[Haskell-beginners] applicative instance

[sasa bogicevic]

Wow thanks for the indepth explanation. I am glad that this got you reading some stuff but the fact is I was just doing an exercise in writing Applicative instances for some types and it was not stated that we should use separate 'helper' functions to achieve this. So I banged my head trying to write the correct implementation but I could only come up with the zipList solution. Thanks again!

Sasa


> On Jan 30, 2017, at 06:57, Graham Gill <math.simplex at gmail.com> wrote:
> 
> 
> On 28-Jan-2017 4:53 AM, sasa bogicevic wrote:
>> Is there a way to do it without defining a separate function like plusPlus ?
> 
> My guess is there isn't. I'm unsure what you mean by your question though.
> 
> Your List is a reimplementation of Haskell []. So, List with the "Cartesian product" Applicative instance will, like Haskell [], extend to a Monad instance. In the Monad instance for [], join = concat, and the work of concat is done using ++.
> 
> For List, we can implement join using concatList:
> 
> concatList :: List (List a) -> List a
> concatList Nil = Nil
> concatList (Cons xs xss) = xs `plusPlus` (concatList xss)
> 
> and then we can add a Monad instance for List:
> 
> instance Monad List where
>     return = pure
>     xs >>= f = concatList (pure f <*> xs)
> 
> or equivalently, bind is given by
>     xs >>= f = concatList (fmap f xs)
> 
> To ask whether you can define the Cartesian product Applicative instance for List without plusPlus, is, I think, like asking whether there is a Cartesian product Applicative instance for List (or []) which doesn't extend to a Monad instance. Because if it does extend to a Monad (that obeys the Monad laws), then there will exist an implementation of join :: List (List a) -> List a, and join will need to collapse a List of Lists into a List. A function like plusPlus is used to accomplish the collapse.
> 
> That's "proof by hand waving."
> 
> The Ziplist Applicative instance for List on the other hand can't be extended to a Monad instance without additional restrictions on the lengths of the lists. Your question led me to some interesting reading with a google search on "list monad vs ziplist". Thanks.
> 
> 
> On 28-Jan-2017 4:53 AM, sasa bogicevic wrote:
>> Yep that worked, thanks.
>> Is there a way to do it without defining a separate function like plusPlus ?
>> 
>> 
>> 
>> 
>> 
>> 
>>> On Jan 28, 2017, at 10:43, Francesco Ariis <fa-ml at ariis.it>
>>>  wrote:
>>> 
>>> On Sat, Jan 28, 2017 at 10:09:10AM +0100, sasa bogicevic wrote:
>>> 
>>>> Ok so how would the implementation look to get the correct result ?
>>>> I can't seem to write something that will compile except ZipList version.
>>>> 
>>> One way is by implementing your own (++):
>>> 
>>>    data List a = Nil | Cons a (List a) deriving (Eq, Show)
>>> 
>>>    plusPlus :: List a -> List a -> List a
>>>    plusPlus Nil         bs = bs
>>>    plusPlus (Cons a as) bs = Cons a (as `plusPlus` bs)
>>> 
>>>    instance Functor List where
>>>        fmap f Nil = Nil
>>>        fmap f (Cons a b) = Cons (f a) (fmap f b)
>>> 
>>>    instance Applicative List where
>>>        pure x = Cons x Nil
>>>        Nil <*> _ = Nil
>>>        _ <*> Nil = Nil
>>>        (Cons x xy) <*> ys = (fmap x ys) `plusPlus` (xy <*> ys)
>>> 
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