{-# OPTIONS_GHC -Wall -fno-warn-orphans #-}
----------------------------------------------------------------------
-- |
-- Module      :  StateAdd
-- Copyright   :  (c) Conal Elliott 2010
-- License     :  BSD3
-- 
-- Maintainer  :  conal@conal.net
-- Stability   :  experimental
-- 
-- Experiments in addition.  Formulated via the State monad
-- See <http://conal.net/blog/posts/adding-numbers/>
----------------------------------------------------------------------

module StateAdd where

import Control.Applicative (Applicative(..))
import Control.Monad.State

import Control.Compose (result)

import qualified AddingMachines as AM

type Carrier = State Bool

-- Add two values and a carry, resulting in a value and a carry.
-- Component of carry-based adding machines.
type Adder a = a -> a -> Carrier a

addBase :: (Ord a, Num a) => a -> Adder a
addBase = (result.result.result) State AM.addBase

adds :: Adder a -> Adder [a]
adds = zipWithM


{--------------------------------------------------------------------
    Misc
--------------------------------------------------------------------}

-- I hope this instance will get added to mtl someday.
instance Applicative (State s) where { pure = return ; (<*>) = ap }


{--------------------------------------------------------------------
    Testing
--------------------------------------------------------------------}

add10 :: Adder Int
add10 = addBase 10

t1 :: (Int,Bool)
t1 = runState (add10 3 1) False -- (4,False)

t2 :: ([Int],Bool)
t2 = runState (adds add10 [3,5,7,8] [1,6,4,1]) False   -- ([4,1,2,0],True)