A question about run-time errors when class members are undefined

[Petr Pudlák]

Hi everyone,

IIRC one of the arguments against having many separate classes is that a
class is not a just set of methods, it's also the relations between them,
such as the important laws between `return` and `>>=`. And then for example
a class with just `return` doesn't give any information what `return x`
means or what should be its properties.

That said, one of really painful points of Haskell is that refactoring a
hierarchy of type-classes means breaking all the code that implements them.
This was also one of the main reasons why reason making Applicative a
superclass of Monad took so long. It'd be much nicer to design type-classes
in such a way that an implementation doesn't have to really care about the
exact hierarchy.

The Go language takes a very simple view on this: A type implements an
interface if all the methods are implemented, without having to explicitly
specify this intent [1]. This looks very nice and clean indeed. But the
drawback is that this further decouples type-classes (interfaces) from
their laws (like monad laws, monoid laws etc.). For example, in Haskell we
could have

class (Return m, Bind m) => Monad m where

without any methods specified. But instances of `Monad` should be only such
types for which `return` and `>>=` satisfy the monad laws. And this would
distinguish them from types that have both `Return` and `Bind` instances,
but don't satisfy the laws.

Unfortunately I'm not sure if there is a good solution for achieving both
these directions.

[1] https://tour.golang.org/methods/10

Cheers,
Petr

čt 4. 10. 2018 v 3:56 odesílatel Anthony Clayden <
anthony_clayden at clear.net.nz> napsal:

> > We are adding classes and instances to Helium.
>
> > We wondered about the aspect that it is allowed to have a class instance
>
> > of which not all fields have a piece of code/value associated with them, ...
>
>
> I have a suggestion for that. But first let me understand where you're going with Helium. Are you aiming to slavishly reproduce Haskell's classes/instances, or is this a chance for a rethink?
>
>
> Will you want to include associated types and associated datatypes in the classes? Note those are just syntactic sugar for top-level type families and data families. It does aid readability to put them within the class.
>
>
> I would certainly rethink the current grouping of methods into classes. Number purists have long wanted to split class Num into Additive vs Multiplicative. (Additive would be a superclass of Multiplicative.) For the Naturals perhaps we want Presburger arithmetic then Additive just contains (+), with `negate` certainly in a different class, perhaps (-) subtract also in a dedicated class. Also there's people wanting Monads with just `bind` not `return`. But restructuring the Prelude classes/methods is just too hard with all that legacy code. Even though you should be able to do:
>
>
> class (Additive a, Subtractive a, Negative a, Multiplicative a, Divisive a) => Num a
>
>
> Note there's a lot of classes with a single method, and that seems to be an increasing trend. Historically it wasn't so easy in Haskell to do that superclass constraints business; if it had been perhaps there would be more classes with a single method. Then there's some disadvantages to classes holding multiple methods:
>
> * the need to provide an overloading for every method, even though it may not make sense
>
>   (or suffer a run-time error, as you say)
>
> * the inability to 'fine tune' methods for a specific datatype [**]
>
> * an internal compiler/object code cost of passing a group of methods in a dictionary as tuple
>
>   (as apposed to directly selecting a single method)
>
>
> [**] Nats vs Integrals vs Fractionals for `Num`; and (this will be controversial, but ...) Some people want to/some languages do use (+) for concatenating Strings/lists. But the other methods in `Num` don't make any sense.
>
>
> If all your classes have a single method, the class name would seem to be superfluous, and the class/instance decl syntax seems too verbose.
>
>
> So here's a suggestion. I'll need to illustrate with some definite syntax, but there's nothing necessary about it. (I'll borrow the Explicit Type Application `@`.) To give an instance overloading for method `show` or (==)
>
>
> show @Int = primShowInt                     -- in effect pattern matching on the type
>
> (==) @Int = primEqInt                       -- so see showList below
>
> That is: I'm giving an overloading for those methods on type `Int`. How do I declare those methods are overloadable? In their signature:
>
>
> show @a :: a -> String                      -- compare show :: Show a => a -> String
>
> (==) @a :: a -> a -> Bool
>
> Non-overladable functions don't have `@a` to the left of `::`.
>
> How do I show that a class has a superclass constraint? That is: a method has a supermethod constraint, we'll still use `=>`:
>
>
> show @a :: showsPrec @a => a -> String      -- supermethod constraint
>
> show @[a] :: show a => [a] -> String        -- instance decl, because not bare a, with constraint =>
>
> show @[a] xss = showList xss
>
> (*) @a :: (+) @a => a -> a -> a
>
>
> Is this idea completely off the wall? Take a look at Wadler's original 1988 memo introducing what became type classes.
> http://homepages.inf.ed.ac.uk/wadler/papers/class-letter/class-letter.txt
>
>
> It reviews several possible designs, but not all those possibilities made it into his paper (with Stephen Blott) later in 1988/January 1989. In particular look at Section 1's 'Simple overloading'. It's what I'm suggesting above (modulo a bit of syntax). At the end of Section 1, Wadler rejects this design because of "potential blow-ups". But he should have pushed the idea a bit further. Perhaps he was scared to allow function/method names into type signatures? (I've already sneaked that in above with constraints.) These days Haskell is getting more relaxed about namespaces: the type `@`pplication exactly allows type names appearing in terms. So to counter his example, the programmer writes:
>
>
> square x = x * x                             -- no explicit signature given
>
> square :: (*) @a => a -> a                   -- signature inferred, because (*) is overloaded
>
> rms = sqrt . square                          -- no explicit signature
>
> rms :: sqrt @a => a -> a                     -- signature inferred
>
>
> Note the inferred signature for `rms` doesn't need `(*) @a` even though it's inferred from `square`. Because (*) is a supermethod of `sqrt`. `sqrt` might also have other supermethods, that amount to `Floating`.
>
>
> > ... a run-time error results.
> >
> > Does anyone know of a rationale for this choice, since it seems rather unhaskell-like.
>
>
> If you allow default method implementations (in the class, as Cale points
> out), then I guess you have to allow instance decls that don't mention all
> the methods. I think there should at least be a warning if there's no
> default method. Also beware the default method might have a more specific
> signature, which means it can't be applied for some particular instance.
>
> Altogether, I'd say, the culprit is the strong bias in early Haskell to
> bunch methods together into classes. These days with Haskell's richer/more
> fine-tuned typeclass features: what do typeclasses do that can't be done
> more precisely at method level -- indeed that would _better_ be done at
> method level?
>
>
> AntC
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