--- This transcript recorded the first half of Doug McIlroy's invited lecture on laziness in Haskell

-- Let's recall a few classic Haskell functions, to remind ourselves of Haskell's style:

ghci> :{ 
ghci| map f (x:xs) = f x : map f xs
ghci| map f [] = []
ghci| :}

ghci> map (\x -> x*2) [1,2,3,4]
[2,4,6,8]

ghci> :t zip
zip       zip3      zipWith   zipWith3

ghci> :t zipWith
zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]

ghci> :{  -- We'll assume lists of the same size
ghci| zipWith f [] [] = [] 
ghci| zipWith f (x:xs) (y:ys) = (f x y) : zipWith f xs ys
ghci| :}
ghci> zipWith (+) [1,2,3] [10,20,30] 
[11,22,33]


ghci> :{
ghci| take 0 xs = [] 
ghci| take n (x:xs) = x : take (n-1) xs
ghci| :}

ghci> take 2 [1,2,3,4,5,6,7]
[1,2]
ghci> take 0 [1,2,3,4,5,6,7]
[]

ghci> :t repeat
repeat :: a -> [a]

ghci> repeat x = x : repeat x

ghci> :i repeat
repeat :: t -> [t] 	-- Defined at <interactive>:132:1

ghci> repeat 1
[1,1,1,1,1,.. skipped..
^C

ghci> take 10 (repeat 1)
[1,1,1,1,1,1,1,1,1,1]

ghci> take 100 (repeat 1)
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]

ghci> nats n = n : nats (n+1)

ghci> nats 1 
[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,
^C

ghci> take 100 (nats 1)
[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100]

ghci> :{ 
ghci| filter f [] = []
ghci| filter f (x:xs) = if (f x) then x : (filter f xs) else filter f xs 
ghci| :}

ghci> filter odd [1,2,3,4]
[1,3]

ghci> nonmults p xs = filter (\x -> x `mod` p /= 0) xs

ghci> nonmults 2 [2,3,4,5,6,7,8,9,10]
[3,5,7,9]

ghci> take 10 (nonmults 2 (nats 2))
[3,5,7,9,11,13,15,17,19,21]

ghci> primes (p:xs) = p : nonmults p (primes xs)

-- GO PRIMES! NO ONE CAN DIVIDE US! (Except one and ourselves)

ghci> primes [2..]
[2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,1601,1607,1609,1613,1619,1621,1627,1637,1657,1663,1667,1669,1693,1697,1699,1709,1721,1723,1733,1741,1747,1753,1759,1777,1783,1787,1789,1801,1811,1823,1831,1847,1861,1867,1871,1873,1877,1879,1889,1901,1907,1913,1931,1933,1949,1951,1973,1979,1987,1993,1997,1999,2003,2011,2017,2027,2029,2039,2053,2063,2069,2081,2083,2087,2089,2099,2111,2113,2129,2131,2137,2141,2143,2153,2161,2179,2203,2207,2213,2221,2237,2239,2243,2251,2267,2269,2273,2281,2287,2293,2297,2309,2311,2333,2339,2341,2347,2351,2357,2371,2377,2381,2383,2389,2393,2399,2411,2417,2423,2437,2441,2447,2459,2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,2557,2579,2591,2593,2609,2617,2621,2633,2647,2657,2659,2663,2671,2677,2683,2687,2689,2693,2699,2707,2711,2713,2719,2729,2731,2741,2749,2753,2767,2777^C,2789,2791,2797,2801,2803
^C

ghci> take 100 (primes [2..])
[2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541]

For even more amazing feats of laziness see Part 2, https://mcilroy.cs.dartmouth.edu/powser.html