module eloadas

import StdEnv


//Start = sqrt (6.0*pi_26)
//   where (pi_26,_) = pi26

pi26 :: (Real, Int)
pi26 = until goodEnough improve (0.0, 1)

goodEnough:: (Real, Int) -> Bool
goodEnough (_, k) = k>10000

improve:: (Real, Int) -> (Real, Int)
improve (s, k) = (s + 1.0/(k2),k+1)
   where
      k2 = toReal (k*k)



//Start = (mkQ -2 2) + (mkQ 2 3)

//Start = take 10 [(mkQ 1 3),(mkQ 13 30)..]

instance + Q
where
 (+):: Q Q -> Q
 (+) {szamlal=sz1, nevez = n1} {szamlal=sz2, nevez=n2}
 = simplify {szamlal=sz1*n2+sz2*n1, nevez=n1*n2}

instance - Q
where
 (-):: Q Q -> Q
 (-) {szamlal=sz1, nevez = n1} {szamlal=sz2, nevez=n2}
 = simplify {szamlal=sz1*n2-sz2*n1, nevez=n1*n2}

instance one Q
where
 one = (mkQ 1 1)

instance zero Q
where
 zero = (mkQ 0 1)

instance < Q
where
 (<):: Q Q -> Bool
 (<) {szamlal=sz1, nevez = n1} {szamlal=sz2, nevez=n2}
 = sz1*n2<sz2*n1


::Q = { szamlal:: Int, nevez:: Int}

mkQ:: Int Int -> Q
mkQ a b = simplify {szamlal=a, nevez=b}

simplify:: Q -> Q
simplify {szamlal=sz, nevez=nev}
 | nev<0 = {szamlal= ~sz/g, nevez= ~nev/g}
 |otherwise = {szamlal=sz/g, nevez=nev/g}
 where
 g = gcd (abs sz) (abs nev)

//Start = sum (iterate ((*) 0.75) 1.0)

//Start = foldl (~~) 0 [1, 2, 3, 4]
(~~):: Int Int -> Int
(~~) x y = 6*x + y


// Start = ikerprim 200

ikerprim:: Int -> [(Int,Int)]
ikerprim n 
 = [(6*k-1,6*k+1) 
    \\ k<-[1..((n-1)/6)] 
    | prim (6*k-1) && prim(6*k+1)
   ]

prim:: Int -> Bool
prim x = (length(osztok x))==0

osztok:: Int -> [Int]
osztok x = [k \\ k<-[2..(x/2)] | x rem k == 0]