From an abstract PL theory POV, Haskell's key innovation over ML was HKTs. It was an experiment at the time, but one that was successful beyond all expectation: I cannot imagine designing a new PL without HKTs. (Note that Rust is also trying to add HKTs, but has been running into difficulties with type-based lifetime tracking IIRC.)

Implicits are a generalisation of default arguments (I don't know where they were pioneered, maybe C++). Implicits were first tried in Haskell [1]. Scala refined them in several steps, the last being [2] which represents implicits on the type leve. Mimicking type classes via implicits is a well-established Scala idiom [3].

[1] J. R. Lewis, J. Launchbury, E. Meijer, M. B. Shields, Implicit Parameters: Dynamic Scoping with Static Types. https://galois.com/wp-content/uploads/2014/08/pub_JL_Implici...

[2] M. Odersky, A. Biboudis, F. Liu, O. Blanvillain, Simplicitly: Foundations and Applications of Implicit Function Types. https://infoscience.epfl.ch/record/229878/files/simplicitly_...

[3] B. C. d. S. Oliveira, A. Moors, M. Odersky, Type Classes as Objects and Implicits. http://ropas.snu.ac.kr/~bruno/papers/TypeClasses.pdf

> Haskell's key innovation over ML was HKTs

In fact, ML modules have had higher-kinded types [1] since before Haskell even existed. I guess Haskell's main innovation in this domain is really its very convenient higher-kinded parametric polymorphism with type classes.

[1] MacQueen, D B (1984). Modules for Standard ML. Conference Record of the 1984 ACM Symposium on LISP and Functional Programming Languages. 198-207.

Thanks. That's really interesting. I need to read MacQueen's paper. Is this full HKT, in the sense that all constructions wiht HKTs can be encoded in MacQueen's system?

If by "all constructions wiht HKTs", you mean what can be done with HKTs in Haskell, then I'd say yes. It is well-known that ML modules provide a very advanced level of expressiveness, especially since OCaml's introduction of first-class modules. Also, Scala took this idea further and provides principled recursive first-class modules (which Scala calls dependent object types).

The problem is that modules in ML have a verbose syntax and are clunky to use compared to type classes. OCaml's modular implicits aim to make this better (see https://arxiv.org/abs/1512.01895), taking inspiration from Sala's implicits.

I understand that making modules first-class gives them a lot of expressivity. But they are a fairly recent development" at least in OCaml the come much after Haskell. But are modules in MacQueen's sense first-class?

> Implicits are a generalisation of default arguments.

There is an extreme semantic difference between an implicit parameter and a default argument. Have you spent any time at all using them? That's like claiming HKT is just a generalization of type constructors. Would you claim that HKT isn't anything new or novel because constructors have been around forever?

> Have you spent any time at all using them?

Sure I have used both.

Default arguments and implicits both have the same key idea: you can omit arguments to functions, and the compiler, guided by type information, synthesises the missing arguments during compilation. In order to understand the difference between both, it is crucial to realise that this compile-time synthesis of missing arguments has two related but different dimensions.

- Declaration that an argument is allowed to be omitted (and hence synthesised automatically).

- Declaration of the missing argument that is used in this synthesis.

Default arguments merge these two into one, e.g. with

   def f ( int x ) ( bool b = false ) = ...
   f (2)
   f (2)

all calls f(2) become f(2)(false). The problem with this is that the devault value to be used in synthesis cannot be context dependent.

Implicit arguments separate these two, enabling the programmer to make default context dependent, e. g.

   def f ( int x ) ( implicit bool b ) = ...
   implicit val c = true
   f (2)
   implicit val c = false
   f (2)

Now the first call f(2) is rewritten to f(2)(true), while the second becomes f(2)(false).

> Would you claim that HKT isn't anything new or novel because constructors have been around forever?

I'm not sure I see the connection: constructors are program constructs, while HKTs are "types for types".

> Default arguments and implicits both have the same key idea: you can omit arguments to functions, and the compiler, guided by type information, synthesises the missing arguments during compilation.

Saying implicits are a generalization of default arguments because they're both synthesized during compilation is like saying steam trains are a generalization of pipes because they're both made of metal. It elides too big a difference to be helpful, to the point that it's actually misleading.

I'm not saying implicits and default parameters are the same thing. I'm saying the key idea behind implicits is the realisation that default arguments merge two ideas that should be kept separate, if we want context dependent defaults. Some of implicit's other features can (and have been) added to default arguments, see my other reply.

> I'm saying the key idea behind implicits is the realisation that default arguments merge two ideas that should be kept separate, if we want context dependent defaults.

This isn't true though - that's not what implicits are for and not how they're used. Indeed the clearest proof is that Scala still has default arguments, and they still have the behaviour given in your OCaml example. They're different things.

I did not say implicits and default arguments are the same thing. I said that implicits improve upon default arguments in various ways, the key realisation being the split between providing elided values in a context-dependent way, and permitting the elision of values.

I should not have said the key idea, but a key idea.

Default arguments are convenient if you don't need context dependence of elided arguments. I'd probably have remove defaults in order to have a smaller and more simple language.

Maybe a disagreement here is fueled by the power level difference in these two features. Beyond the superficial injection examples, Scala implicits also support injecting values constructed dynamically and also recursive/derived implicits.

> injecting values constructed dynamically

You can also do this with default arguments, e.g. like so:

   let f x y = 
      let g (a = x+1) b = ...
      ...

For example the following is valid OCaml:

   let bump ?(step = 1) x =
     let waa ?( a = step+17 ) b = a * b in
     x + step + waa 666;;

Here the function waa has a default argument whose default argument depends on bump's default argument.

> recursive/derived implicits

Recursion is quite restricted, for example this is not valid Scala:

    def f ( x : Int ) ( implicit y : Int ) : Int = {
      implicit val a = 17
      f ( x+1 ) }

Your example of nested functions with default arguments does not correspond to what derived implicits do. As a result of implicit resolution, an expression with an arbitrary number of subexpressions may be synthesized, the shape of which depends on the types involves. Default parameters simply cannot do that.

The example you give to justify "recursion is quite restricted" is not a restriction on recursion at all, it's an ambiguity problem. Define `a` as `y` to shadow the function parameter, and it compiles.

> does not correspond to what derived implicits do

I did not claim it did. The first example disproved ionforce's claim that default values cannot be constructed dynamically.

> Define `a` as `y` to shadow the function parameter,

Whoops, yes that's correct. I didn't realise this was possible.

> The first example disproved ionforce's claim that default values cannot be constructed dynamically.

But I don't think that is what they meant. I think they meant something along the lines of what I said above:

> an expression with an arbitrary number of subexpressions may be synthesized, the shape of which depends on the types involves

OK, maybe I misunderstood ionforce. I don't deny that type-driven synthesis is a core element of implicits.

Thanks for the Simplicity reference, hadn't seen that yet. Seems like it builds on the implicit calculus [1], which applies more generally to any lambda calculus than in the Scala context.

[1] http://homepages.inf.ed.ac.uk/wadler/papers/implicits/implic...