--- a/agda/delta/functor.agda	Tue Feb 03 12:46:20 2015 +0900
+++ b/agda/delta/functor.agda	Tue Feb 03 12:57:13 2015 +0900
@@ -11,20 +11,21 @@
 
 -- Functor-laws
 
--- Functor-law-1 : T(id) = id'
-functor-law-1 :  {l : Level} {A : Set l} {n : Nat} ->  (d : Delta A (S n)) -> (delta-fmap id) d ≡ id d
-functor-law-1 (mono x)    = refl
-functor-law-1 (delta x d) = cong (delta x) (functor-law-1 d)
+-- functor-law 1 : T(id) = id'
+delta-preserve-id :  {l : Level} {A : Set l} {n : Nat} ->  (d : Delta A (S n)) -> (delta-fmap id) d ≡ id d
+delta-preserve-id (mono x)    = refl
+delta-preserve-id (delta x d) = cong (delta x) (delta-preserve-id d)
 
--- Functor-law-2 : T(f . g) = T(f) . T(g)
-functor-law-2 : {l : Level} {n : Nat} {A B C : Set l} ->
+
+-- functor-law 2 : T(f . g) = T(f) . T(g)
+delta-covariant : {l : Level} {n : Nat} {A B C : Set l} ->
                 (f : B -> C) -> (g : A -> B) -> (d : Delta A (S n)) ->
                 (delta-fmap (f ∙ g)) d ≡ ((delta-fmap f) ∙ (delta-fmap g)) d
-functor-law-2 f g (mono x)    = refl
-functor-law-2 f g (delta x d) = cong (delta (f (g x))) (functor-law-2 f g d)
+delta-covariant f g (mono x)    = refl
+delta-covariant f g (delta x d) = cong (delta (f (g x))) (delta-covariant f g d)
 
 
-delta-fmap-equiv : {l : Level} {A B : Set l} {n : Nat} {f g : A -> B} 
+delta-fmap-equiv : {l : Level} {A B : Set l} {n : Nat} {f g : A -> B}
                    (eq : (x : A) -> f x ≡ g x) -> (d : Delta A (S n)) ->
                    delta-fmap f d ≡ delta-fmap g d
 delta-fmap-equiv {l} {A} {B} {O} {f} {g} eq (mono x) = begin
@@ -41,7 +42,7 @@
 
 delta-is-functor : {l : Level} {n : Nat} -> Functor {l} (\A -> Delta A (S n))
 delta-is-functor = record { fmap       = delta-fmap
-                          ;preserve-id = functor-law-1
-                          ; covariant  = \f g -> functor-law-2 g f
+                          ; preserve-id = delta-preserve-id
+                          ; covariant  = \f g -> delta-covariant g f
                           ; fmap-equiv = delta-fmap-equiv
                           }