Remove Symbol typeclass

lambda.hs

@@ -1,57 +1,37 @@
+
 import Data.List
 
-data StrSymbol = StrSymbol { symBase :: String -- lowercase a to z
-                           , symLen :: Int
-                           }
+-- A symbol denoting a variable; consists of a textual name and some (or no) apostrophes to ensure uniqueness
+data Symbol = Symbol { symBase :: String -- lowercase a to z
+                     , symLen  :: Int    -- nonnegative
+                     }
 
-instance Show StrSymbol where
-  show (StrSymbol s n) = s ++ (replicate n '\'')
+instance Show Symbol where
+  show (Symbol s n) = s ++ (replicate n '\'')
 
-class Symbol a where
-  -- Should we use a set instead of a list here? ~G
-  --   Hardly five minutes away and you're already overengineering. ~X
-  --   Overengineering is fun! ~G
-  -- Also, what is the second parameter? ~X
-  --   The original symbol for which a new name should be found ~G (grammer is herd)
-  --     Do we need that or can we just let it return a new symbol? ~X
-  --     If we just let it return a new symbol, we would lose the thing where something called a will be renamed to a'
-  --     and later back to a (keep the same name) ~G
-  --     How about we define a findNewName that just finds a new unique symbol that is not in the list, so we can try out both
-  --     things later on. ~G
-  findName :: [a] -> a -> a
-  findNewName :: [a] -> a
-
-instance Symbol StrSymbol where
-  findName other (StrSymbol base n) =
-    let sameBase = filter ((base ==) . symBase) other
-        lengths = map symLen sameBase
-        freeLengths = [0..] \\ (nub lengths)
-    in  StrSymbol base (head freeLengths) -- [0..] is infinite
-  
-  -- findNewName basically finds a new unique base ~G
-  -- try to find a name in the sequence
-  -- a..z, aa..zz, aaa........
-  {-
-  findNewName other =
-    let bases = nub $ map symBase other
-  -}
+-- Present symbols (not including symbol to change) -> symbol to change ->
+--   unique symbol with same base and minimal amount of apostrophes
+findName :: [Symbol] -> Symbol -> Symbol
+findName other (Symbol base n) =
+  let sameBase = filter ((base ==) . symBase) other
+      lengths = map symLen sameBase
+      freeLengths = [0..] \\ (nub lengths)
+  in Symbol base (head freeLengths) -- [0..] is infinite
 
+-- An expression. Can be a mere symbol, a lambda application, or a lambda abstraction.
 data Expression s = ESymbol s
                   | EExpr   (Expression s) (Expression s)
                   | ELambda s (Expression s)
 
 instance (Show s) => Show (Expression s) where
   show (ESymbol s) = show s
-  -- show (EExpr a e@(EExpr _ _)) = "(" ++ show a ++ " " ++ (drop 1 $ show e) -- hack hack hack
-  show (EExpr a@(EExpr _ _) b) = (init $ show a) ++ " " ++ show b ++ ")" -- hack hack hack
+  -- ((a b) c) is equivalent to (a b c)
+  show (EExpr a@(EExpr _ _) b) = (init $ show a) ++ " " ++ show b ++ ")"
   show (EExpr a b) = "(" ++ show a ++ " " ++ show b ++ ")"
   show (ELambda s e) = "\\" ++ show s ++ "." ++ show e
 
-_s :: String -> Expression StrSymbol
-_s s = ESymbol (StrSymbol s 0)
-
-_ss :: String -> StrSymbol
-_ss s = (StrSymbol s 0)
+_s :: String -> Expression Symbol
+_s s = ESymbol $ Symbol s 0
 
 main = do
   print (EExpr (_s "a") (EExpr (_s "b") (_s "c")))
@@ -59,11 +39,12 @@ main = do
   print (EExpr (EExpr (_s "a") (_s "b")) (_s "c"))
   print (EExpr (EExpr (EExpr (_s "a") (_s "b")) (_s "c")) (_s "d"))
   print (EExpr (EExpr (_s "a") (EExpr (_s "b") (_s "c"))) (_s "d"))
-  print (ELambda (StrSymbol "a" 0) (_s "a"))
-  print (ELambda (StrSymbol "a" 0) (EExpr (EExpr (_s "a") (EExpr (_s "b") (_s "c"))) (_s "d")))
+  print (ELambda (Symbol "a" 0) (_s "a"))
+  print (ELambda (Symbol "a" 0) (EExpr (EExpr (_s "a") (EExpr (_s "b") (_s "c"))) (_s "d")))
   
   -- test of findName (seems to be working) ~G
-  print $ findName [(StrSymbol "a" 0), (StrSymbol "b" 0), (StrSymbol "a" 1)] (StrSymbol "a" 4)
-  print $ findName [(StrSymbol "a" 0), (StrSymbol "b" 0), (StrSymbol "a" 1)] (StrSymbol "b" 3)
-  print $ findName [(StrSymbol "a" 0), (StrSymbol "b" 0), (StrSymbol "a" 1)] (StrSymbol "c" 2)
-  print $ findName [(StrSymbol "a" 1), (StrSymbol "a" 3), (StrSymbol "a" 0)] (StrSymbol "a" 1)
+  print $ findName [(Symbol "a" 0), (Symbol "b" 0), (Symbol "a" 1)] (Symbol "a" 4)
+  print $ findName [(Symbol "a" 0), (Symbol "b" 0), (Symbol "a" 1)] (Symbol "b" 3)
+  print $ findName [(Symbol "a" 0), (Symbol "b" 0), (Symbol "a" 1)] (Symbol "c" 2)
+  print $ findName [(Symbol "a" 1), (Symbol "a" 3), (Symbol "a" 0)] (Symbol "a" 1)
+