Solve Regex task

Exercises/exercise-3/Regex.hs

@@ -7,6 +7,9 @@ data Regex
     = Empty
     | Epsilon
     | Symbol Char
+    | Sequence Regex Regex
+    | Star Regex
+    | Choice Regex Regex
     -- | Sequence, Star, Choice fehlen noch.
     deriving Show
 
@@ -26,7 +29,13 @@ data Regex
         tails (\s -> length s >= 1) "abcde" == ["bcde","cde","de","e",""]
 -}
 tails :: (String -> Bool) -> String -> [String]
-tails f s = error "fixme"
+tails f s = concatMap
+    (\x -> if f (take x s) then [(drop x s)] else [])
+    [0..(length s)]
+
+-- >>> tails (\s -> length s >= 1) "abcde"
+-- ["bcde","cde","de","e",""]
+--
 
 {- Helper function 2:
     By repeatedly calling the tails function, this function checks if
@@ -41,7 +50,16 @@ segmentable f s
     | s == "" = True
     | "" `elem` leads = True
     | leads == [] = False
-    | otherwise = error "fixme"
+    | otherwise = or (map (\x -> segmentable f x) leads)
+    where
+        leads = tails f s
+
+-- >>> segmentable (\s -> length s == 2) "abcde"
+-- False
+--
+-- >>> segmentable (\s -> length s == 2) "abcd"
+-- True
+--
 
 {- Helper function 3:
     Given two predicates and a string, this function checks if it is
@@ -54,7 +72,22 @@ segmentable f s
         combinable (\s -> length s == 2) (\s -> length s == 3) "123456" == False
 -}
 combinable :: (String -> Bool) -> (String -> Bool) -> String -> Bool
-combinable f g s = error "fixme"
+combinable f g s =
+    or (
+        map
+            (\x -> f (take x s) && g (drop x s))
+            (reverse [0..len])
+    )
+    where
+        len = length s
+
+-- >>> combinable (\s -> length s == 2) (\s -> length s == 3) "12345"
+-- >>> combinable (\s -> length s == 2) (\s -> length s == 3) "1234"
+-- >>> combinable (\s -> length s == 2) (\s -> length s == 3) "123456"
+-- True
+-- False
+-- False
+--
 
 {-
     Matching a particular string to a regex a regex now simply means to check
@@ -62,12 +95,12 @@ combinable f g s = error "fixme"
 -}
 match :: Regex -> String -> Bool
 match r s = case r of
-    Empty -> error "fixme"
-    Epsilon -> error "fixme"
-    Symbol c -> error "fixme"
-    Choice r1 r2 -> error "fixme"
-    Sequence r1 r2 -> error "fixme"
-    Star r1 -> error "fixme"
+    Empty -> s == ""
+    Epsilon -> False
+    Symbol c -> s == [c]
+    Choice r1 r2 -> (match r1 s || match r2 s)
+    Sequence r1 r2 -> combinable (match r1) (match r2) s
+    Star r1 -> segmentable (match r1) s
 {-
     Examples/test-cases
 -}
@@ -101,24 +134,49 @@ r4 = Sequence (Symbol 'a') $ Star $ Choice (Symbol 'a') (Symbol 'b')
 
 shouldBeTrue1 :: Bool
 shouldBeTrue1 = match r1 "abbbbaccca"
+-- >>> match r1 "abbbbaccca"
+-- True
+--
 
 shouldBeFalse1 :: Bool
 shouldBeFalse1 = match r1 "abbcc"
+-- >>> match r1 "abbcc"
+-- False
+--
 
 
 shouldBeTrue2 :: Bool
 shouldBeTrue2 = match r2 "abbbbacccabxxxx"
+-- >>> match r2 "abbbbacccabxxxx"
+-- True
+--
 
 shouldBeFalse2 :: Bool
 shouldBeFalse2 = match r2 "abbxxxacc"
+-- >>> match r2 "abbxxxacc"
+-- False
+--
 
 shouldBeTrue3 :: Bool
 shouldBeTrue3 = match r3 "ab"
+-- >>> match r3 "ab"
+-- True
+--
 
 shouldBeFalse3 :: Bool
 shouldBeFalse3 = match r3 "aba"
+-- >>> match r3 "aba"
+-- False
+--
 
 shouldBeTrue4 :: Bool
 shouldBeTrue4 = match r4 "abbbab"
+-- >>> match r4 "abbbab"
+-- True
+--
 
-shouldBeFalse4 :: Bool
+shouldBeFalse4 :: Bool
+shouldBeFalse4 = match r4 "abbabc"
+-- >>> match r4 "abbabc"
+-- False
+--