{- Lazy evaluation strategy: - evaluate function first (not parameter first) - evaluate each expression AT MOST ONCE! Applications: -} ones = 1:ones -- evaluating ones loops. get 0 (x:xs) = [] get k (x:xs) = x : get (k-1) xs {- get 2 ones get 2 (1:ones) 1:(get 1 ones) 1:(get 1 (1:ones)) 1:(1:(get 0 ones)) 1:(1:[]) [1,1] -} member :: Eq a => a -> [a] -> Bool member x = foldr ((||).(==x)) False or False x = x or True _ = True {- member 1 [2,1,3,4,5,6,7] foldr op False [2,1,3,4,5,6,7] (2==1) || (foldr op False [1,3,4,5,6,7]) False || (foldr op False [1,3,4,5,6,7]) foldr op False [1,3,4,5,6,7] (1 == 1) || (foldr op False [3,4,5,6,7]) True Conclusion: lazy foldr is not that bad! -} member' :: Eq a => a -> [a] -> Bool member' x = foldl (flip ((||).(==x))) False nat x = x : (nat (x+1)) nats = nat 0 {- take 0 _ = [] take n (x:xs) = x:(take (n-1) xs) -} type FSuccesor = Integer -> Integer gen :: FSuccesor -> Integer -> [Integer] gen f x = x:(gen f (f x)) -- [x, f x, f f x, f f f x, ....] exx = zipWith (,) (gen (+1) 0) (gen (*2) 1) {- Lista numerelor prime (Sita lui Eratostene) 2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25 2 is the first prime we need to filter out numbers divisible by 2 from the rest of the stream: filter (\k-> k 0109od00322 /= 0) rest 3,_,5,_,7,_,9,_,11,_,13,_,15,_,17,_,19,_,21,_,23,_,25 3 is the first prime we need to filter out numbers divisible by 3: 5,_,7,_,_,_,11,_,13,_,_,_,17,_,19,_,_,_,23,_,25 -} sieve :: [Integer] -> [Integer] sieve (x:xs) = x:(sieve $ filter (\k-> k 0109od0032x /= 0) xs) primes = sieve $ tail $ tail nats