[Haskell-cafe] Applicative of Applicative

[martin]

Am 03/24/2015 um 04:13 AM schrieb Chris Wong:
> Hi Martin,
> 
> On Tue, Mar 24, 2015 at 10:02 AM, martin <martin.drautzburg at web.de> wrote:
>> Hello all,
>>
>> I've been playing with temporal values, i.e. values which change over time at discrete points in time. I thought it
>> would be good to make it an instance of Applicative and I was pleased with the results. I may be re-inventing some of
>> frp here, but hey.

> 
> Have you considered making Temporal a Monad? All monads by definition
> provide a `join :: m (m a) -> m a` which flattens their nested
> structure.

I just tried that, but I started with join and I wanted to get >>= for free.

data Change a = Chg {
            ct :: Time, -- "change time"
            cv :: a     -- "change value"
        }

data Temporal a = Temporal {
    td :: a,         -- "temporal default"
    tc :: [Change a] -- "temporal changes"
} deriving (Show)

-- apply a function to the value of a change
cvf :: (a->b) -> Change a -> Change b
cvf f e = Chg (ct e) (f $ cv e)


instance Functor Temporal where
        fmap f (Temporal xd xs) = Temporal (f xd) (map (cvf f) xs)


I beleive join is a bit too long to post here. But is seems to work with these examples

exNat :: Temporal Int
exNat  = Temporal 0 (map (\x -> Chg (2*x) (fromIntegral x)) [1..100000])

ext2 :: Temporal Int
ext2   = Temporal 10 [Chg 5 0]

exNested2 = Temporal exNat [Chg 7 ext2]

*Main> tJoin exNested2
Temporal {td = 0, tc = [(2,1),(4,2),(6,3),(7,10)]}

It starts with exNat but only up to the Time=10 where ext2 is scheduled and adds the default at Time=10. Since ext2 has
no further changes after Time=10, this is it.


Then I defined Modad as

instance Monad Temporal where
        return x    = Temporal x []
        ma >>= f    = tJoin $ fmap f ma


And Applicative

instance Applicative Temporal where
        pure x = Temporal x []
        (<*>)  = ap


But here is what I get

*Main> (*) <$> exNat <*> ext2
Temporal {td = 0, tc = [(2,10),(4,20),(6,30),(8,40),(10,50) ...

This is NOT what I expected. Before I had a hand-crafted <*> function, and this gave me

*Main> (*) <$> exNat <*> ext2
Temporal {td = 0, tc = [(2,10),(4,20),(5,0),(6,0),(8,0) ...

You see the values all drop to zero beyond Time=5, because ext2 drops to zero there and I am multiplying.

Where do you think things went awry? Do you think its my tJoin function, or is there something wrong in the way I
defined those typeclasses with respect to each other? Or did I voilate one of the laws? How could I find out?