Yeah, sorry, I think I'm in a little over my head here. :) But I think I can ask a more answerable question now: how does one pronounce "forall a -> a -> Int"? Den tis 17 nov. 2020 16:27Richard Eisenberg skrev:

Hi Bryan,

I don't think I understand what you're getting at here. The difference between `forall b .` and `forall b ->` is only that the choice of b must be made explicit. Importantly, a function of type e.g. `forall b -> b -> b` can *not* pattern-match on the choice of type; it can bind a variable that will be aliased to b, but it cannot pattern-match (say, against Int). Given this, can you describe how `forall b ->` violates your intuition for the keyword "forall"?

Thanks! Richard

...

On Nov 17, 2020, at 1:47 AM, Bryan Richter wrote:

Dear forall ghc-devs. ghc-devs,

As I read through the "Visible 'forall' in types of terms" proposal[1], I stumbled over something that isn't relevant to the proposal itself, so I thought I would bring it here.

Given

f :: forall a. a -> a (1)

I intuitively understand the 'forall' in (1) to represent the phrase "for all". I would read (1) as "For all objects a in Hask, f is some relation from a to a."

After reading the proposal, I think my intuition may be wrong, since I discovered `forall a ->`. This means something similar to, but practically different from, `forall a.`. Thus it seems like 'forall' is now simply used as a sigil to represent "here is where some special parameter goes". It could as well be an emoji.

What's more, the practical difference between the two forms is *only* distinguished by ` ->` versus `.`. That's putting quite a lot of meaning into a rather small number of pixels, and further reduces any original connection to meaning that 'forall' might have had.

I won't object to #281 based only on existing syntax, but I *do* object to the existing syntax. :) Is this a hopeless situation, or is there any possibility of bringing back meaning to the syntax of "dependent quantifiers"?

-Bryan

[1]: https://github.com/ghc-proposals/ghc-proposals/pull/281 _______________________________________________ ghc-devs mailing list ghc-devs@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/ghc-devs

Semantically, `forall a -> a -> Int` is the same as `forall a. a -> Int`. The two only differ in how you use them: * For the first one, you have to explicitly provide the type to use for `a` at every call site, while * for the second one, you usually omit the type and let GHC infer it. So overall I think it's a pretty simple idea. For me it's hard to see that from the text in #281, but I think a lot of the complexity there is about a fancy notation for explicitly providing the type at call sites. -Iavor On Wed, Nov 18, 2020 at 9:51 AM Richard Eisenberg wrote:

Hi Bryan,

First off, sorry if my first response was a bit snippy -- it wasn't meant to be, and I appreciate the angle you're taking in your question. I just didn't understand it!

This second question is easier to answer. I say "forall a arrow a arrow Int".

But I still think there may be a deeper question here left unanswered...

Richard

On Nov 18, 2020, at 6:11 AM, Bryan Richter wrote:

Yeah, sorry, I think I'm in a little over my head here. :) But I think I can ask a more answerable question now: how does one pronounce "forall a -> a -> Int"?

Den tis 17 nov. 2020 16:27Richard Eisenberg skrev:

...

Hi Bryan,

I don't think I understand what you're getting at here. The difference between `forall b .` and `forall b ->` is only that the choice of b must be made explicit. Importantly, a function of type e.g. `forall b -> b -> b` can *not* pattern-match on the choice of type; it can bind a variable that will be aliased to b, but it cannot pattern-match (say, against Int). Given this, can you describe how `forall b ->` violates your intuition for the keyword "forall"?

Thanks! Richard

...

On Nov 17, 2020, at 1:47 AM, Bryan Richter wrote:

Dear forall ghc-devs. ghc-devs,

As I read through the "Visible 'forall' in types of terms" proposal[1], I stumbled over something that isn't relevant to the proposal itself, so I thought I would bring it here.

Given

f :: forall a. a -> a (1)

I intuitively understand the 'forall' in (1) to represent the phrase "for all". I would read (1) as "For all objects a in Hask, f is some relation from a to a."

After reading the proposal, I think my intuition may be wrong, since I discovered `forall a ->`. This means something similar to, but practically different from, `forall a.`. Thus it seems like 'forall' is now simply used as a sigil to represent "here is where some special parameter goes". It could as well be an emoji.

What's more, the practical difference between the two forms is *only* distinguished by ` ->` versus `.`. That's putting quite a lot of meaning into a rather small number of pixels, and further reduces any original connection to meaning that 'forall' might have had.

I won't object to #281 based only on existing syntax, but I *do* object to the existing syntax. :) Is this a hopeless situation, or is there any possibility of bringing back meaning to the syntax of "dependent quantifiers"?

-Bryan

[1]: https://github.com/ghc-proposals/ghc-proposals/pull/281 _______________________________________________ ghc-devs mailing list ghc-devs@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/ghc-devs

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Thanks for the replies! Let's see if I can make a stab at those deeper questions now. I'm playing a form of devil's advocate here, dissecting the syntax with my intuition as a ghc *user*, and trying to bridge the gap to how ghc *devs* understand it. So correct me if I'm wrong: from an implementation perspective, `forall a. a -> Int` is a function of two arguments, one of which can be elided, while `forall a -> a -> Int` is a function of two arguments, all of which must be provided. If that's right, then it bumps into my intuition, which says that the former is a function of only one argument. I never thought of `f @Int` as partial function application, for instance. :) Is my intuition leading me astray? *Should* I consider both functions as having two arguments? If so, is that somehow "mathematically true" (a very not-mathematical phrase, haha), or is it just an "implementation detail"? So that's one avenue of query I have, but it's actually not the one I started off with. Focusing on the simpler case of `forall a -> a`, which is a function of one argument, I take issue with how the quantification is packed into the syntax for the argument, itself. I.e., my intuition tells me this function is valid for all types, takes the name of a type as an argument, and returns a value of that type, which is three distinct pieces of information. I'd expect a syntax like `forall a. elem x a. a -> x`, or maybe `forall a. nameof a -> a`. The packing and punning conspire to make the syntax seem overly clever. If I had to explain `forall a -> a` to one of my Haskell-curious colleagues, I'd have to say "Oh that means you pass the name of a type to the function" -- something they'd have no chance of figuring out on their own! The 'forall' comes across as meaningless. (Case in point: I had no idea what the syntax meant when I saw it -- but I'm already invested enough to go digging.) I guess my question, then, is if there is some way to make this syntax more intuitive for users! On Wed, Nov 18, 2020 at 10:10 PM Carter Schonwald wrote:

I do think explaining it relative to the explicit vs implicit arg syntax of agda function argument syntax.

f: Forall a . B is used with f x. This relates to the new forall -> syntax.

g: forall {c}. D is used either as f or f {x}, aka implicit or forcing it to be explicit. This maps to our usual Haskell forall with explicit {} being the @ analogue

On Wed, Nov 18, 2020 at 12:09 PM Iavor Diatchki wrote:

...

Semantically, `forall a -> a -> Int` is the same as `forall a. a -> Int`. The two only differ in how you use them: * For the first one, you have to explicitly provide the type to use for `a` at every call site, while * for the second one, you usually omit the type and let GHC infer it.

So overall I think it's a pretty simple idea. For me it's hard to see that from the text in #281, but I think a lot of the complexity there is about a fancy notation for explicitly providing the type at call sites.

-Iavor

On Wed, Nov 18, 2020 at 9:51 AM Richard Eisenberg wrote:

...

Hi Bryan,

First off, sorry if my first response was a bit snippy -- it wasn't meant to be, and I appreciate the angle you're taking in your question. I just didn't understand it!

This second question is easier to answer. I say "forall a arrow a arrow Int".

But I still think there may be a deeper question here left unanswered...

Richard

On Nov 18, 2020, at 6:11 AM, Bryan Richter wrote:

Yeah, sorry, I think I'm in a little over my head here. :) But I think I can ask a more answerable question now: how does one pronounce "forall a -> a -> Int"?

Den tis 17 nov. 2020 16:27Richard Eisenberg skrev:

...

Hi Bryan,

I don't think I understand what you're getting at here. The difference between `forall b .` and `forall b ->` is only that the choice of b must be made explicit. Importantly, a function of type e.g. `forall b -> b -> b` can *not* pattern-match on the choice of type; it can bind a variable that will be aliased to b, but it cannot pattern-match (say, against Int). Given this, can you describe how `forall b ->` violates your intuition for the keyword "forall"?

Thanks! Richard

...

On Nov 17, 2020, at 1:47 AM, Bryan Richter wrote:

Dear forall ghc-devs. ghc-devs,

As I read through the "Visible 'forall' in types of terms" proposal[1], I stumbled over something that isn't relevant to the proposal itself, so I thought I would bring it here.

Given

f :: forall a. a -> a (1)

I intuitively understand the 'forall' in (1) to represent the phrase "for all". I would read (1) as "For all objects a in Hask, f is some relation from a to a."

After reading the proposal, I think my intuition may be wrong, since I discovered `forall a ->`. This means something similar to, but practically different from, `forall a.`. Thus it seems like 'forall' is now simply used as a sigil to represent "here is where some special parameter goes". It could as well be an emoji.

What's more, the practical difference between the two forms is *only* distinguished by ` ->` versus `.`. That's putting quite a lot of meaning into a rather small number of pixels, and further reduces any original connection to meaning that 'forall' might have had.

I won't object to #281 based only on existing syntax, but I *do* object to the existing syntax. :) Is this a hopeless situation, or is there any possibility of bringing back meaning to the syntax of "dependent quantifiers"?

-Bryan

[1]: https://github.com/ghc-proposals/ghc-proposals/pull/281 _______________________________________________ ghc-devs mailing list ghc-devs@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/ghc-devs

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How do you feel about

...

f :: forall (a :: Type) -> a or g :: (a :: Type) -> a

The former has the same problem as the current syntax. The latter seems better, but then I might be confused again. :) My main concern is with the choice of keyword. With data, instance, class, module, ..., the pattern is clear: name the sort of thing you are introducing. forall, on the other hand, doesn't introduce a "forall". It's making explicit the existing universal quantification. But somewhere, an author decided to reuse the same keyword to herald a type argument. It seems they stopped thinking about the meaning of the word itself, saw that it was syntactically in the right spot, and borrowed it to mean something else. I feel like that borrowing introduced a wart. Consider `forall a -> a -> a`. There's still an implicit universal quantification that is assumed, right? I.e., this type signature would be valid for all types `a` ? But then how do we make that quantification explicit? `forall a. forall a -> a -> a`? But oops, have we now introduced a new type argument? I keep referring to the thing as a "type argument". I know it's hard to introduce a new keyword, but imagine if we had `forall a. typearg a -> a -> a`. It would at least point to its meaning. I guess that's pretty close to your

g :: (a :: Type) -> a

which is why I think it seems a bit better. On Fri, Nov 20, 2020 at 10:56 PM Richard Eisenberg wrote:

Hi Bryan,

Thanks for this longer post -- it's very helpful to see this with fresh eyes.

...

On Nov 19, 2020, at 2:18 PM, Bryan Richter wrote:

So correct me if I'm wrong: from an implementation perspective, `forall a. a -> Int` is a function of two arguments, one of which can be elided, while `forall a -> a -> Int` is a function of two arguments, all of which must be provided.

Yes, that's how I read these.

...

If that's right, then it bumps into my intuition, which says that the former is a function of only one argument. I never thought of `f @Int` as partial function application, for instance. :) Is my intuition leading me astray? *Should* I consider both functions as having two arguments? If so, is that somehow "mathematically true" (a very not-mathematical phrase, haha), or is it just an "implementation detail"?

I don't think there's one right answer here. And I'm not quite sure how to interpret "mathematically true". The best I can get is that, if we consider System F (a direct inspiration for Haskell's type system), then both functions really do take 2 arguments (as they do in GHC Core).

...

So that's one avenue of query I have, but it's actually not the one I started off with. Focusing on the simpler case of `forall a -> a`, which is a function of one argument, I take issue with how the quantification is packed into the syntax for the argument, itself. I.e., my intuition tells me this function is valid for all types, takes the name of a type as an argument, and returns a value of that type, which is three distinct pieces of information. I'd expect a syntax like `forall a. elem x a. a -> x`, or maybe `forall a. nameof a -> a`. The packing and punning conspire to make the syntax seem overly clever.

How do you feel about

...

f :: forall (a :: Type) -> a

or

...

g :: (a :: Type) -> a

Somehow, for me too, having the type of `a` listed makes it clearer. The syntax for f echoes that in Coq, a long-standing dependently typed language, but it uses , instead of ->. The type of `a` is optional. (An implicit parameter is put in braces.) The syntax for g echoes that in Agda and Idris; the type of `a` is not optional. Haskell cannot use the syntax for `g`, because it looks like a kind annotation.

In the end, I've never loved the forall ... -> syntax, but I've never seen anything better. The suggestions you make are akin to those in https://github.com/ghc-proposals/ghc-proposals/pull/281#issuecomment-7279070.... This alternative might work out, but I've never seen this approach taken in another language, and it would be quite different from what we have today.

...

If I had to explain `forall a -> a` to one of my Haskell-curious colleagues, I'd have to say "Oh that means you pass the name of a type to the function" -- something they'd have no chance of figuring out on their own! The 'forall' comes across as meaningless. (Case in point: I had no idea what the syntax meant when I saw it -- but I'm already invested enough to go digging.)

I agree that the new syntax is not adequately self-describing.

...

I guess my question, then, is if there is some way to make this syntax more intuitive for users!

I agree! But I somehow don't think separating out all the pieces will make it easier, in the end.

Richard

...

On Wed, Nov 18, 2020 at 10:10 PM Carter Schonwald wrote:

...

I do think explaining it relative to the explicit vs implicit arg

...

...

f: Forall a . B is used with f x. This relates to the new forall ->

syntax.

...

g: forall {c}. D is used either as f or f {x}, aka implicit or forcing

it to be explicit. This maps to our usual Haskell forall with explicit {} being the @ analogue

...

On Wed, Nov 18, 2020 at 12:09 PM Iavor Diatchki <

iavor.diatchki@gmail.com> wrote:

...

...

Semantically, `forall a -> a -> Int` is the same as `forall a. a ->

Int`. The two only differ in how you use them:

...

* For the first one, you have to explicitly provide the type to use for `a` at every call site, while * for the second one, you usually omit the type and let GHC infer it.

So overall I think it's a pretty simple idea. For me it's hard to see

...

...

...

is about a fancy notation for explicitly providing the type at call sites.

-Iavor

On Wed, Nov 18, 2020 at 9:51 AM Richard Eisenberg wrote:

...

Hi Bryan,

First off, sorry if my first response was a bit snippy -- it wasn't

meant to be, and I appreciate the angle you're taking in your question. I just didn't understand it!

...

This second question is easier to answer. I say "forall a arrow a

arrow Int".

...

But I still think there may be a deeper question here left

unanswered...

...

Richard

On Nov 18, 2020, at 6:11 AM, Bryan Richter wrote:

Yeah, sorry, I think I'm in a little over my head here. :) But I

syntax of agda function argument syntax. that from the text in #281, but I think a lot of the complexity there think I can ask a more answerable question now: how does one pronounce "forall a -> a -> Int"?

...

...

...

...

Den tis 17 nov. 2020 16:27Richard Eisenberg skrev:

...

Hi Bryan,

I don't think I understand what you're getting at here. The

difference between `forall b .` and `forall b ->` is only that the choice of b must be made explicit. Importantly, a function of type e.g. `forall b -> b -> b` can *not* pattern-match on the choice of type; it can bind a variable that will be aliased to b, but it cannot pattern-match (say, against Int). Given this, can you describe how `forall b ->` violates your intuition for the keyword "forall"?

...

...

Thanks! Richard

> On Nov 17, 2020, at 1:47 AM, Bryan Richter wrote: > > Dear forall ghc-devs. ghc-devs, > > As I read through the "Visible 'forall' in types of terms" > proposal[1], I stumbled over something that isn't relevant to the > proposal itself, so I thought I would bring it here. > > Given > > f :: forall a. a -> a (1) > > I intuitively understand the 'forall' in (1) to represent the phrase > "for all". I would read (1) as "For all objects a in Hask, f is some > relation from a to a." > > After reading the proposal, I think my intuition may be wrong,

since I

...

> discovered `forall a ->`. This means something similar to, but > practically different from, `forall a.`. Thus it seems like 'forall' > is now simply used as a sigil to represent "here is where some special > parameter goes". It could as well be an emoji. > > What's more, the practical difference between the two forms is *only* > distinguished by ` ->` versus `.`. That's putting quite a lot of > meaning into a rather small number of pixels, and further reduces any > original connection to meaning that 'forall' might have had. > > I won't object to #281 based only on existing syntax, but I *do* > object to the existing syntax. :) Is this a hopeless situation, or is > there any possibility of bringing back meaning to the syntax of > "dependent quantifiers"? > > -Bryan > > [1]: https://github.com/ghc-proposals/ghc-proposals/pull/281 > _______________________________________________ > ghc-devs mailing list > ghc-devs@haskell.org > http://mail.haskell.org/cgi-bin/mailman/listinfo/ghc-devs

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I must be confused, because it sounds like you are contradicting yourself. :) In one sentence you say that there is no assumed universal quantification going on, and in the next you say that the function does indeed work for all types. Isn't that the definition of universal quantification? (We're definitely getting somewhere interesting!) Den tors 3 dec. 2020 17:56Richard Eisenberg skrev:

On Dec 3, 2020, at 10:23 AM, Bryan Richter wrote:

Consider `forall a -> a -> a`. There's still an implicit universal quantification that is assumed, right?

No, there isn't, and I think this is the central point of confusion. A function of type `forall a -> a -> a` does work for all types `a`. So I think the keyword is appropriate. The only difference is that we must state what `a` is explicitly. I thus respectfully disagree with

But somewhere, an author decided to reuse the same keyword to herald a type argument. It seems they stopped thinking about the meaning of the word itself, saw that it was syntactically in the right spot, and borrowed it to mean something else.

Does this help clarify? And if it does, is there a place you can direct us to where the point could be made more clearly? I think you're far from the only one who has tripped here.

Richard

I don't know if this has been discussed but couldn't we reuse the lambda abstraction syntax for this? That is instead of writing: forall a -> Write: \a -> Sylvain On 03/12/2020 17:21, Vladislav Zavialov wrote:

There is no *implicit* universal quantification in that example, but there is an explicit quantifier. It is written as follows:

  forall a ->

which is entirely analogous to:

  forall a.

in all ways other than the additional requirement to instantiate the type vatiable visibly at use sites.

- Vlad

On Thu, Dec 3, 2020, 19:12 Bryan Richter mailto:b@chreekat.net> wrote:

I must be confused, because it sounds like you are contradicting yourself. :) In one sentence you say that there is no assumed universal quantification going on, and in the next you say that the function does indeed work for all types. Isn't that the definition of universal quantification?

(We're definitely getting somewhere interesting!)

Den tors 3 dec. 2020 17:56Richard Eisenberg mailto:rae@richarde.dev> skrev:

...

On Dec 3, 2020, at 10:23 AM, Bryan Richter mailto:b@chreekat.net> wrote:

Consider `forall a -> a -> a`. There's still an implicit universal quantification that is assumed, right?

No, there isn't, and I think this is the central point of confusion. A function of type `forall a -> a -> a` does work for all types `a`. So I think the keyword is appropriate. The only difference is that we must state what `a` is explicitly. I thus respectfully disagree with

...

But somewhere, an author decided to reuse the same keyword to herald a type argument. It seems they stopped thinking about the meaning of the word itself, saw that it was syntactically in the right spot, and borrowed it to mean something else.

Does this help clarify? And if it does, is there a place you can direct us to where the point could be made more clearly? I think you're far from the only one who has tripped here.

Richard

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On Dec 3, 2020, at 11:11 AM, Bryan Richter wrote:

I must be confused, because it sounds like you are contradicting yourself. :) In one sentence you say that there is no assumed universal quantification going on, and in the next you say that the function does indeed work for all types. Isn't that the definition of universal quantification?

I agree with Vlad's comment here: There *is* universal quantification here, but there is not *implicit* universal quantification, as it's *explicit*. You've made the universal quantification with your `forall a ->`. Richard

Hm, yes, I might share Eric's intuition. I think I'm starting to get it, though. It originally sounded to me like "forall a ->" was being introduced as a new syntax for function arguments. In fact, it is a new syntax for quantification -- one that happens to borrow the syntax for function application. And well it might, because the sort of quantification it introduces is one that requires passing the name of a type to the function! Den tors 3 dec. 2020 18:39Eric Seidel skrev:

I think the confusion for me is that I've trained myself to think of `forall` as explicitly introducing an implicit argument, and `->` as introducing an explicit argument. So the syntax `forall a ->` looks to me like a contradiction.

On Thu, Dec 3, 2020, at 10:56, Richard Eisenberg wrote:

...

...

On Dec 3, 2020, at 10:23 AM, Bryan Richter wrote:

Consider `forall a -> a -> a`. There's still an implicit universal

quantification that is assumed, right?

...

No, there isn't, and I think this is the central point of confusion. A function of type `forall a -> a -> a` does work for all types `a`. So I think the keyword is appropriate. The only difference is that we must state what `a` is explicitly. I thus respectfully disagree