Help needed: Restrictions of proc-notation with RebindableSyntax

MarLinn monkleyon at
Wed Dec 21 06:43:02 UTC 2016

Sorry to barge into the discussion with neither much knowledge of the 
theory nor the implementation. I tried to look at both, but my 
understanding is severely lacking. However I do feel a tiny bit 
emboldened because my own findings turned out to at least have the same 
shadow as the contents of this more thorough overview.

The one part of the existing story I personally found the most promising 
was to explore the category hierarchy around Arrows, in other words the 
Gibbard/Trinkle perspective. Therefore I want to elaborate my own naive 
findings a tiny bit. Bear in mind that much of this is gleaned from 
experimental implementations or interpreted, but I do not have proofs, 
or even theory.
Almost all parts necessary for an Arrow seem to already be contained in 
a symmetrical braided category. Fascinatingly, even the braiding might 
be superfluous in some cases, leaving only the need for a monoidal 
category. But to get from a braided category to a full Arrow, there 
seems to be a need for "constructors" like (arr $ \x -> (x,x)) and 
"destructors" like (arr fst). There seem to be several options for 
those, and a choice would have to be made. Notably: is introduction done 
by duplicating existing values, or by introducing new "unit" values (for 
a suitable definition of "unit")? That choice doesn't seem impactful, 
but my gut feeling is that that's just because I cannot see the 
potential points of impact.

What makes this story worse is that the currently known hierarchies 
around ArrowChoice and ArrowLoop seem to be coarser still – although the 
work around profunctors might help. That said, my understanding is so 
bad that I can not even see any benefits or drawbacks of the structure 
of ArrowLoop's "loop" versus a more "standard" fix-point structure.

I do, however, think there is something to be gained. The good old 
Rosetta Stone paper still makes me think that what is now Arrow notation 
might be turned into a much more potent tool – exactly because we might 
be able to lift those restrictions. One particular idea I have in mind: 
If the notation can support purely braided categories, it might be used 
to describe reversible computation, which in turn is used in describing 
quantum computation.

The frustrating part for me is that I would like to contribute to this 
effort. But again, my understanding of each and every component is 
fleeting at best.


On 2016-12-21 06:15, Edward Kmett wrote:
> Arrows haven't seen much love for a while. In part this is because 
> many of the original applications for arrows have been shown to be 
> perfectly suited to being handled by Applicatives. e.g. the 
> Swiestra/Duponcheel parser that sort of kickstarted everything.
> There are several options for improved arrow desugaring.
> Megacz's work on GArrows at first feels like it should be applicable 
> here, as it lets you change out the choice of pseudo-product while 
> preserving the general arrow feel. Unfortunately, the GArrow class 
> isn't sufficient for most arrow desguaring, due to the fact that the 
> arrow desugaring inherently involves breaking apart patterns for 
> almost any non-trivial use and nothing really requires the GArrow 
> 'product' to actually even be product like.
> Cale Gibbard and Ryan Trinkle on the other hand like to use a more 
> CCC-like basis for arrows. This stays in the spirit to the GArrow 
> class, but you still have the problems around pattern matching. I 
> don't think they actually wrote anything to deal with the actual arrow 
> notation and just programmed in the alternate style to get better 
> introspection on the operations involved. I think the key insight 
> there is that much of the notation can be made to work with weaker 
> categorical structures than full arrows, but the existing class 
> hierarchy around arrows is very coarse.
> As a minor data point both of these sorts of encodings of arrow 
> problems start to drag in language extensions that make the notation 
> harder to standardize. Currently they work with bog standard Haskell 
> 98/2010.
> If you're looking for an interesting theoretical direction to extend 
> Arrow notation:
> An arrow is a strong monad in the category of profunctors [1].
> Using the profunctors library [2] (Strong p, Category p) is equivalent 
> in power to Arrow p.
> Exploiting that, a profunctor-based desugaring could get away with 
> much weaker constraints than Arrow depending on how much of proc 
> notation you use.
> Alternately a separate class hierarchy that only required covariance 
> in the second argument is an option, but my vague recollection from 
> the last time that I looked into this is that while such a desguaring 
> only uses covariance in the second argument of the profunctor, you can 
> prove that contravariance in the first argument follows from the pile 
> of laws. This subject came up the last time someone thought to extend 
> the Arrow desguaring. You can probably find a thread on the mailing 
> list from Ross Paterson a few years ago.
> This version has the benefit of fitting pretty close to the existing 
> arrow desugaring and not needing new language extensions.
> On the other hand, refactoring the Arrow class in this (or any other) 
> way is somewhat of an invasive exercise. The profunctors package 
> offers moral equivalents to most of the Arrow subclasses, but no 
> effort has been made to match the existing Arrow hierarchy.
> Given that little new code seems to be being written with Arrows in 
> mind, while some older code makes heavy use of it (hxt, etc.), 
> refactoring the arrow hierarchy is kind of a hard sell. It is by no 
> means impossible, just something that would require a fair bit of 
> community wrangling and a lot of work showing clear advantages to a 
> new status quo at a time when its very hard to get anybody to care 
> about arrow notation at all.
> -Edward
> [1] 
> <>
> [2] 
> On Fri, Dec 2, 2016 at 10:57 AM, Jan Bracker via ghc-devs 
> <ghc-devs at <mailto:ghc-devs at>> wrote:
>     Simon, Richard,
>     thank you for your answer! I don't have time to look into the GHC
>     sources right now, but I will set aside some time after the
>     holidays and take a close look at what the exact restrictions on
>     proc-notation are and document them.
>     Since you suggested a rewrite of GHC's handling of proc-syntax,
>     are there any opinions on integrating generalized arrows (Joseph
>     2014) in the process? I think they would greatly improve arrows! I
>     don't know if I have the time to attempt this, but if I find the
>     time I would give it a try. Why wasn't this integrated while it
>     was still actively developed?
>     Best,
>     Jan
>     [Joseph 2014]
>     <>
>     2016-11-29 12:41 GMT+00:00 Simon Peyton Jones
>     <simonpj at <mailto:simonpj at>>:
>         Jan,
>         Type checking and desugaring for arrow syntax has received
>         Absolutely No Love for several years.  I do not understand how
>         it works very well, and I would not be at all surprised if it
>         is broken in corner cases.
>         It really needs someone to look at it carefully, document it
>         better, and perhaps refactor it – esp by using a different
>         data type rather than piggy-backing on HsExpr.
>         In the light of that understanding, I think rebindable syntax
>         will be easier.
>         I don’t know if you are up for that, but it’s a rather
>         un-tended part of GHC.
>         Thanks
>         Simon
>         *From:*ghc-devs [mailto:ghc-devs-bounces at
>         <mailto:ghc-devs-bounces at>] *On Behalf Of *Richard
>         Eisenberg
>         *Sent:* 28 November 2016 22:30
>         *To:* Jan Bracker <jan.bracker at
>         <mailto:jan.bracker at>>
>         *Cc:* ghc-devs at <mailto:ghc-devs at>
>         *Subject:* Help needed: Restrictions of proc-notation with
>         RebindableSyntax
>         Jan’s question is a good one, but I don’t know enough about
>         procs to be able to answer. I do know that the answer can be
>         found by looking for uses of `tcSyntaxOp` in the TcArrows
>         module.... but I just can’t translate it all to source
>         Haskell, having roughly 0 understanding of this end of the
>         language.
>         Can anyone else help Jan here?
>         Richard
>             On Nov 23, 2016, at 4:34 AM, Jan Bracker via ghc-devs
>             <ghc-devs at <mailto:ghc-devs at>> wrote:
>             Hello,
>             I want to use the proc-notation together with
>             RebindableSyntax. So far what I am trying to do is working
>             fine, but I would like to know what the exact restrictions
>             on the supplied functions are. I am introducing additional
>             indices and constraints on the operations. The
>             documentation [1] says the details are in flux and that I
>             should ask directly.
>             Best,
>             Jan
>             [1]
>             <>
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