<div dir="ltr">Awesome work. For now, I put it in a branch 'classes' in the main repo and granted you commit rights. I will try it out on UlfNorell/agda-prelude, which uses a lot of instance arguments.<br><div><br>
</div><div>/ Ulf</div></div><div class="gmail_extra"><br><br><div class="gmail_quote">On Fri, Jul 11, 2014 at 12:26 PM, Guillaume Brunerie <span dir="ltr"><<a href="mailto:guillaume.brunerie@gmail.com" target="_blank">guillaume.brunerie@gmail.com</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Hello all,<br>
<br>
As some of you know, I started working on recursive instance search<br>
during the previous AIM and the code is now available on my GitHub<br>
here : <a href="https://github.com/guillaumebrunerie/agda" target="_blank">https://github.com/guillaumebrunerie/agda</a> (should I open a pull<br>
request against the official Agda?)<br>
<br>
The main outstanding issue is that there is no termination check yet<br>
so if you’re not careful when defining your instances you can easily<br>
make Agda loop.<br>
Also, I haven’t really thought about namespace management, for<br>
instance 'hiding' does not hide instances (but serialization should<br>
work, though).<br>
<br>
I copy-pasted the relevant part of the CHANGELOG below (I borrowed<br>
part of the text in issue 938) and you can also look at the two files<br>
test/succeed/RecursiveInstanceSearch{,Level}.agda to see some more<br>
advanced examples of recursive instance search.<br>
<br>
Of course I welcome any feedback/bug reports.<br>
<br>
Cheers,<br>
Guillaume<br>
<br>
<br>
<br>
<br>
* Instance search is now more efficient and recursive (see issue 938)<br>
(but without termination check yet)<br>
<br>
A new keyword `instance' has been introduced (in the style of<br>
`abstract' and `private') which must now be used for every<br>
definition/postulate that has to be taken into account during instance<br>
resolution. For example:<br>
<br>
{-# OPTIONS --copatterns #-}<br>
<br>
record RawMonoid (A : Set) : Set where<br>
field<br>
nil : A<br>
_++_ : A -> A -> A<br>
open RawMonoid<br>
<br>
instance<br>
rawMonoidList : {A : Set} -> RawMonoid (List A)<br>
rawMonoidList = record { nil = []; _++_ = List._++_ }<br>
<br>
-- using copatterns to define this recursive instance:<br>
<br>
rawMonoidMaybe : {A : Set} {{m : RawMonoid A}} -> RawMonoid (Maybe A)<br>
nil rawMonoidMaybe = nothing<br>
_++_ rawMonoidMaybe nothing mb = mb<br>
_++_ rawMonoidMaybe ma nothing = ma<br>
_++_ (rawMonoidMaybe {{m}}) (just a) (just b) = just (_++_ m a b)<br>
<br>
Moreover, each type of an instance must end in (something that reduces<br>
to) a named type (e.g. a record, a datatype or a postulate). This<br>
allows us to build a simple index structure<br>
<br>
data/record name --> possible instances<br>
<br>
that speeds up instance search.<br>
<br>
Instance search takes into account all local bindings and all global<br>
'instance' bindings and the search is recursive. For instance,<br>
searching for<br>
<br>
? : RawMonoid (Maybe (List A))<br>
<br>
will consider the candidates {rawMonoidList, rawMonoidMaybe}, fail to<br>
unify the first one, succeeding with the second one<br>
<br>
? = rawMonoidMaybe {A = List A} {{m = ?m}} : RawMonoid (Maybe (List A))<br>
<br>
and continue with goal<br>
<br>
?m : RawMonoid (List A)<br>
<br>
This will then find<br>
<br>
?m = rawMonoidList {A = A}<br>
<br>
and putting together we have the solution.<br>
<br>
Be careful that there is no termination check for now, you can easily<br>
make Agda loop by declaring the identity function as an instance. But<br>
it shouldn’t be possible to make Agda loop by only declaring<br>
structurally recursive instances (whatever that means).<br>
<br>
Additionally:<br>
<br>
* Uniqueness of instances is up to definitional equality (see issue 899)<br>
<br>
* Instance search will not be attempted if there are unsolved metas in<br>
the goal. The issue is that trying to typecheck [? ++ ?] would<br>
generate a constraint of type `RawMonoid ?' to be solved by instance<br>
search, but unification with `rawMonoidMaybe' will succeed and<br>
generate a new constraint of type `RawMonoid ?2' to be solved by<br>
instance search, and so on, so Agda would loop.<br>
<br>
As a special case, if none of the instances declared for that type<br>
is recursive, then instance search is attempted as usual even if<br>
there are unsolved metas (no risk of looping here).<br>
<br>
* Instances of the following form are allowed:<br>
<br>
Π-level : {n : ℕ} {A : Set} {B : A → Set}<br>
{{_ : (a : A) → has-level n (B a)}}<br>
→ has-level n ((a : A) → B a)<br>
<br>
When searching recursively for an instance of type `(a : A) →<br>
has-level n (B a)', a lambda will automatically be introduced and<br>
instance search will search for something of type `has-level n (B<br>
a)' in the context extended by `a : A'.<br>
<br>
* There is no longer any attempt to solve irrelevant metas by instance<br>
search<br>
<br>
* Constructors of records and datatypes are automatically added to the<br>
instance table<br>
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</blockquote></div><br></div>