = do
         setInfo t (TyVarUnsol info)
     --
     -- TyVarPrim cases
-    ( TyVarUnsol info@TyVarPrim {},
-      TyVarEql {}
-      ) ->
-        setInfo t (TyVarUnsol info)
     ( TyVarUnsol (TyVarPrim _ v_pts),
       TyVarPrim t_loc t_pts
       ) ->
@@ -533,10 +520,6 @@ unionTyVars reason bcs v t = do
             </> indent 2 (pretty (Sum cs1))
             </> "with type"
             </> indent 2 (pretty (Scalar (Record fs)))
-    ( TyVarUnsol (TyVarSum _ cs1),
-      TyVarEql _
-      ) ->
-        mapM_ (mapM_ (mustSupportEql reason)) cs1
     --
     -- TyVarRecord cases
     ( TyVarUnsol (TyVarRecord _ fs1),
@@ -559,20 +542,6 @@ unionTyVars reason bcs v t = do
             </> indent 2 (pretty (Record fs1))
             </> "with type"
             </> indent 2 (pretty (Scalar (Sum cs)))
-    ( TyVarUnsol (TyVarRecord _ fs1),
-      TyVarEql _
-      ) ->
-        mapM_ (mustSupportEql reason) fs1
-    --
-    -- TyVarEql cases
-    (TyVarUnsol (TyVarEql _), TyVarPrim {}) ->
-      pure ()
-    (TyVarUnsol (TyVarEql _), TyVarEql {}) ->
-      pure ()
-    (TyVarUnsol (TyVarEql _), TyVarRecord _ fs) ->
-      mustSupportEql reason $ Scalar $ Record fs
-    (TyVarUnsol (TyVarEql _), TyVarSum _ cs) ->
-      mustSupportEql reason $ Scalar $ Sum cs
     --
     -- Internal error cases
     (TyVarSol {}, _) ->
@@ -750,21 +719,6 @@ solveTyVar (tv, (_, TyVarSum loc cs1)) = do
           </> "Must be a sum type with constructors"
           </> indent 2 (pretty (Scalar (Sum cs1)))
     Right _ -> pure ()
-solveTyVar (tv, (_, TyVarEql loc)) = do
-  tv_t <- lookupTyVar tv
-  case tv_t of
-    Left TyVarEql {} ->
-      typeError loc mempty $
-        "Type is ambiguous (must be equality type)"
-          </> "Add a type annotation to disambiguate the type."
-    Left _ -> pure ()
-    Right ty
-      | orderZero ty -> pure ()
-      | otherwise ->
-          typeError loc mempty $
-            "Type"
-              </> indent 2 (align (pretty ty))
-              </> "does not support equality (may contain function)."
 solveTyVar (tv, (lvl, TyVarFree loc l)) = do
   tv_t <- lookupTyVar tv
   case tv_t of
diff --git a/src/Language/Futhark/TypeChecker/Rank.hs b/src/Language/Futhark/TypeChecker/Rank.hs
index 24254d7392..deb578facb 100644
--- a/src/Language/Futhark/TypeChecker/Rank.hs
+++ b/src/Language/Futhark/TypeChecker/Rank.hs
@@ -167,8 +167,6 @@ addTyVarInfo tv (_, TyVarRecord {}) =
   addConstraint $ rank tv ~==~ constant 0
 addTyVarInfo tv (_, TyVarSum {}) =
   addConstraint $ rank tv ~==~ constant 0
-addTyVarInfo tv (_, TyVarEql {}) =
-  addConstraint $ rank tv ~==~ constant 0
 
 mkLinearProg :: [Ct] -> TyVars -> LinearProg
 mkLinearProg cs tyVars =
@@ -454,7 +452,6 @@ instance SubstRanks TyVarInfo where
     TyVarRecord loc <$> traverse substRanks fs
   substRanks (TyVarSum loc cs) =
     TyVarSum loc <$> (traverse . traverse) substRanks cs
-  substRanks tv@TyVarEql {} = pure tv
 
 instance SubstRanks (Int, TyVarInfo) where
   substRanks (lvl, tv) = (lvl,) <$> substRanks tv
diff --git a/src/Language/Futhark/TypeChecker/Terms.hs b/src/Language/Futhark/TypeChecker/Terms.hs
index 48f82ad5ea..b6009887ed 100644
--- a/src/Language/Futhark/TypeChecker/Terms.hs
+++ b/src/Language/Futhark/TypeChecker/Terms.hs
@@ -1143,6 +1143,14 @@ mustBeIrrefutable p = do
         "Refutable pattern not allowed here.\nUnmatched cases:"
           </> indent 2 (stack (map pretty ps'))
 
+supportsEquality :: TypeBase dim u -> Bool
+supportsEquality (Array _ _ t) = supportsEquality $ Scalar t
+supportsEquality (Scalar Prim {}) = True
+supportsEquality (Scalar TypeVar {}) = False
+supportsEquality (Scalar (Record fs)) = all supportsEquality fs
+supportsEquality (Scalar (Sum fs)) = all (all supportsEquality) fs
+supportsEquality (Scalar Arrow {}) = False
+
 -- | Traverse the expression, emitting warnings and errors for various
 -- problems:
 --
@@ -1163,6 +1171,12 @@ localChecks = void . check
               </> indent 2 (stack (map pretty ps'))
     check e@(AppExp (LetPat _ p _ _ _) _) =
       mustBeIrrefutable p *> recurse e
+    check e@(AppExp (BinOp (v, loc) _ (x, _) _ _) _)
+      | qualLeaf v == intrinsicVar "==" =
+          checkEquality loc (typeOf x) *> recurse e
+    check e@(Var v (Info t) loc)
+      | qualLeaf v == intrinsicVar "==" =
+          checkEquality loc t *> recurse e
     check e@(Lambda ps _ _ _ _) =
       mapM_ (mustBeIrrefutable . fmap toStruct) ps *> recurse e
     check e@(AppExp (LetFun _ (_, ps, _, _, _) _ _) _) =
@@ -1188,6 +1202,13 @@ localChecks = void . check
     check e = recurse e
     recurse = astMap identityMapper {mapOnExp = check}
 
+    checkEquality loc t =
+      unless (supportsEquality t) $
+        typeError loc mempty $
+          "Comparing equality of values of type"
+            </> indent 2 (pretty t)
+            </> "which does not support equality."
+
     bitWidth ty = 8 * intByteSize ty :: Int
 
     inBoundsI x (Signed t) = x >= -2 ^ (bitWidth t - 1) && x < 2 ^ (bitWidth t - 1)
diff --git a/src/Language/Futhark/TypeChecker/Terms2.hs b/src/Language/Futhark/TypeChecker/Terms2.hs
index 975b7ae9e1..679dc6317b 100644
--- a/src/Language/Futhark/TypeChecker/Terms2.hs
+++ b/src/Language/Futhark/TypeChecker/Terms2.hs
@@ -438,7 +438,7 @@ lookupVar loc qn@(QualName qs name) = do
           -- TODO - qualify type names, like in the old type checker.
           pure t'
     Just EqualityF -> do
-      argtype <- tyVarType Observe <$> newTyVarWith "t" (TyVarEql (locOf loc))
+      argtype <- tyVarType Observe <$> newTyVarWith "t" (TyVarFree (locOf loc) Unlifted)
       pure $ foldFunType [argtype, argtype] $ RetType [] $ Scalar $ Prim Bool
     Just (OverloadedF ts pts rt) -> do
       argtype <- newTypeOverloaded loc "t" ts
diff --git a/tests/types/inference-error9.fut b/tests/types/inference-error9.fut
index 0c6886c881..6cead89cec 100644
--- a/tests/types/inference-error9.fut
+++ b/tests/types/inference-error9.fut
@@ -2,4 +2,4 @@
 -- ==
 -- error: equality
 
-def main 't (x: t) = x == x
+def f 't (x: t) = x == x