Type classes vs interfaces

38

I find this topic fascinating, because I feel like this is an instance of the Blub paradox for me. I don’t know if this is related to your viewpoint @graninas, but a while ago I also encountered a difference between type classes and backpack modules. I came up with Semigroup as the example:

class Semigroup a where
   (<>) :: a -> a -> a

Now the thing type classes can do and backpack modules can’t is to instantiate this with another parametrised (what Java calls generic) type:

instance Semigroup [a] where
   (<>) = (++)

So now you have:

(<>) :: [a] -> [a] -> [a]

If we instead had a backpack signature:

signature Semigroup where
  type S
  (<>) :: S -> S -> S

Then we cannot instantiate it like this:

module Semigroup where
  type S = [a]

Because the a would come from nowhere. At best we could use a forall:

  type S = forall a. [a]

But now the type of (<>) doesn’t work: (<>) :: (forall a. [a]) -> (forall a. [a]) -> (forall a. [a]).

I think Java interfaces have the same problem as backpack modules in this respect.

By the way, I think it is a bit easier to read backpack-style interface declaration that free monad ones. Here’s how I would translate your example:

signature Meal where
  type Meal
  -- we don't have subtyping, so we need manual conversions
  -- but I think that is a separate concern
  class IsMeal a where
    toMeal :: a -> Meal

signature PizzaRecipe where
  type PizzaRecipe
  ...

signature CookingMethod where
  import PizzaRecipe

  type CookingMachine a
  instance Functor CookingMachine
  instance Applicative CookingMachine
  instance Monad CookingMachine

  makePizza :: PizzaRecipe -> CookingMachine Pizza
  makeSandwich :: SandwichRecipe -> CookingMachine Sandwich
  makeRandomPizzaRecipe :: CookingMachine PizzaRecipe

And used as:

import Meal
import CookingMethod

sampleCookingMachine :: CookingMachine [Meal]
sampleCookingMachine = do
 pizza <- makePizza myPizza

 rndPizzaRecipe <- makeRandomPizzaRecipe    -- asking for rnd recipe 
 rndPizza <- makePizza rndPizzaRecipe       -- evaluating
 pure [toMeal pizza, toMeal rndPizza]
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