[Haskell-cafe] Design Question - Functions taking 'subtype' like arguments but has to be restricted to one type

[Guru Devanla]

@Marlin  Thank you for the example.  Looks very interesting. Initially,
when I was modelling this problem, I did consider Phanton types. But, you
do provide a nice extension using type classes.

Here are the obstacles/discomfort I faced while I took the Phantom
Polymorphism approach:

1.  With the definition of Basket c,  how do I create a  type such as

 Cart = [Basket].  The only way to create such a cart is  Cart c = [Basket
c]. But, that ties the Cart to one definition of Basket.  Is there a way
around this? I might be missing something simple.

2.  In your approach or in the approach suggested by others, ultimately, I
end up handling the 'Frozen' type during run-time. There is no way from
stopping somene write code that calls update's on Frozen. (For example
while mapping..).  Is that understanding correct?


Does this approach give me any more power than the previous approaches?
The one power is that we stop the user from being able to construct the
Frozen type, and we leave it to the compiler to return that type based on
the inference. Correct? Is there any other power.

Thank you for the help. Just with this thread, I have learnt more than 3
different ways of modelling approaches for this kind of  a problem!




On Sun, Jul 31, 2016 at 11:41 AM, MarLinn via Haskell-Cafe <
haskell-cafe at haskell.org> wrote:

> This sounds like a perfect opportunity to use phantom types. I'll be using
> it's DataKind-enhanced variant for added beauty.
>
> --  An Item that can be of two types,  one whose value can be changed, one
> whose value are frozen once created
> data Item = FreeToChange {freeToChangeCount:: Int}
>   | CannotChange {frozenCount:: Int}
>
> I assume all items are equal apart from their changeability. Not that it's
> necessary, but it makes the demonstration simpler. If changeable and
> unchangeable items have differing structure you may need additional tools
> like smart constructors. Accordingly, my items have the type
>
>     data PlainItem = PlainItem { count :: Int }
>
> Changeability will be added on top:
>
>     data Changeability = Changeable | Unchangeable
>
>     data Item (c :: Changeability) = Item { plainItem :: PlainItem }
>
> Why separate *Item* and *PlainItem*? One second, please.
>
> -- The item is part of a basket
> data Basket = Basket { name:: String, item::Item }
>
>     data Basket c = Basket { name :: String, item :: Item c }  -- No kind signature necessary. Thanks, solver.
>
>
> Therefore, valid operation are:
>
> 1. I can create an Basket with either FreeToChange item or CannotChange
> item.
>
>
> The new *Basket* constructor can do that by default.
>
> 2. I can update the count for FreeToChange item in the Basket
>
>     changeItem :: (PlainItem -> PlainItem) -> Item 'Changeable -> Item 'Changeable
>
>     changeItem f (Item i) = Item (f i)
>
>     changeBasket :: (PlainItem -> PlainItem) -> Basket 'Changeable -> Basket 'Changeable
>
>     changeBasket f basket at Basket{..} = basket { item = changeItem f item }
>
>
> And that's why *PlainItem* was separated, so we can have a simple type
> signature here. You might worry that it was exposed, but it will not give
> anyone access to a frozen basket. And of course you are free to further
> restrict access to it. And as we're speaking about freezing, that's
> extremely simple as well.
>
>     freezeItem :: Item c -> Item 'Unchangeable
>
>     freezeItem (Item i) = Item i
>
>     freezeBasket :: Basket c -> Basket 'Unchangeable
>
>     freezeBasket basket at Basket{..} = basket { item = freezeItem item }
>
>
> You later mention that you might want to map updates only over some of the
> baskets in a cart. That's not hard either. As an example, here's a way to
> implement a function that updates changeable baskets while ignoring
> unchangeable ones:
>
>     class MaybeUpdateBasket c where
>         updateBasket :: (PlainItem -> PlainItem) -> Basket c -> Basket c
>     instance MaybeUpdateBasket 'Changeable where
>         updateBasket = changeBasket
>     instance MaybeUpdateBasket 'Unchangeable where
>         updateBasket _ = id
>
> Just *map* it over your cart as always.
>
> If you want more complicated things (eg. you want a cart to freeze once
> any bucket freezes) you just have to expand the ideas here. You may need
> MultiParamTypeClasses and FunctionalDependencies, but the basic ideas are
> the same.
>
> Cheers.
>
>
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