Hi.

> Thanks Carlos. I wish I could say thank you for clarifying, but I'm
> afraid this is as muddled as all the comments on the two proposals.
>
> I don't want to go over it again. I just want to say that my
> suggestion earlier in the thread is fundamentally different.
>
>>    Global instance scope is not ok either: instances should be modular.
> I just plain disagree. Fundamentally.

Global instance scope is not required for principal typing: a
principal type is (just) a type of an expression in a given typing
context that has all other types of this expression in that typing
context as instances.

(Also: instance modularity is not the central issue.)

    >>> Wadler & Blott's 1988 paper last paragraph had already explained: "But
    >>> there is no principal type! "

    >> There is always a principal type, for every expression.
    >> Of course the type depends on the context where the expression occurs.

> Then it's not a _principal_ type for the expression, it's just a local type.
> http://foldoc.org/principal

A type system has the principal type property if, given a
term and a typing context, there exists a type for this term in this
typing context such that all other types for this term in this typing
context are an instance of this type.

> We arrive at the principal type by unifying the principal types of
> the sub-expressions, down to the principal types of each atom. W&B
> are pointing out that without global scope for instances, typing
> cannot assign a principal type to each method. (They left that as an
> open problem at the end of the paper. Haskell has resolved that
> problem by making all instances global. Changing Haskell to modular
> instances would be a breakage. Fundamentally.)
>
> Under my suggestion, we can assign a (global) principal type to each
> method -- indeed you must, by giving a signature very similar to a
> class declaration; and that distinguishes overloaded functions from
> parametric polymorphic functions.

A principal type theorem has been proved: see, for example, Theorem 1 in [1].

Kind regards,

Carlos

[1] Ambiguity and Constrained Polymorphism,
    Carlos Camarão, Lucília Figueiredo, Rodrigo Ribeiro,
    Science of Computer Programming 124(1), 1--19, August 2016.


On Mon, 8 Oct 2018 at 20:03, Anthony Clayden <anthony_clayden@clear.net.nz> wrote:
On Tue, 9 Oct 2018 at 7:30 AM, <camarao@dcc.ufmg.br> wrote:

Thanks Carlos. I wish I could say thank you for clarifying, but I'm afraid this is as muddled as all the comments on the two proposals.

I don't want to go over it again. I just want to say that my suggestion earlier in the thread is fundamentally different.

Em 2018-10-08 06:21, Anthony Clayden escreveu:
> On Mon, 8 Oct 2018 at 8:41 PM, Simon Peyton Jones wrote:
>

Strange: Simon's message has not appeared on the forum (he did send to it). I've quoted it in full in my reply, but did break it into separate pieces.



Global instance scope is not ok either: instances should be modular.

I just plain disagree. Fundamentally.


>
> Wadler & Blott's 1988 paper last paragraph had already explained: "But
> there is no principal type! "

There is always a principal type, for every expression.
Of course the type depends on the context where the expression occurs.

Then it's not a _principal_ type for the expression, it's just a local type.

We arrive at the principal type by unifying the principal types of the sub-expressions, down to the principal types of each atom. W&B are pointing out that without global scope for instances, typing cannot assign a principal type to each method. (They left that as an open problem at the end of the paper. Haskell has resolved that problem by making all instances global. Changing Haskell to modular instances would be a breakage. Fundamentally.)

Under my suggestion, we can assign a (global) principal type to each method -- indeed you must, by giving a signature very similar to a class declaration; and that distinguishes overloaded functions from parametric polymorphic functions.


AntC
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