{-# LANGUAGE NoImplicitPrelude #-}
import Internals

data List a = Nil | Cons a (List a)

--infixr 9 .
infixr 5 :
infixr 0 $

f $ x = f x

id x = x

foldr _ e [] = e
foldr f e (x: xs) = f x $ foldr f e xs
{-
foldr x1 x2 x3 = case x3 of
    [] -> x2
    x: xs -> x1 x $ foldr x1 x2 xs
-}

filter p = foldr (\x xs -> if p x then x: xs else xs) []

True && a = a
False && _ = False

and = foldr (&&) True

map f = foldr (\x xs -> f x: xs) []

mod = primModInt
iSqrt a = primRound (primSqrtFloat (primIntToFloat a))
(+) = primAddInt
(-) = primSubInt

a == b = case primCompareInt a b of
    EQ -> True
    _ -> False

a <= b = case primCompareInt a b of
    GT -> False
    _ -> True

not False = True
not True = False

infix 4 ==

a /= b = not $ a == b

takeWhile p (x: xs) | p x = x: takeWhile p xs
takeWhile _ _ = []

from n = n: from (n + 1)
{- todo
primes :: [Int]
primes = 2:3: filter (\n -> and $ map (\p -> n `mod` p /= 0) (takeWhile (\x -> x <= iSqrt n) primes)) (from 5)
-}
(x: _) !! 0 = x
(_ : xs) !! n = xs !! (n-1)

{-
main = -- case 3: [] of x : xs -> x
    primes !! 0 -- TODO: 100
-}