Monad laws.

category-theory/monad-laws.hs

@@ -0,0 +1,27 @@
+import Control.Monad
+
+-- left identity: return x >>= f == f x
+a1 = return 3 >>= (\x -> Just (x+100000))
+a2 = (\x -> Just (x+100000)) 3
+leftIdentity = a1 == a2 
+
+-- right identity: m >>= return == m
+b1 = Just "move on up" >>= (\x -> return x)  
+b2 = [1,2,3,4] >>= (\x -> return x)  
+b3 = putStrLn "Wah!" >>= (\x -> return x)
+
+-- associativity: (m >>= f) >>= g == m >>= (\x -> f x >>= g)
+c1 = return (0,0) >>= landRight 2 >>= landLeft 2 >>= landRight 2
+c2 = ((return (0,0) >>= landRight 2) >>= landLeft 2) >>= landRight 2
+--c3 = return (0,0) >>= (\x -> 
+--	landRight 2 x >>= (\y -> 
+--	landLeft 2 y >>= (\z -> 
+--	landRight 2 z)))
+-- needs the functions landRight and landLeft defined in monad.hs
+associativity = c1 == c2 -- == c3
+
+-- composing functions using Monads
+f x = [x,-x]  
+g x = [x*3,x*2]  
+h = f <=< g  
+example = h 3