Pythagoreans

Pythagoreans.dcl

definition module Pythagoreans

:: ListTree a = Node a [ListTree a]

primitivePythagoreanTree :: ListTree [Int]

pythagoreans :: ([Int] -> Bool) -> [[Int]]

Pythagoreans.icl

implementation module Pythagoreans
import StdEnv

primitivePythagoreanTree :: ListTree [Int]
primitivePythagoreanTree =: f [3,4,5] where
    f xs = Node xs ((map f o gen) xs)
    gen [x0,x1,x2] = map (\x = map (sumProd x) P) xs where
        P = [[-1,-2,2],[-2,-1,2],[-2,-2,3]] 
        xs = [[~x0,x1,x2],[x0,~x1,x2],[~x0,~x1,x2]]
        sumProd xs ys = sum [x*y \\ x <- xs & y <- ys]

pythagoreans :: ([Int] -> Bool) -> [[Int]]
pythagoreans cond = (flatten o map f) ps where
    f ps = takeWhile cond [map ((*) x) ps \\ x <- [1..]]
    ps = f primitivePythagoreanTree where
        f (Node xs ts)
            | cond xs   = [xs:(flatten o map f) ts]
            | otherwise = []