Hiding general recursion inside a monad

Tue, 19 Dec 2006 20:14:31 GMT

I’ve been thinking a bit about using a monad to hide general recursion. By hide, I mean that you cannot construct a function fix with type (∀a. (a -> a) -> a). The first monad I tried was basically a reader monad with a run function that just used fix. Needless to say this doesn’t hide the recursion. My next attempt is more successful and has the interface below:

data Rec a b
instance Monad (Rec a)
instance MonadReader a (Rec a)
recurse :: a -> Rec a a
runRec :: a -> Rec a a -> a

And here’s an example of using it to write a fibonacci function.

-- Fibonacci sequence
fib :: Integer -> Integer
fib n = runRec n $ do
  n <- ask
  case n of
    0 -> return 0
    1 -> return 1
    _ -> do
      x <- recurse (n-2)
      y <- recurse (n-1)
      return (x + y)

The next thing I want to try is to prove that you can’t construct fix. I guess my argument would start need to start off with looking at runRec and where I’m going to get something for its first argument.

Chemical computing

Thu, 14 Dec 2006 21:17:56 GMT

"Generalized Multisets for Chemical Programming", Banâtre, Fradet, Radenac.
And accompanying slides.

[pointed out by rgs in #perl6]

Benjamin Smith

Hiding general recursion inside a monad

Chemical computing