module Sol10 where

import HL10COR

-- | 10.1 Write a corecursive definition that generates the even natural numbers.
-- >>> take 5 evens
-- [0,2,4,6,8]
evens = 0 : map (+ 2) evens

-- | 10.2 Use iterate to define the infinite stream of even natural numbers.
-- >>> take 5 theEvens
-- [0,2,4,6,8]
theEvens = iterate (+ 2) 0

-- | 10.3 Thue-Morse sequence
-- >>> take 100 thue
-- "0110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110"
swap "" = ""
swap ('1' : xs) = '0' : swap xs
swap ('0' : xs) = '1' : swap xs

morse xs = xs ++ morse (xs ++ swap xs)

thue = '0' : morse "1"

-- | 10.5 How would you implement a generator for streams of 0’s and 1’s with, in the long run, a proportion of 0’s and 1’s of 2 to 1?
-- >>>
random001s :: Int -> [Int]
random001s i = map (`mod` 2) (randomInts 2 i)

-- | 10.10 Vending machine from text
-- >>>
vend, vend1, vend2, vend3, vend4 :: Process
vend (0 : xs) = "coin" : vend1 xs
vend (1 : xs) = "coin" : vend4 xs
vend1 (0 : xs) = "coin" : vend2 xs
vend1 (1 : xs) = vend1 xs
vend2 (0 : xs) = "beer" : vend xs
vend2 (1 : xs) = "coin" : vend3 xs
vend3 (0 : xs) = "moneyback" : vend xs
vend3 (1 : xs) = vend3 xs
vend4 (0 : xs) = "water" : vend xs
vend4 (1 : xs) = vend4 xs