Re: [Haskell-cafe] Applicative of Applicative

I haven't read all the code, but it seems to me that the most likely candidate is that your old <*> is breaking the applicative laws. <*> "can't" depend on the values it's applied to (but based on what you said, it looks like your old <*> was making choices) On Thu, Mar 26, 2015 at 11:24 AM, martin wrote:

Am 03/24/2015 um 04:13 AM schrieb Chris Wong:

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Hi Martin,

On Tue, Mar 24, 2015 at 10:02 AM, martin wrote:

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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.

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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?

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