[Haskell-cafe] Course-of-value recursion by defining a sequence as a self-referential infinite list

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) 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 wrote up the example: http://vmchale.com/static/serve/Comb.pdf Reinhard Zumkeller has a lot of examples on OEIS: https://oeis.org/A000081 Cheers, Vanessa McHale