Explain/document a few functions

Lambda.hs

@@ -20,6 +20,7 @@ data Expression s = ESymbol s
                   | ELambda s (Expression s)
   deriving (Show)
 
+-- comparison checks for alpha-equivalency
 instance (Eq s) => Eq (Expression s) where
   (ESymbol a)    == (ESymbol b)    = a == b
   (EReference a) == (EReference b) = a == b
@@ -27,8 +28,9 @@ instance (Eq s) => Eq (Expression s) where
   (ELambda _ a)  == (ELambda _ b)  = a == b
   _              == _              = False
 
+-- Map over all the symbols in the expression (including those in the ELambdas).
 instance Functor Expression where
-  fmap f (EReference n) = EReference n
+  fmap f (EReference r) = EReference r
   fmap f (ESymbol a)    = ESymbol (f a)
   fmap f (ELambda s e)  = ELambda (f s) (fmap f e)
   fmap f (EExpr a b)    = EExpr (fmap f a) (fmap f b)
@@ -43,11 +45,13 @@ instance Functor Expression where
 makeUnique :: [String] -> String -> String
 makeUnique context s =
   let apostrophes = iterate ('\'' :) ""
-      modified = zipWith (++) (repeat s) apostrophes
-      available = filter (not . (`elem` context)) modified
-  in head available -- list of available names is infinite
+      modified    = zipWith (++) (repeat s) apostrophes
+      available   = filter (not . (`elem` context)) modified
+  in head available -- re. head: list of available names is infinite
 
 -- Expression -> Expression with unique symbol names
+-- Converts all the symbols in the expression to strings and
+-- then makes them unique in their context.
 renameUniquely :: (Show s) => Expression s -> Expression String
 renameUniquely = rename_ []
   -- rename_ :: (Show s) => [String] -> Expression s -> Expression String
@@ -57,6 +61,10 @@ renameUniquely = rename_ []
         rename_ c (ELambda s e)  = let name = makeUnique c . show $ s
                                    in  ELambda name (rename_ (name : c) e)
 
+-- unicode? -> Expression -> Maybe String
+-- Converts the expression to a string, if possible.
+-- (Not possible if a reference is too high)
+-- If unicode is True, uses λ instead of \.
 display :: (Show s) => Bool -> Expression s -> String
 display unicode = d [] . renameUniquely
   where l = if unicode then "λ" else "\\"
@@ -76,8 +84,10 @@ display unicode = d [] . renameUniquely
  - Evaluating expressions
  -}
 
--- Expression to be inserted -> Expression to be inserted into -> result
--- TODO: Make clearer what insert does - better description, ...
+-- level to insert at -> Expression to be inserted
+-- -> Expression to be inserted into -> result
+-- Inserts an expression into another expression on a certain level.
+-- The level points towards an ELambda, like an EReference.
 insertExpr :: Int -> Expression s -> Expression s -> Expression s
 insertExpr level replace ref@(EReference n)
   | n == level = replace
@@ -85,18 +95,24 @@ insertExpr level replace ref@(EReference n)
 insertExpr level replace (EExpr a b)   = EExpr (insertExpr level replace a)
                                                (insertExpr level replace b)
 insertExpr level replace (ELambda s e) = ELambda s (insertExpr (level + 1) replace e)
-insertExpr _     _       symbol        = symbol
+insertExpr _     _       other         = other
 
+-- Expression -> Expression applied once
+-- Attempts beta-reduction, applying the leftmost expression (if there is one) to
+-- the expression to its right (if there is one).
+-- TODO: Apply leftmost function, not leftmost expression.
 apply :: Expression s -> Expression s
 apply (EExpr l@(ELambda s e) b) = insertExpr 0 b e
 apply (EExpr e@(EExpr _ _) b) = EExpr (apply e) b
 apply e = e
 
+-- Takes elements as long as it hasn't seen them before.
 takeWhileUnique :: (Eq a) => [a] -> [a]
 takeWhileUnique l = map fst
                   $ takeWhile (\a -> not $ fst a `elem` snd a)
                   $ zip l (inits l)
 
+-- Applies a function until there is a loop or it can't be applied any further.
 evaluate :: (Eq s) => Expression s -> [Expression s]
 evaluate = takeWhileUnique . iterate apply
 
@@ -104,7 +120,8 @@ evaluate = takeWhileUnique . iterate apply
  - Parsing expressions
  -}
 
--- "munchified" versions of many, many1 and chainl1 that try to match as much as possible.
+-- "munchified" versions of many, many1 and chainl1 that try to match as much as
+-- possible. They only match the maximum amount, not all numbers in-between.
 many' :: ReadP a -> ReadP [a]
 many' p = many1' p <++ return []
 
@@ -114,18 +131,22 @@ many1' p = liftM2 (:) p (many' p)
 chainl1' :: ReadP a -> ReadP (a -> a -> a) -> ReadP a
 chainl1' p f = foldl1 <$> f <*> many1' p
 
+-- List of (opening parenthesis, closing parenthesis) pairs.
 parens :: [(Char, Char)]
 parens = [ ('(', ')')
          , ('[', ']')
          , ('{', '}')
          ]
 
+-- Is opening parenthesis?
 isOpeningParen :: Char -> Bool
 isOpeningParen a = isJust $ lookup a parens
 
+-- Is closing parenthesis to this opening parenthesis?
 isClosingParen :: Char -> Char -> Bool
 isClosingParen a b = fromMaybe False $ (== b) <$> lookup a parens
 
+-- Put a pair of matching parentheses around a parser
 parenthesize :: ReadP a -> ReadP a
 parenthesize parser = do
   paren <- satisfy isOpeningParen