diff --git a/lib/Quox/Equal.idr b/lib/Quox/Equal.idr
index a422cbf..e23dde2 100644
--- a/lib/Quox/Equal.idr
+++ b/lib/Quox/Equal.idr
@@ -17,8 +17,12 @@ public export
 EqualEff = [ErrorEff, EqModeState]
 
 public export
-0 EqualE : Type -> Type
-EqualE = Eff $ EqualEff
+0 Equal : Type -> Type
+Equal = Eff $ EqualEff
+
+export
+runEqual : EqMode -> Equal a -> Either Error a
+runEqual mode = extract . runExcept . evalState mode
 
 
 export %inline
@@ -28,19 +32,19 @@ mode = get
 
 parameters (ctx : EqContext n)
   private %inline
-  clashT : Term 0 n -> Term 0 n -> Term 0 n -> EqualE a
+  clashT : Term 0 n -> Term 0 n -> Term 0 n -> Equal a
   clashT ty s t = throw $ ClashT ctx !mode ty s t
 
   private %inline
-  clashTy : Term 0 n -> Term 0 n -> EqualE a
+  clashTy : Term 0 n -> Term 0 n -> Equal a
   clashTy s t = throw $ ClashTy ctx !mode s t
 
   private %inline
-  clashE : Elim 0 n -> Elim 0 n -> EqualE a
+  clashE : Elim 0 n -> Elim 0 n -> Equal a
   clashE e f = throw $ ClashE ctx !mode e f
 
   private %inline
-  wrongType : Term 0 n -> Term 0 n -> EqualE a
+  wrongType : Term 0 n -> Term 0 n -> Equal a
   wrongType ty s = throw $ WrongType ctx ty s
 
 
@@ -141,7 +145,7 @@ parameters (defs : Definitions)
       |||
       ||| ⚠ **assumes that `s`, `t` have already been checked against `ty`**. ⚠
       export covering %inline
-      compare0 : EqContext n -> (ty, s, t : Term 0 n) -> EqualE ()
+      compare0 : EqContext n -> (ty, s, t : Term 0 n) -> Equal ()
       compare0 ctx ty s t =
         wrapErr (WhileComparingT ctx !mode ty s t) $ do
           let Val n = ctx.termLen
@@ -162,7 +166,7 @@ parameters (defs : Definitions)
                   (ty, s, t : Term 0 n) ->
                   (0 nty : NotRedex defs ty) => (0 tty : So (isTyCon ty)) =>
                   (0 ns  : NotRedex defs s)  => (0 nt  : NotRedex defs t) =>
-                  EqualE ()
+                  Equal ()
       compare0' ctx (TYPE _) s t = compareType ctx s t
 
       compare0' ctx ty@(Pi {qty, arg, res}) s t {n} = local_ Equal $
@@ -187,7 +191,7 @@ parameters (defs : Definitions)
           ctx' : EqContext (S n)
           ctx' = extendTy qty res.name arg ctx
 
-          eta : Elim 0 n -> ScopeTerm 0 n -> EqualE ()
+          eta : Elim 0 n -> ScopeTerm 0 n -> Equal ()
           eta e (S _ (Y b)) = compare0 ctx' res.term (toLamBody e) b
           eta e (S _ (N _)) = clashT ctx ty s t
 
@@ -281,7 +285,7 @@ parameters (defs : Definitions)
     ||| compares two types, using the current variance `mode` for universes.
     ||| fails if they are not types, even if they would happen to be equal.
     export covering %inline
-    compareType : EqContext n -> (s, t : Term 0 n) -> EqualE ()
+    compareType : EqContext n -> (s, t : Term 0 n) -> Equal ()
     compareType ctx s t = do
       let Val n = ctx.termLen
       Element s ns <- whnfT defs s
@@ -297,7 +301,7 @@ parameters (defs : Definitions)
                    (0 ns : NotRedex defs s) => (0 ts : So (isTyCon s)) =>
                    (0 nt : NotRedex defs t) => (0 tt : So (isTyCon t)) =>
                    (0 st : So (sameTyCon s t)) =>
-                   EqualE ()
+                   Equal ()
     -- equality is the same as subtyping, except with the
     -- "≤" in the TYPE rule being replaced with "="
     compareType' ctx (TYPE k) (TYPE l) =
@@ -363,7 +367,7 @@ parameters (defs : Definitions)
     private covering
     computeElimType : EqContext n -> (e : Elim 0 n) ->
                       (0 ne : NotRedex defs e) ->
-                      EqualE (Term 0 n)
+                      Equal (Term 0 n)
     computeElimType ctx (F x) _ = do
       defs <- lookupFree' defs x
       pure $ injectT ctx defs.type
@@ -383,7 +387,7 @@ parameters (defs : Definitions)
     private covering
     replaceEnd : EqContext n ->
                  (e : Elim 0 n) -> DimConst -> (0 ne : NotRedex defs e) ->
-                 EqualE (Elim 0 n)
+                 Equal (Elim 0 n)
     replaceEnd ctx e p ne = do
       (ty, l, r) <- expectEqE defs ctx !(computeElimType ctx e ne)
       pure $ ends l r p :# dsub1 ty (K p)
@@ -397,7 +401,7 @@ parameters (defs : Definitions)
       ||| ⚠ **assumes that they have both been typechecked, and have
       ||| equal types.** ⚠
       export covering %inline
-      compare0 : EqContext n -> (e, f : Elim 0 n) -> EqualE ()
+      compare0 : EqContext n -> (e, f : Elim 0 n) -> Equal ()
       compare0 ctx e f =
         wrapErr (WhileComparingE ctx !mode e f) $ do
           let Val n = ctx.termLen
@@ -411,7 +415,7 @@ parameters (defs : Definitions)
       compare0' : EqContext n ->
                   (e, f : Elim 0 n) ->
                   (0 ne : NotRedex defs e) -> (0 nf : NotRedex defs f) ->
-                  EqualE ()
+                  Equal ()
       -- replace applied equalities with the appropriate end first
       -- e.g. e : Eq [i ⇒ A] s t ⊢ e 𝟎 = s : A‹𝟎/i›
       --
@@ -459,7 +463,7 @@ parameters (defs : Definitions)
               !(lookupArm t earms) !(lookupArm t farms)
           expectEqualQ epi fpi
         where
-          lookupArm : TagVal -> CaseEnumArms d n -> EqualE (Term d n)
+          lookupArm : TagVal -> CaseEnumArms d n -> Equal (Term d n)
           lookupArm t arms = case lookup t arms of
             Just arm => pure arm
             Nothing  => throw $ TagNotIn t (fromList $ keys arms)
@@ -496,7 +500,7 @@ parameters (defs : Definitions)
       compare0' ctx (s :# a) (t :# b) _ _ =
           Term.compare0 ctx !(bigger a b) s t
         where
-          bigger : forall a. a -> a -> EqualE a
+          bigger : forall a. a -> a -> Equal a
           bigger l r = mode <&> \case Super => l; _ => r
 
       compare0' ctx   (s :# a) f        _ _ = Term.compare0 ctx a s (E f)