Mercurial > hg > Papers > 2015 > atton-thesis

diff src/delta_covariant.agda @ 42:4cc65012412f

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Add proofs of functor-laws on delta
author Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
date Fri, 13 Feb 2015 17:13:23 +0900
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--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/delta_covariant.agda	Fri Feb 13 17:13:23 2015 +0900
@@ -0,0 +1,6 @@
+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
+delta-covariant f g (mono x)    = refl
+delta-covariant f g (delta x d) = cong (delta (f (g x)))
+                                       (delta-covariant f g d)