<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<meta name="Generator" content="Microsoft Word 15 (filtered medium)">
<style><!--
/* Font Definitions */
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0cm;
margin-bottom:.0001pt;
font-size:11.0pt;
font-family:"Calibri",sans-serif;}
a:link, span.MsoHyperlink
{mso-style-priority:99;
color:blue;
text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
{mso-style-priority:99;
color:purple;
text-decoration:underline;}
p.Code, li.Code, div.Code
{mso-style-name:Code;
margin-top:0cm;
margin-right:0cm;
margin-bottom:0cm;
margin-left:22.7pt;
margin-bottom:.0001pt;
font-size:10.0pt;
font-family:"Courier New";
font-weight:bold;}
p.msonormal0, li.msonormal0, div.msonormal0
{mso-style-name:msonormal;
mso-margin-top-alt:auto;
margin-right:0cm;
mso-margin-bottom-alt:auto;
margin-left:0cm;
font-size:11.0pt;
font-family:"Calibri",sans-serif;}
span.EmailStyle19
{mso-style-type:personal-reply;
font-family:"Calibri",sans-serif;
color:windowtext;}
.MsoChpDefault
{mso-style-type:export-only;
font-family:"Calibri",sans-serif;
mso-fareast-language:EN-US;}
.MsoPapDefault
{mso-style-type:export-only;
margin-top:6.0pt;
margin-right:0cm;
margin-bottom:6.0pt;
margin-left:0cm;}
@page WordSection1
{size:612.0pt 792.0pt;
margin:72.0pt 72.0pt 72.0pt 72.0pt;}
div.WordSection1
{page:WordSection1;}
--></style><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1026" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1" />
</o:shapelayout></xml><![endif]-->
</head>
<body lang="EN-GB" link="blue" vlink="purple">
<div class="WordSection1">
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:36.0pt">
Therefore many uses of `mkFin` et al *require* that I introduce local equality constraints. And those sadly spoil lots of desired type inference by making outer tyvars untouchable.<o:p></o:p></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US">One would need to think carefully here. For example, just changing (a~b) to (IsEqual a b) doesn’t really make it less of an equality constraint, does it? Yet (IsEqual a b) isn’t an equality constraint,
and hence would not make outer type variables untouchable. Does that threaten predictable type inference, as an (a~b) constraint does? I’m not sure.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US">Perhaps if it was defined as<o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US"> class IsEqual a b<o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US"> instance IsEqual a a<o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US">all would be well. But NOT if you defined it as<o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US"> class (a~b) => IsEqual2 a b<o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US"> instance IsEqual2 a a<o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US">because of the superclass.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US">Interesting. I’d never thought of that. cc’ing Richard.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US">Simon<o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<div style="border:none;border-left:solid blue 1.5pt;padding:0cm 0cm 0cm 4.0pt">
<div>
<div style="border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0cm 0cm 0cm">
<p class="MsoNormal"><b><span lang="EN-US">From:</span></b><span lang="EN-US"> Libraries <libraries-bounces@haskell.org>
<b>On Behalf Of </b>Nicolas Frisby<br>
<b>Sent:</b> 21 May 2019 02:48<br>
<b>To:</b> Haskell Libraries <libraries@haskell.org><br>
<b>Subject:</b> request: a Nat ordering constraint that is not an equality constraint<o:p></o:p></span></p>
</div>
</div>
<p class="MsoNormal"><o:p> </o:p></p>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
This email proposes an extension and possible change to GHC.TypeLits module in the core `base` library.<o:p></o:p></p>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
<o:p> </o:p></p>
</div>
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
Is there support for this kind of extension/change to GHC.TypeLits? If so, I'll open a GHC GitLab Issue.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
<o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
(If not, I would be very appreciate if someone were able to suggest a nice workaround.)<o:p></o:p></p>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
<o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
# The Proposed Extension<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
<o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
Please add an alternative to <= that is not defined via ~. For example:<o:p></o:p></p>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
<o:p> </o:p></p>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
```<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
module GHC.TypeLits.Passive where<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
<o:p></o:p></p>
</div>
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
class IsTrue (a :: Bool)<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
instance IsTrue 'True<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
instance TypeError ... => IsTrue 'False<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
<o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
type (<=) x y = IsTrue (x <=? y)<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
```<o:p></o:p></p>
</div>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
<o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
as opposed to the existing definition:<o:p></o:p></p>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:0cm">
<br>
```<br>
module GHC.TypeLits where<o:p></o:p></p>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
type (<=) x y = (x <=? y) ~ 'True<o:p></o:p></p>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
```<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
<o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
Its name should be an operator and should be somewhat obvious -- I can't think of one other than <=, so I hedged here by putting in a new module instead.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:0cm">
<br>
There should be a means of *explicitly* converting back and forth between evidence of the two constraints; they are equi-satisfiable but affect type inference in their scope differently.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:0cm">
# The Optional Change<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:0cm">
I anticipate most users would prefer Passive.<= to today's <=, so the optional library change in this proposal is to redefine <= and relegate its old definition to a new name. Perhaps:<o:p></o:p></p>
<div>
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
```<o:p></o:p></p>
</div>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
module GHC.TypeLits where<o:p></o:p></p>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
<br>
type (<=) x y = IsTrue (x <=? y)<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
type (<=!) x y = (x <=? y) ~ 'True<o:p></o:p></p>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
```<o:p></o:p></p>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
<o:p> </o:p></p>
</div>
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
# The Motivation<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
<o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
I'll explain with an example for some concreteness. <o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
I wrote an interface for size-indexed vectors for my employer. It involves some code like this:<o:p></o:p></p>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
<o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
```<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
import GHC.TypeLits<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
<br>
newtype Fin (n :: Nat) = Unsafe_MkFin{forgetFin :: Integer}<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:0cm">
<br>
mkFin :: (KnownNat i,i <= n) => proxy i -> Fin n<br>
mkFin = Unsafe_MkFin . natVal<br>
```<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
Constraints like `(i <= n)` show up throughout the library's interface.<br>
The problem is that <= is an equality constraint.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
Therefore many uses of `mkFin` et al *require* that I introduce local equality constraints.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
And those sadly spoil lots of desired type inference by making outer tyvars untouchable.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
<o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
That's the problem: I have to choose between GHC's specialized solving of <= constraints and unspoiled type inference in their scope.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
<o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
# Additional Context<o:p></o:p></p>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
<o:p> </o:p></p>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
It is important that today's <= be an equality constraint, because it participates in some constraint improvements that introduce equality constraints. For example (x <= y,y <= x) implies x ~ y (c.f. the scary <a href="https://nam06.safelinks.protection.outlook.com/?url=https%3A%2F%2Fgitlab.haskell.org%2Fghc%2Fghc%2Fissues%2F16586&data=02%7C01%7Csimonpj%40microsoft.com%7Cfd400e22fed34cacdc8108d6dd8e8002%7C72f988bf86f141af91ab2d7cd011db47%7C1%7C0%7C636940001438800796&sdata=M53kCihvu6RqXOutwOT4Ha7MzPHqmYgcfqzCA1%2BSvYE%3D&reserved=0">https://gitlab.haskell.org/ghc/ghc/issues/16586</a>).
Because <= constraints have the potential to "become" an equality constraint, tyvars outside of a <= constraint must be untouchable in its scope from the get go.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
<br>
However, neither my library nor any of its uses relies on such constraint improvements enabled by <= constraints.<o:p></o:p></p>
</div>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:0cm">
In this context, I would much rather that <= could never "become" an equality constraint, so that it need not be an equality constraint, so that it would never render a tyvar untouchable.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
# An Alternative<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
<br>
As a partial workaround, I could write<br>
<br>
```<br>
data Dict i n = (i <= n) => MkDict<br>
<br>
mkFinD :: (KnownNat i) => Dict i n -> proxy i -> Fin n<br>
mkFinD MkDict = mkFin<br>
```<br>
<br>
and then take pains to only introduce the <= constraints in the argument of `mkFinD`. By limiting the scope of the ~ constraints like that, I could prevent them from spoiling the desired type inference. But it's very cumbersome to manage their scopes manually.<br>
<br>
# Work Estimation<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
<o:p> </o:p></p>
</div>
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
I just thought of the `IsTrue`-based approach while writing this email, so that detail is somewhat half-baked. It has the right *indicative* semantics, but I doubt today's GHC solver would know what to do with a Given `IsTrue (3 <=? 5)` constraint -- so I'm
guessing that exact approach at least would require some significant changes in TcTypeNats.<o:p></o:p></p>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
<o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:0cm">
Thank you for your time. -Nick<br>
<br>
P.S. - Some of the issue tracker links at <a href="https://nam06.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwiki.haskell.org%2FLibrary_submissions%23The_Libraries&data=02%7C01%7Csimonpj%40microsoft.com%7Cfd400e22fed34cacdc8108d6dd8e8002%7C72f988bf86f141af91ab2d7cd011db47%7C1%7C0%7C636940001438810751&sdata=0mdfCDTlrytqy%2Fu4htfH4kF%2F9l9NcJnJNcaPHIi0lRk%3D&reserved=0">https://wiki.haskell.org/Library_submissions#The_Libraries</a> respond
with 404.<br>
<br>
P.P.S. - Is there a standard place to find something like `IsTrue`? More generally: a test for type equality that does not drive unification? Thanks again.<o:p></o:p></p>
</div>
</div>
</div>
</div>
</div>
</div>
</body>
</html>