David, Thanks for you clear and helpful answers. Pat On 21 May 2018 at 13:31, David McBride 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 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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