nice readme, rename M to MIU system

Logic/Language/Impl/MIU.hs

@@ -3,17 +3,17 @@ module Logic.Language.Impl.M where
 import Logic.Language (Language(..), ConcatShowList(..))
 import Logic.Language.Derivation (Derivation(..))
 
--- The language M
+-- The MIU system
 -- (from "Gödel, Escher, Bach: An Eternal Golden Braid" by Douglas Hofstadter)
-data AlphaM
+data AlphaMIU
   = M
   | I
   | U
   deriving (Eq, Show)
 
-type StringM = [AlphaM]
+type StringMIU = [AlphaMIU]
 
-instance Language AlphaM where
+instance Language AlphaMIU where
   isWellFormed (M:_) = True
   isWellFormed _ = False
 
@@ -26,19 +26,19 @@ instance Language AlphaM where
     ]
 
 -- RULE I: If you possess a string whose last letter is I, you can add on a U at the end.
-mRule1 :: StringM -> [StringM]
+mRule1 :: StringMIU -> [StringMIU]
 mRule1 [I] = [[I, U]]
 mRule1 (x:xs) = (x:) <$> mRule1 xs
 mRule1 _ = []
 
 -- RULE II: Suppose you have Mx. Then you may add Mxx to your collection.
-mRule2 :: StringM -> [StringM]
+mRule2 :: StringMIU -> [StringMIU]
 mRule2 string@(M:xs) = [string ++ xs]
 mRule2 _ = []
 
 -- RULE III: If III occurs in one of the strings in your collection, you may
 -- make a new string with U in place of III.
-mRule3 :: StringM -> [StringM]
+mRule3 :: StringMIU -> [StringMIU]
 mRule3 string@(M:xs) = (M:) <$> aux xs
   where
     aux (x@I:xs@(I:I:xs')) = (U:xs'):((x:) <$> aux xs)
@@ -47,7 +47,7 @@ mRule3 string@(M:xs) = (M:) <$> aux xs
 mRule3 _ = []
 
 -- RULE IV: If UU occurs inside one of your strings, you can drop it.
-mRule4 :: StringM -> [StringM]
+mRule4 :: StringMIU -> [StringMIU]
 mRule4 string@(M:xs) = (M:) <$> aux xs
   where
     aux (x@U:xs@(U:xs')) = xs':((x:) <$> aux xs)
@@ -56,13 +56,13 @@ mRule4 string@(M:xs) = (M:) <$> aux xs
 mRule4 _ = []
 
 {-
-ghci> map ConcatShowList infer0 :: [ConcatShowList AlphaM]
+ghci> map ConcatShowList infer0 :: [ConcatShowList AlphaMIU]
 [MI]
 ghci> map ConcatShowList $ concat $ map ($ [M, I, I, I, I, U, U, I]) infer1
 [MIIIIUUIU,MIIIIUUIIIIIUUI,MUIUUI,MIUUUI,MIIIII]
 -}
 
-deriveMIIUII :: Derivation AlphaM
+deriveMIIUII :: Derivation AlphaMIU
 deriveMIIUII =
   Infer1 3 0 $
   Infer1 2 2 $