On Sun, 19 Jan 2025, Vanessa McHale wrote:
Laziness turns out to allow course-of-value recursion where one might use memoization in other languages. But I hadn’t seen this articulated!
Famously, one can use this to define the Fibonacci numbers, viz.
fibs :: [Integer] fibs = 1 : 1: zipWith (+) fibs (tail fibs)
This example is old and well-known, right?
Or the Catalan numbers:
catalan :: [Integer] catalan = 1 : 1 : [ sum [ (-1)^(k+1) * (pc (n - ((k*(3*k-1)) /. 2)) + pc (n - ((k*(3*k+1))/.2))) | k <- [1..n] ] | n <- [2..] ] where pc m | m >= 0 = part !! m | otherwise = 0
infixl 6 /. (/.) = quot
I have: catalanNumbers :: Num a => [a] catalanNumbers = let xs = 1 : PowerSeries.mul xs xs in xs https://hackage.haskell.org/package/combinatorial-0.1.1/docs/src/Combinatori...