Partiality monad in Haskell using Free Maybe.

Partiality.hs

module Partiality where

import Control.Monad.Free

type Partiality = Free Maybe

never :: Partiality a
never = Free $ Just never

bad :: Partiality a
bad = Free Nothing

partialFromJust :: Maybe a -> Partiality a
partialFromJust (Just x) = Pure x
partialFromJust Nothing = Free Nothing -- bad

partialCollatz :: Int -> Int -> Partiality Int
partialCollatz x n | n == 1 = Pure x
                   | odd n = next $ 3 * n + 1
                   | even n = next $ n `div` 2
               where next = Free . Just . partialCollatz (succ x)

partialRun :: Int -> Partiality a -> Maybe a
partialRun _ (Pure a) = Just a
partialRun _ (Free Nothing) = Nothing
partialRun 0 _ = Nothing
partialRun n (Free (Just p)) = partialRun (pred n) p