# HG changeset patch
# User Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
# Date 1412662157 -32400
# Node ID e0ba1bf564ddc2508712d4bc5d84de2483d6aa09
# Parent  6e6d646d7722f4e2c2fa787e3885961c652a168f
Apply level to some functions

diff -r 6e6d646d7722 -r e0ba1bf564dd agda/basic.agda
--- a/agda/basic.agda	Tue Oct 07 14:55:40 2014 +0900
+++ b/agda/basic.agda	Tue Oct 07 15:09:17 2014 +0900
@@ -1,10 +1,12 @@
+open import Level
+
 module basic where
 
-id : {A : Set} -> A -> A
+id : {l : Level} {A : Set} -> A -> A
 id x = x
 
-_∙_ : {A B C : Set} -> (A -> B) -> (B -> C) -> (A -> C)
-f ∙ g = \x -> g (f x)
+_∙_ : {l ll lll : Level} {A : Set l} {B : Set ll} {C : Set lll} -> (B -> C) -> (A -> B) -> (A -> C)
+f ∙ g = \x -> f (g x)
 
 postulate String : Set
 postulate show   : {A : Set} -> A -> String
\ No newline at end of file
diff -r 6e6d646d7722 -r e0ba1bf564dd agda/similar.agda
--- a/agda/similar.agda	Tue Oct 07 14:55:40 2014 +0900
+++ b/agda/similar.agda	Tue Oct 07 15:09:17 2014 +0900
@@ -1,17 +1,19 @@
 open import list
 open import basic
+
+open import Level
 open import Relation.Binary.PropositionalEquality
 open ≡-Reasoning
 
 module similar where
 
-data Similar (A : Set) : Set where
+data Similar {l : Level} (A : Set l) : (Set (suc l)) where
   similar : List String -> A -> List String -> A -> Similar A
 
-fmap : {A B : Set} -> (A -> B) -> (Similar A) -> (Similar B)
+fmap : {l ll : Level} {A : Set l} {B : Set ll} -> (A -> B) -> (Similar A) -> (Similar B)
 fmap f (similar xs x ys y) = similar xs (f x) ys (f y)
 
-mu : {A : Set} -> Similar (Similar A) -> Similar A
+mu : {l : Level} {A : Set l} -> Similar (Similar A) -> Similar A
 mu (similar lx (similar llx x _ _) ly (similar _ _ lly y)) = similar (lx ++ llx) x (ly ++ lly) y
 
 return : {A : Set} -> A -> Similar A
@@ -23,10 +25,23 @@
 returnSS : {A : Set} -> A -> A -> Similar A
 returnSS x y = similar [[ (show x) ]] x [[ (show y) ]] y
 
+--monad-law-1 : mu ∙ (fmap mu) ≡ mu ∙ mu
 
-monad-law-1 : mu ∙ (fmap mu) ≡ mu ∙ mu
-monad-law-1 = {!!} 
+monad-law-1 : {l : Level} {A : Set l} -> (s : Similar (Similar (Similar A))) -> ((mu ∙ (fmap mu)) s) ≡ ((mu ∙ mu) s)
+monad-law-1 s = begin
+    ((mu ∙ (fmap mu)) s)
+  ≡⟨⟩
+    mu (fmap mu s)
+  ≡⟨ {!!} ⟩
+     mu (mu s)
+  ≡⟨⟩
+    ((mu ∙ mu) s)
+  ∎
 
+
+
+
+{-
 --monad-law-2 : mu ∙ fmap return ≡ mu ∙ return ≡id
 monad-law-2-1 : mu ∙ fmap return ≡ mu ∙ return
 monad-law-2-1 = {!!}
@@ -35,7 +50,8 @@
 monad-law-2-2 = {!!}
 
 monad-law-3 : ∀{f} -> return ∙ f ≡ fmap f ∙ return
-monad-law-3 = {!!} 
+monad-law-3 = {!!}
 
 monad-law-4 : ∀{f} -> mu ∙ fmap (fmap f) ≡ fmap f ∙ mu
-monad-law-4 = {!!} 
+monad-law-4 = {!!}
+-}