-- THE non-deterministic operation:
coin :: Int
coin = 0
coin = 1

-- the same without overlapping rules:
coin2 :: Int
coin2 = zeroOne x
 where 
  x free

  zeroOne 0 = 0
  zeroOne 1 = 1

aBool :: Bool
aBool = False
aBool = True


-- Permuations:
-- insert an element arbitrarily into a list
insert :: a -> [a] -> [a]
insert x ys     = x : ys
insert x (y:ys) = y : insert x ys

perm :: [a] -> [a]
perm []     = []
perm (x:xs) = insert x (perm xs)

-- The identity on sorted lists, fails otherwise
sorted :: Ord a => [a] -> [a]
sorted []  = []
sorted [x] = [x]
sorted (x:y:zs) | x <= y = x : sorted (y:zs)

-- Sort a list
sort :: Ord a => [a] -> [a]
--sort xs = sorted (perm xs)
sort = sorted . perm

double :: Int -> Int
double x = x + x

double12 :: Int
double12 = double (1 ? 2)

-- Implementation of run-time choice:
doubleRTC :: (() -> Int) -> Int
doubleRTC x = x () + x ()

double12RTC :: Int
double12RTC = doubleRTC (\() -> 1 ? 2)