Add Regex template

Exercises/exercise-3/Regex.hs

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+
+{- Syntax
+    Implementieren Sie den AST (abstract syntax tree) entsprechend den Vorgaben
+    auf dem Übungsblatt.
+-}
+data Regex
+    = Empty
+    | Epsilon
+    | Symbol Char
+    -- | Sequence, Star, Choice fehlen noch.
+    deriving Show
+
+{- Semantik
+    Ziel ist es die Funktion 'match :: Regex -> String -> Bool' zu implementieren,
+    die überprüft ob ein gegebener String zu einer gegebenen Regex passt. Im
+    folgenden werden dafür zuerst drei Hilfsfunktionen implementiert, die Sie dann
+    für 'match' verwenden können.
+-}
+
+{- Helper function 1:
+    Given a predicate and a string this function returns all (proper) tails
+    of the string that are obtained by removing an initial segment that
+    satisfies the predicate.
+    Examples:
+        tails (\s -> length s == 1) "abcde" == ["bcde"]
+        tails (\s -> length s >= 1) "abcde" == ["bcde","cde","de","e",""]
+-}
+tails :: (String -> Bool) -> String -> [String]
+tails f s = error "fixme"
+
+{- Helper function 2:
+    By repeatedly calling the tails function, this function checks if
+    it is possible to partition a given string into consecutive segments
+    each of which satisfies the predicate.
+    Examples:
+        segmentable (\s -> length s == 2) "abcde" == False
+        segmentable (\s -> length s == 2) "abcd" == True
+-}
+segmentable :: (String -> Bool) -> String -> Bool
+segmentable f s
+    | s == "" = True
+    | "" `elem` leads = True
+    | leads == [] = False
+    | otherwise = error "fixme"
+
+{- Helper function 3:
+    Given two predicates and a string, this function checks if it is
+    possible to partition the string into a prefix and a suffix such that
+    the prefix satisfies the first predicate and the suffix satisfies the
+    second predicate.
+    Examples:
+        combinable (\s -> length s == 2) (\s -> length s == 3) "12345" == True
+        combinable (\s -> length s == 2) (\s -> length s == 3) "1234" == False
+        combinable (\s -> length s == 2) (\s -> length s == 3) "123456" == False
+-}
+combinable :: (String -> Bool) -> (String -> Bool) -> String -> Bool
+combinable f g s = error "fixme"
+
+{-
+    Matching a particular string to a regex a regex now simply means to check
+    to cover the base cases and use the helper functions.
+-}
+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"
+{-
+    Examples/test-cases
+-}
+
+-- (ab*|ac*)*
+r1 :: Regex
+r1 = Star
+        ( Choice
+            ( Sequence
+                ( Symbol 'a')
+                ( Star (Symbol 'b'))
+            )
+            (Sequence
+                (Symbol 'a')
+                (Star (Symbol 'c'))
+            )
+        )
+
+-- (ab*|ac*)*x*
+r2 :: Regex
+r2 = Sequence r1 (Star (Symbol 'x'))
+
+-- ab
+r3 :: Regex
+r3 = Sequence (Symbol 'a') (Symbol 'b')
+
+-- a(a|b)*
+r4 :: Regex
+r4 = Sequence (Symbol 'a') $ Star $ Choice (Symbol 'a') (Symbol 'b')
+
+
+shouldBeTrue1 :: Bool
+shouldBeTrue1 = match r1 "abbbbaccca"
+
+shouldBeFalse1 :: Bool
+shouldBeFalse1 = match r1 "abbcc"
+
+
+shouldBeTrue2 :: Bool
+shouldBeTrue2 = match r2 "abbbbacccabxxxx"
+
+shouldBeFalse2 :: Bool
+shouldBeFalse2 = match r2 "abbxxxacc"
+
+shouldBeTrue3 :: Bool
+shouldBeTrue3 = match r3 "ab"
+
+shouldBeFalse3 :: Bool
+shouldBeFalse3 = match r3 "aba"
+
+shouldBeTrue4 :: Bool
+shouldBeTrue4 = match r4 "abbbab"
+
+shouldBeFalse4 :: Bool