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_clay...@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 > _______________________________________________ > Haskell-prime mailing list > Haskell-prime@haskell.org > http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-prime >
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