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Today I achieved something I long lusted to acheive, I made the step from fix to loop. Basically by going from the applicative order Y combinator: (define (y f) ((lambda (ff) (lambda (xx) (f (ff ff) xx))) (lambda (ff) (lambda (xx) (f (ff ff) xx))))) (define (fak f n) (if (= 0 n) 1 (* (f (- n 1)) n))) ((y fak) 5) to writing the same in lazy haskell: y f = f $ y f fak r 0 = 1 fak r n = n * r (n - 1) -- ghci> y fak 5 ----> 120 someone told me that fix = y and that fix and loop are closely related. I found an aspiring blogpost and thought it would be fun to do the fibonacci recursion instead of the simple factorial. That resulted in: data SF a b = SF {runSF :: [a] -> [b]} instance Arrow SF where arr f = SF (map f) (SF f) >>> (SF g) = SF (f >>> g) first (SF f) = SF $ unzip >>> (first f) >>> zip' instance ArrowLoop SF where loop (SF f) = SF (\ins -> let (outs, r