Clearer definition for apply

src/Research.hs

@@ -55,15 +55,24 @@ data EvaluatedForm = TreeCalculus | FSL | AST | Ternary | Ascii | Decode
 -- Environment containing previously evaluated TC terms
 type Env = Map.Map String T
 
--- Tree Calculus Reduction
+-- Tree Calculus Reduction Rules
+{- 
+  The t operator is left associative.
+  1.  t  t      a b       -> a
+  2.  t (t a)   b c       -> a c (b c)
+  3a. t (t a b) c t       -> a
+  3b. t (t a b) c (t u)   -> b u
+  3c. t (t a b) c (t u v) -> c u v
+-}
 apply :: T -> T -> T
-apply Leaf b                            = Stem b
-apply (Stem a) b                        = Fork a b
-apply (Fork Leaf a) _                   = a
-apply (Fork (Stem a1) a2) b             = apply (apply a1 b) (apply a2 b)
-apply (Fork (Fork a1 a2) a3) Leaf       = a1
-apply (Fork (Fork a1 a2) a3) (Stem u)   = apply a2 u
-apply (Fork (Fork a1 a2) a3) (Fork u v) = apply (apply a3 u) v
+apply (Fork Leaf a)         _         = a
+apply (Fork (Stem a) b) c             = apply (apply a c) (apply b c)
+apply (Fork (Fork a  b) c)  Leaf      = a
+apply (Fork (Fork a  b) c) (Stem u)   = apply b u
+apply (Fork (Fork a  b) c) (Fork u v) = apply (apply c u) v
+-- Left associative `t`
+apply  Leaf b                         = Stem b
+apply (Stem a) b                      = Fork a b
 
 -- Booleans
 _false :: T
@@ -77,7 +86,7 @@ _not = Fork (Fork _true (Fork Leaf _false)) Leaf
 
 -- Marshalling
 ofString :: String -> T
-ofString str = ofList (map ofNumber (map fromEnum str))
+ofString str = ofList $ map (ofNumber . fromEnum) str
 
 ofNumber :: Int -> T
 ofNumber 0 = Leaf
@@ -87,8 +96,7 @@ ofNumber n =
     (ofNumber (n `div` 2))
 
 ofList :: [T] -> T
-ofList [] = Leaf
-ofList (x:xs) = Fork x (ofList xs)
+ofList = foldr Fork Leaf
 
 toNumber :: T -> Either String Int
 toNumber Leaf = Right 0
@@ -126,7 +134,7 @@ toSimpleT s = T.unpack
   $ replace "Fork" "t"
   $ replace "Stem" "t"
   $ replace "Leaf" "t"
-  $ (T.pack s)
+  $ T.pack s
 
 toTernaryString :: T -> String
 toTernaryString Leaf = "0"