L1 Haskell

module L1 where
-- 1. Scrieti o functie care rezolva ecuatia de gradul 2 (folositi error pentru
Delta<0)
-- TODO
-- 2. Definiti functia reverse pe liste.
reverse' :: [a] -> [a]
reverse' [] = []
reverse' (x:xs) = (reverse' $ xs) ++ [x]
-- 3. Scrieti o functie care verifica daca un sir e palindrom
isPalindrome :: Eq a => [a] -> Bool
isPalindrome [] = True
isPalindrome [x] = True
isPalindrome (x:xs) = (x == last xs) && isPalindrome(init xs)
-- 4.
e are
zip3'
zip3'
zip3'

Scrieti un exemplu de folosire a functiei zip. Scrieti o functie zip3 car
ca argumente 3 liste.
:: [a] -> [b] -> [c] -> [(a, b, c)]
(a:aas) (b:bbs) (c:ccs) = (a, b, c) : zip3' aas bbs ccs
_
_
_
= []

zip3a' :: [a] -> [b] -> [c] -> [(a, b, c)]
zip3a' aas bbs ccs = [ (a, b, c) | a <- aas, b <- bbs, c <- ccs]
-- 5. Scrieti in doua moduri o functie map2 care are ca argument o functie cu do
ua argumente f si doua liste [x1,x2 ], [y1,y2,..] si intoarce lista [f(x1,y1), f
(x2,y2),..].
map2 :: (a -> b) -> [a] -> [a] -> [(b, b)]
map2 f (a:aas) (b:bbs) = (f a, f b) : map2 f aas bbs
map2 f _
_
= []
-- 6. Scrieti o functie fn care are ca argument o functie f si un numar n iar c
a rezultat fn(x)=f(f(..(f(x)))) (de n ori)
fn :: (Num b, Eq b) => (a -> a) -> b -> a -> a
fn f 1 x = f x
fn f n x = f $ fn f (n - 1) x
-- 7. Folosind ciurul lui Eratostene creati o lista infinita care contine numere
le prime.
primes = sieve [2..]
where sieve (p:xs) =
p : sieve [x | x <- xs, x `mod` p /= 0]