[Haskell-beginners] Understanding type variables in Haskell class declarations

[PATRICK BROWNE]

David,
Thanks for you clear and helpful answers.
Pat

On 21 May 2018 at 13:31, David McBride <toad3k at gmail.com> wrote:

> 1, a and b are distinct types.  However b is of kind * while a is of kind
> * -> *, which means it takes a type and returns a type.  That means that b
> can be a type like Int, (), or Char, while a has to be a type like Maybe,
> [], or (Either ()).  That way they fit together into a type like (Maybe
> Char) or [Int].
>
> 2. In the constraint Boats b p, there it says b and p are two types that
> form an instance the Boats class (the class of boats and the things that
> are on a boat. usually people).  The next constraint says that h and (b p)
> are each two types that satisfy the Houses constraint (the class of houses
> and things that are in houses in this case boats, but boats have things
> aboard them, so that has to be listed).
>
> 3. Haskell98 did not allow classes or instances with two type variables.
> FlexibleInstances and MultiParamTypeClasses remove that limitation, and
> they've been around for a very long time and will probably end up as part
> of the standard at some point.  You can read about them here, along with
> other similar language features.  http://downloads.haskell.org/~
> ghc/latest/docs/html/users_guide/glasgow_exts.html#class-declarations
>
> On Mon, May 21, 2018 at 6:20 AM, PATRICK BROWNE <patrick.browne at dit.ie>
> wrote:
>
>> I am trying to understand how to interpret  type variables in Haskell
>> class declarations from a paper
>> <http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=1EA31D76684217BC728F916144BC6C38?doi=10.1.1.109.6853&rep=rep1&type=pdf>
>> .
>> With respect to the code below I have the following questions:
>> 1. What is the difference between "a b" in the header of the Container
>> class and "a b" in the signature of the class methods? Does the whitespace
>> in header mean 2 distinct types and in the methods mean function
>> application?
>> 2. In the Boathouse class what is the difference between the first
>> ocurance of "b p" and the second bracketed "(b p)"?
>> 3. When I try to make instance of these classes I seem to need
>> FlexibleInstances. Why is this?
>>
>>
>>
>> {-# LANGUAGE MultiParamTypeClasses #-}
>> -- Containers a b stands for all container types a holding things of type
>> b.
>> -- from :info command a has kind *->*, b has kind *
>> class Containers a b where
>>  insert :: b -> a b -> a b
>>  remove :: b -> a b -> a b
>>  whatsIn :: a b -> [b]
>>
>>
>> class Surfaces a b where
>>  put :: b -> a b -> a b
>>  takeOff :: b -> a b -> a b
>>  whatsOn :: a b -> [b]
>>
>> -- from :info command  "p" has kind  *, "h" and "b" have kind *->*
>> class People p
>> class Containers h p => Houses h p where
>> class (People p, Surfaces h p) => Boats h p where
>> class (Boats b p,Houses h (b p)) => BoatHouses h b p  where
>> class (People p, Houses h (b p),Boats b p) => HouseBoats h b p
>>
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>

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