One more cool trick from the same article (slightly modified). It's a factorial function computed on an "infinite spreadsheet". But how? fact = loeb fact'

One more cool trick from the same article (slightly modified). It's a factorial function computed on an "infinite spreadsheet". But how? fact = loeb fact' where fact' 0 _ = 1 fact' n f = n*f (n-1) If we ask GHC for the type of `fact'` then we see that it is Int -> ((Int -> Int) -> Int) which we can interpret via the `Reader Int` monad as being m (m Int -> Int) -- for m a = (Int -> a) Now, `f :: (Int -> a)` as a functor is isomorphic to an infinite stream map f [0, 1, ...] if we ignore the negative numbers. So we can think of `fact'` as having the type Stream (Stream Int -> Int) where each function in the stream takes its own index and multiplies it by the value at the previous index. Then `loeb` completes the computation using spreadsheet recursion.