COMPLETE pragmas

Edward Kmett ekmett at
Mon Aug 31 22:26:30 UTC 2020

I'd be over the moon with happiness if I could hang COMPLETE pragmas on
polymorphic types.

I have 3 major issues with COMPLETE as it exists.

1.) Is what is mentioned here:

Examples for me come up when trying to build a completely unboxed 'linear'
library using backpack. In the end I want/need to supply a pattern synonym
that works over, say, all the 2d vector types, extracting their elements,
but right now I just get spammed by incomplete coverage warnings.

type family Elem t :: Type
class D2 where
  _V2 :: Iso' t (Elem t, Elem t)

pattern V2 :: D2 t => Elem t -> Elem t -> t
pattern V2 a b <- (view _V2 -> (a,b)) where
  V2 a b = review _V2 (a,b)

There is no way to hang a COMPLETE pragma on that.

2.) Another scenario that I'd really love to see supported with COMPLETE
pragmas is a way to use | notation with them like you can with MINIMAL

If you make smart constructors for a dozen constructors in your term type
(don't judge me!), you wind up needing 2^12 COMPLETE pragmas to describe
all the ways you might mix regular and start constructors today.

{# COMPLETE (Lam | LAM), (Var | VAR), ... #-}

would let you get away with a single such definition. This comes up when
you have some kind of monoid that acts on terms and you want to push it
down through
the syntax tree invisibly to the user. Explicit substitutions, shifts in
position in response to source code edits, etc.

3.) I had one other major usecase where I failed to be able to use a
COMPLETE pragma:

type Option a = (# a | (##) #)

pattern Some :: a -> Option a
pattern Some a = (# a | #)

pattern None :: Option a
pattern None = (# | (##) #)

{-# COMPLETE Some, None #-}

These worked _within_ a module, but was forgotten across module boundaries,
which forced me to rather drastically change the module structure of a
package, but it sounds a lot like the issue being discussed. No types to
hang it on in the interface file. With the ability to define unlifted
newtypes I guess this last one is less of a concern now?


On Mon, Aug 31, 2020 at 2:29 PM Richard Eisenberg <rae at> wrote:

> Hooray Sebastian!
> Somehow, I knew cluing you into this conundrum would help find a solution.
> The approach you describe sounds quite plausible.
> Yet: types *do* matter, of course. So, I suppose the trick is this: have
> the COMPLETE sets operate independent of types, but then use types in the
> PM-checker when determining impossible cases? And, about your idea for
> having pattern synonyms store pointers to their COMPLETE sets: I think data
> constructors can also participate. But maybe there is always at least one
> pattern synonym (which would be a reasonable restriction), so I guess you
> can look at the pattern-match as a whole and use the pattern synonym to
> find the relevant COMPLETE set(s).
> Thanks for taking a look!
> Richard
> On Aug 31, 2020, at 4:23 PM, Sebastian Graf <sgraf1337 at> wrote:
> Hi Richard,
> Am Mo., 31. Aug. 2020 um 21:30 Uhr schrieb Richard Eisenberg <
> rae at>:
>> Hi Sebastian,
>> I enjoyed your presentation last week at ICFP!
> Thank you :) I'm glad you liked it!
> This thread (
>> played out before you became so interested in pattern-match coverage. I'd
>> be curious for your thoughts there -- do you agree with the conclusions in
>> the thread?
> I vaguely remember reading this thread. As you write there
> <>
> And, while I know it doesn't work today, what's wrong (in theory) with
>> {-# COMPLETE LL #-}
>> No types! (That's a rare thing for me to extol...)
>> I feel I must be missing something here.
> Without reading the whole thread, I think that solution is very possible.
> The thread goes on to state that we currently attach COMPLETE sets to type
> constructors, but that is only an implementational thing. I asked Matt (who
> implemented it) somewhere and he said the only reason to attach it to type
> constructors was because it was the easiest way to implement serialisation
> to interface files.
> The thread also mentions that type-directed works better for the
> pattern-match checker. In fact I disagree; we have to thin out COMPLETE
> sets all the time anyway when new type evidence comes up, for example. It's
> quite a hassle to find all the COMPLETE sets of the type constructors a
> given type can be "represented" (I mean equality modulo type family
> reductions here) as. I'm pretty sure it's broken in multiple ways, as
> #18276 <> points out.
> Disregarding a bit of busy work for implementing serialisation to
> interface files, it's probably far simpler to give each COMPLETE set a
> Name/Unique and refer to them from the pattern synonyms that mention them
> (we'd have to get creative for orphans, though). The relation is quite like
> between a type class instance and the type in its head. A more worked
> example is here:
> So, it's on my longer term TODO list to fix this.
>> My motivation for asking is (you
>> don't need to read the whole thing), which can be boiled down to a request
>> for a COMPLETE pragma that works at a polymorphic result type. (Or a
>> COMPLETE pragma written in a module that is not the defining module for a
>> pattern synonym.)
>> describes a similar, but even more challenging scenario.
> I'll answer in the thread. (Oh, you also found #14422.) I think the
> approach above will also fix #14422.
>> Do you see any ways forward here?
> .
>> Thanks!
>> Richard
> Maybe I'll give it a try tomorrow.
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