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May 15, 2014 13:59
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State Monad
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-- | |
-- Excerpt from Monads for functional programming | |
-- http://homepages.inf.ed.ac.uk/wadler/papers/marktoberdorf/baastad.pdf | |
-- | |
-- 2.1 Variation zero: The basic evaluator | |
-- | |
data Term = Con Int | Div Term Term | |
eval :: Term -> Int | |
eval (Con a) = a | |
eval (Div t v) = div (eval t) (eval v) | |
answer :: Term | |
answer = Div (Div (Con 1972) (Con 2)) (Con 23) | |
err :: Term | |
err = Div (Con 1) (Con 0) | |
-- 2.3 Variation two: State | |
-- | |
type M a = State -> (a, State) | |
type State = Int | |
eval1 :: Term -> M Int | |
eval1 (Con a) x = (a, x) | |
eval1 (Div t v) x = let (a, y) = eval1 t x in | |
let (b, z) = eval1 v y in | |
(div a b, z+1) | |
-- eval1 :: Term -> M Int | |
-- Term -> State -> (a, State) (by def. M Int = State -> (a, State) ) | |
-- 2.8 Variation two, revisited: State | |
-- | |
unit :: a -> M a | |
unit a = λx -> (a, x) | |
bind :: M a -> (a -> M b) -> M b | |
bind m k = λx -> let (a, y) = m x in | |
let (b, z) = k a y in | |
(b, z) | |
tick :: M () | |
tick = λx -> ((), x+1) | |
eval2 :: Term -> M Int | |
eval2 (Con a) = unit a | |
eval2 (Div t v) = (eval2 t) `bind` λa -> eval2 v `bind` λb -> unit (div a b) | |
eval2' :: Term -> M Int | |
eval2' (Con a) = unit a | |
eval2' (Div t v) = (eval2' t) `bind` λa -> eval2' v `bind` λb -> (tick `bind` λx -> unit (div a b)) | |
-- ex) | |
-- eval2' Div (Con 10) (Con 5) | |
-- | |
-- A `bind` B `bind` C `bind` D | |
-- | |
-- ** C `bind` D PART *********************************************** | |
-- | |
-- tick `bind \x -> unit (div a b) | |
-- \y -> ((), y+1) `bind` \x -> unit (div a b) | |
-- \z -> = (\y -> ((), y+1)) z | |
-- = (\z -> ((), y+1)) | |
-- = (((), z+1)) | |
-- let ((), z+1) = | |
-- = (\x -> unit (div a b)) () z+1 | |
-- = (() -> unit (div a b)) z+1 | |
-- = (unit (div a b)) z+1 | |
-- = (\w -> ((div a b), w) z+1 | |
-- = ((div a b), z+1) | |
-- let (div a b, z+1) | |
-- \z -> (div a b, z+1) | |
-- | |
-- ** A `bind` B PART *********************************************** | |
-- | |
-- eval2' (Con 10) `bind` \a -> eval2' (Con 5) | |
-- unit 10 `bind` \a -> eval2' (Con 5) | |
-- \x -> (10, x) `bind` \a -> (\y -> (5, y)) | |
-- \z -> = (\x -> (10, x)) z | |
-- = (10, z) | |
-- let (10, z) | |
-- = \a -> (\y -> (5, y)) 10 z | |
-- = [a = 10] (\y -> (5, y) z | |
-- = [a = 10] (5, z) | |
-- [a=10] \z -> (5, z) | |
-- | |
-- ** [A `bind` B PART] `bind` [C `bind` D PART] ********************* | |
-- | |
-- [a=10] \z -> (5, z) `bind` \b -> (\z' -> (div a b, z'+1)) | |
-- \z -> (5, z) `bind` \b -> (\z' -> (div 10 b, z'+1)) | |
-- \z'' -> = \z -> (5, z) z'' | |
-- = (5, z'') | |
-- let (5, z'') | |
-- = \b -> (\z' -> (div 10 b , z'+1)) 5 z'' | |
-- = \z' -> (div 10 5, z'+1 ) z'' | |
-- = (div 10 5, z''+1) | |
-- \z'' -> (div a 5, z''+1) | |
-- | |
-- (\z'' -> (2, z''+1) ) ZERO | |
-- (2,1) |
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