-- Programare Logica si Functionala, Seria 36
-- Proba: Testare Haskell, 11.07.2025

-- Redenumiti fisierul in grupa_nume_prenume.hs 
-- Daca aveti mai multe nume de familie, respectiv mai multe prenume, le scrieti in continuare, cu majuscula si fara cratima! 
-- de exemplu Popescu Ionescu Ion Andrei de la 365 si-ar denumi sursa 365_PopescuIonescu_IonAndrei.hs 
-- va rog sa nu folositi diacritice! 

-- NUME: 
-- PRENUME: 
-- GRUPA: 

import Data.Char
import Data.Maybe
import Control.Monad
import Control.Applicative
import System.Random
import Data.List

-- START SOLUTII



-- END SOLUTII

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------------------FINAL TESTARE----------------------------------------------------------------------------------------
--------------------------------FINAL TESTARE--------------------------------------------------------------------------
----------------------------------------------FINAL TESTARE------------------------------------------------------------
-- NU SCHIMBATI NIMIC MAI JOS 
-- NU SCRIETI NICIO REZOLVARE MAI JOS!!!
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 ------Module QuickCheck-----------------------------------
 --- sursa: https://www.cse.chalmers.se/~rjmh/QuickCheck/QuickCheck.hs

infixr 0 ==>
infix  1 `classify`

--------------------------------------------------------------------
-- Generator

newtype Gen a
  = Gen (Int -> StdGen -> a)

sized :: (Int -> Gen a) -> Gen a
sized fgen = Gen (\n r -> let Gen m = fgen n in m n r)

resize :: Int -> Gen a -> Gen a
resize n (Gen m) = Gen (\_ r -> m n r)

rand :: Gen StdGen
rand = Gen (\n r -> r)

promote :: (a -> Gen b) -> Gen (a -> b)
promote f = Gen (\n r -> \a -> let Gen m = f a in m n r)

variant :: Int -> Gen a -> Gen a
variant v (Gen m) = Gen (\n r -> m n (rands r !! (v+1)))
 where
  rands r0 = r1 : rands r2 where (r1, r2) = split r0

generate :: Int -> StdGen -> Gen a -> a
generate n rnd (Gen m) = m size rnd'
 where
  (size, rnd') = randomR (0, n) rnd

--instance Functor Gen where
--  fmap f m = m >>= return . f

instance Monad Gen where
  Gen m >>= k =
    Gen (\n r0 -> let (r1,r2) = split r0
                      Gen m'  = k (m n r1)
                   in m' n r2)
                   
instance Applicative Gen where
  pure a = Gen (\n r -> a)
  mf <*> ma = do
    f <- mf
    a <- ma
    return (f a)       

instance Functor Gen where              
  fmap f ma = pure f <*> ma                     

-- derived

choose :: Random a => (a, a) -> Gen a
choose bounds = (fst . randomR bounds) `fmap` rand

elements :: [a] -> Gen a
elements xs = (xs !!) `fmap` choose (0, length xs - 1)

vector :: Arbitrary a => Int -> Gen [a]
vector n = sequence [ arbitrary | i <- [1..n] ]

oneof :: [Gen a] -> Gen a
oneof gens = elements gens >>= id

frequency :: [(Int, Gen a)] -> Gen a
frequency xs = choose (1, tot) >>= (`pick` xs)
 where
  tot = sum (map fst xs)

  pick n ((k,x):xs)
    | n <= k    = x
    | otherwise = pick (n-k) xs

-- general monadic

two :: Monad m => m a -> m (a, a)
two m = liftM2 (,) m m

three :: Monad m => m a -> m (a, a, a)
three m = liftM3 (,,) m m m

four :: Monad m => m a -> m (a, a, a, a)
four m = liftM4 (,,,) m m m m

--------------------------------------------------------------------
-- Arbitrary

class Arbitrary a where
  arbitrary   :: Gen a
  --coarbitrary :: a -> Gen b -> Gen b

instance Arbitrary () where
  arbitrary     = return ()
 -- coarbitrary _ = variant 0

instance Arbitrary Bool where
  arbitrary     = elements [True, False]
  --coarbitrary b = if b then variant 0 else variant 1

instance Arbitrary Char where
  arbitrary     = choose (32,255) >>= \n -> return (chr n)
 -- coarbitrary n = variant (ord n)

instance Arbitrary Int where
  arbitrary     = sized $ \n -> choose (-n,n)
 -- coarbitrary n = variant (if n >= 0 then 2*n else 2*(-n) + 1)


instance Arbitrary Integer where
  arbitrary     = sized $ \n -> choose (-fromIntegral n,fromIntegral n)
  --coarbitrary n = variant $ (fromInteger(if n >= 0 then 2*n else 2*(-n) + 1)) 

instance Arbitrary Float where
  arbitrary     = liftM3 fraction arbitrary arbitrary arbitrary 
  --coarbitrary x = coarbitrary (decodeFloat x)

instance Arbitrary Double where
  arbitrary     = liftM3 fraction arbitrary arbitrary arbitrary 
 -- coarbitrary x = coarbitrary (decodeFloat x)

fraction a b c = fromInteger a + (fromInteger b / (abs (fromInteger c) + 1))

{-
instance Arbitrary Integer where
  arbitrary     = sized $ \n -> choose (-fromInt n,fromInt n)
  coarbitrary n = variant (fromInteger (if n >= 0 then 2*n else 2*(-n) + 1))

instance Arbitrary Float where
  arbitrary     = liftM3 fraction arbitrary arbitrary arbitrary 
  coarbitrary x = coarbitrary (decodeFloat x)

instance Arbitrary Double where
  arbitrary     = liftM3 fraction arbitrary arbitrary arbitrary 
  coarbitrary x = coarbitrary (decodeFloat x)

fraction a b c = fromInteger a + (fromInteger b / (abs (fromInteger c) + 1))
-}


instance (Arbitrary a, Arbitrary b) => Arbitrary (a, b) where
  arbitrary          = liftM2 (,) arbitrary arbitrary
 -- coarbitrary (a, b) = coarbitrary a . coarbitrary b

instance (Arbitrary a, Arbitrary b, Arbitrary c) => Arbitrary (a, b, c) where
  arbitrary             = liftM3 (,,) arbitrary arbitrary arbitrary
  --coarbitrary (a, b, c) = coarbitrary a . coarbitrary b . coarbitrary c

instance (Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d)
      => Arbitrary (a, b, c, d)
 where
  arbitrary = liftM4 (,,,) arbitrary arbitrary arbitrary arbitrary
  --coarbitrary (a, b, c, d) =
  --  coarbitrary a . coarbitrary b . coarbitrary c . coarbitrary d

instance Arbitrary a => Arbitrary [a] where
  arbitrary          = sized (\n -> choose (0,n) >>= vector)
 -- coarbitrary []     = variant 0
 -- coarbitrary (a:as) = coarbitrary a . variant 1 . coarbitrary as

--instance (Arbitrary a, Arbitrary b) => Arbitrary (a -> b) where
 -- arbitrary         = promote (`coarbitrary` arbitrary)
 -- coarbitrary f gen = arbitrary >>= ((`coarbitrary` gen) . f)

--------------------------------------------------------------------
-- Testable

data Result
  = Result { ok :: Maybe Bool, stamp :: [String], arguments :: [String] }

nothing :: Result
nothing = Result{ ok = Nothing, stamp = [], arguments = [] }

newtype Property
  = Prop (Gen Result)

result :: Result -> Property
result res = Prop (return res)

evaluate :: Testable a => a -> Gen Result
evaluate a = gen where Prop gen = property a

class Testable a where
  property :: a -> Property

instance Testable () where
  property _ = result nothing

instance Testable Bool where
  property b = result (nothing{ ok = Just b })

instance Testable Result where
  property res = result res

instance Testable Property where
  property prop = prop

instance (Arbitrary a, Show a, Testable b) => Testable (a -> b) where
  property f = forAll arbitrary f

forAll :: (Show a, Testable b) => Gen a -> (a -> b) -> Property
forAll gen body = Prop $
  do a   <- gen
     res <- evaluate (body a)
     return (argument a res)
 where
  argument a res = res{ arguments = show a : arguments res }

(==>) :: Testable a => Bool -> a -> Property
True  ==> a = property a
False ==> a = property ()

label :: Testable a => String -> a -> Property
label s a = Prop (add `fmap` evaluate a)
 where
  add res = res{ stamp = s : stamp res }

classify :: Testable a => Bool -> String -> a -> Property
classify True  name = label name
classify False _    = property

trivial :: Testable a => Bool -> a -> Property
trivial = (`classify` "trivial")

collect :: (Show a, Testable b) => a -> b -> Property
collect v = label (show v)

--------------------------------------------------------------------
-- Testing

data Config = Config
  { maxTest :: Int
  , maxFail :: Int
  , size    :: Int -> Int
  , every   :: Int -> [String] -> String
  }

quick :: Config
quick = Config
  { maxTest = 100
  , maxFail = 1000
  , size    = (+ 3) . (`div` 2)
  , every   = \n args -> let s = show n in s ++ [ '\b' | _ <- s ]
  }
         
verbose :: Config
verbose = quick
  { every = \n args -> show n ++ ":\n" ++ unlines args
  }

test, quickCheck, verboseCheck :: Testable a => a -> IO ()
test         = check quick
quickCheck   = check quick
verboseCheck = check verbose
         
check :: Testable a => Config -> a -> IO ()
check config a =
  do rnd <- newStdGen
     tests config (evaluate a) rnd 0 0 []

tests :: Config -> Gen Result -> StdGen -> Int -> Int -> [[String]] -> IO () 
tests config gen rnd0 ntest nfail stamps
  | ntest == maxTest config = do done "OK, passed" ntest stamps
  | nfail == maxFail config = do done "Arguments exhausted after" ntest stamps
  | otherwise               =
      do putStr (every config ntest (arguments result))
         case ok result of
           Nothing    ->
             tests config gen rnd1 ntest (nfail+1) stamps
           Just True  ->
             tests config gen rnd1 (ntest+1) nfail (stamp result:stamps)
           Just False ->
             putStr ( "Falsifiable, after "
                   ++ show ntest
                   ++ " tests:\n"
                   ++ unlines (arguments result)
                    )
     where
      result      = generate (size config ntest) rnd2 gen
      (rnd1,rnd2) = split rnd0

done :: String -> Int -> [[String]] -> IO ()
done mesg ntest stamps =
  do putStr ( mesg ++ " " ++ show ntest ++ " tests" ++ table )
 where
  table = display
        . map entry
        . reverse
        . sort
        . map pairLength
        . group
        . sort
        . filter (not . null)
        $ stamps

  display []  = ".\n"
  display [x] = " (" ++ x ++ ").\n"
  display xs  = ".\n" ++ unlines (map (++ ".") xs)

  pairLength xss@(xs:_) = (length xss, xs)
  entry (n, xs)         = percentage n ntest
                       ++ " "
                       ++ concat (intersperse ", " xs)

  percentage n m        = show ((100 * n) `div` m) ++ "%"

--------------------------------------------------------------------
-- the end.

-- PARSER
newtype Parser a = Parser { apply :: String -> [(a, String)] }

parse :: Parser a -> String -> a 
parse m s = head [x | (x, t) <- apply m s, t == ""]

anychar :: Parser Char 
anychar = Parser f 
    where 
        f [] = [] 
        f (c:s) = [(c, s)]

satisfy :: (Char -> Bool) -> Parser Char 
satisfy p = Parser f 
    where 
        f [] = [] 
        f (c:s) 
            | p c = [(c, s)]
            | otherwise = [] 

char :: Char -> Parser Char 
char c = satisfy (== c)

string :: String -> Parser String 
string [] = Parser (\s -> [([], s)])
string (x:xs) = Parser f 
    where 
        f s = [(y:z, zs) | (y, ys) <- apply (char x) s, (z, zs) <- apply (string xs) ys]

digit = satisfy isDigit 

alt :: Parser a -> Parser a -> Parser a 
alt p1 p2 = Parser f 
    where 
        f s = apply p1 s ++ apply p2 s 

failP :: Parser a 
failP = Parser (\s -> [])

instance Monad Parser where 
    return x = Parser (\s -> [(x, s)])
    m >>= k = Parser (\s -> [ (y, u) | (x, t) <- apply m s, (y, u) <- apply (k x) t])

instance Applicative Parser where 
    pure = return 
    mf <*> ma = do 
        f <- mf 
        a <- ma 
        return (f a)

instance Functor Parser where 
    fmap f ma = pure f <*> ma 

many :: Parser Char -> Parser String 
many p = alt (Main.some p) (return "")

some :: Parser Char -> Parser String 
some p = do 
    x <- p 
    xs <- Main.many p
    return (x:xs)

decimal :: Parser Int 
decimal = do 
    s <- Main.some digit 
    return (read s)

negdecimal :: Parser Int 
negdecimal = do 
    char '-'
    n <- decimal 
    return (-n)

integer :: Parser Int 
integer = alt decimal negdecimal 

iden :: Parser Char -> Parser Char -> Parser String 
iden firstCh nextCh = do 
    c <- firstCh 
    s <- Main.many nextCh 
    return (c:s)

skipSpace :: Parser () 
skipSpace = do 
    _ <- Main.many (satisfy isSpace)
    return () 

token :: Parser a -> Parser a 
token p = do 
    skipSpace 
    x <- p 
    skipSpace 
    return x 

-- END PARSER