[Agda] I'm not sure... case for the constructor ..., because
I get stuck when trying to solve...
Andreas Abel
abela at chalmers.se
Sat Dec 6 13:21:40 CET 2014
Unfortunately, the order of arguments in the constructor matters for the
coverage checker in such delicate cases. I filed an issue derived from
your problem:
https://code.google.com/p/agda/issues/detail?id=1384
If you take look there, putting the equality proof in the constructor
earlier works.
Ideally, every program that is generated by subsequent splits (C-c C-c)
should be accepted by Agda. Unfortunately, in the resulting code the
split order is no longer visible, and Agda tries to guess an order that
works. It does not always.
Sorry, at the moment you are forced to try and error. Agda logging can
be enabled with the -v option, but I am afraid the logs only make sense
if you read the source code side by side. There is no user-friendly log
where Agda gives an executive summary of what it did. (Contributions
welcome!)
Note that sets of clauses that do not cover all cases are making the
problem for the coverage checker even harder! This is why you get the
failure when you comment-out the catch-all.
The following snippet of the CHANGELOG gives a hint on the strategy of
the coverage checker:
* Improved coverage checker. The coverage checker splits on
arguments that have constructor or literal pattern, committing
to the left-most split that makes progress.
Consider the lookup function for vectors:
data Fin : Nat → Set where
zero : {n : Nat} → Fin (suc n)
suc : {n : Nat} → Fin n → Fin (suc n)
data Vec (A : Set) : Nat → Set where
[] : Vec A zero
_∷_ : {n : Nat} → A → Vec A n → Vec A (suc n)
_!!_ : {A : Set}{n : Nat} → Vec A n → Fin n → A
(x ∷ xs) !! zero = x
(x ∷ xs) !! suc i = xs !! i
In Agda up to 2.3.0, this definition is rejected unless we add
an absurd clause
[] !! ()
This is because the coverage checker committed on splitting
on the vector argument, even though this inevitably lead to
failed coverage, because a case for the empty vector [] is missing.
The improvement to the coverage checker consists on committing
only on splits that have a chance of covering, since all possible
constructor patterns are present. Thus, Agda will now split
first on the Fin argument, since cases for both zero and suc are
present. Then, it can split on the Vec argument, since the
empty vector is already ruled out by instantiating n to a suc _.
On 06.12.2014 12:03, Dmytro Starosud wrote:
> Sorry :)
> One more issue. Please see another gist
> https://gist.github.com/dima-starosud/f27ffd54895822a7db03
> Here I (hopefully) did as you proposed.
> But I still able to make Agda showing that annoying unification problem
> error message.
>
> Looks like the problem is related to totality checker?
> I think the real cause is simply shadowed?
>
> Please help me understating this.
> Is there any way to enable Agda logging or something else to see what
> happens behind the scene?
>
> Thanks a lot,
> Dmytro
>
>
> 2014-12-06 12:37 GMT+02:00 Dmytro Starosud <d.starosud at gmail.com
> <mailto:d.starosud at gmail.com>>:
>
> ...and one more question.
>
> How the way you are proposing differs from "reduce₃"?
>
> Does not "reduce₃" turn non-pattern indexes to good one?
> Since as you can see "reduce₂" doesn't produce error messages.
>
> Thanks,
> Dmytro
>
>
> 2014-12-06 12:28 GMT+02:00 Dmytro Starosud <d.starosud at gmail.com
> <mailto:d.starosud at gmail.com>>:
>
> Thanks, Andreas,
>
> I had a kind of similar thoughts, but needed confirmation.
> So, the rule is "do not use functional dependencies as a family
> indexes, but just constructors".
> Please correct if this is not accurate statement.
>
> What is the root cause (I mean what difficulties in
> compiler/theory) which sometimes doesn't allow solving such
> unification problems?
>
> Thanks a lot,
> Dmytro
>
>
> 2014-12-06 10:57 GMT+02:00 Andreas Abel <abela at chalmers.se
> <mailto:abela at chalmers.se>>:
>
> The problem is that you are indexing your family Term by
> non-patterns in some of the constructor cases. Then Agda
> can sometimes not solve the unification constraints involved
> in dependent pattern matching, and gives up or produces
> error messages. The solution is to use explicit proofs of
> equality in your constructors instead.
>
> Here is a cut-down version of your plight:
>
> module _ where
>
> open import Data.Bool
> open import Relation.Binary.__PropositionalEquality
>
> module NonPatternFamily where
>
> data Term : Bool → Set where
> I : Term false
> App : (a b : Bool) → Term a → Term b → Term (a ∨ b)
> -- Non-pattern in target of App
> -- _∨_ is a defined function, not a constructor.
>
> fails : Term false → Set
> fails (App false false I x) = Bool
> fails _ = Bool
>
> -- a ∨ b != false of type Bool
> -- when checking that the pattern App false false I x has
> type
> -- Term false
>
> -- Radical fix: no index to Term, just parameter:
>
> module JustData where
>
> -- Version with no indices at all, only parameters.
>
> data Term (i : Bool) : Set where
> I : i ≡ false → Term i
> App : (a b : Bool) → i ≡ a ∨ b → Term a → Term b → Term i
>
> test : Term false → Set
> test (App false false refl (I refl) x) = Bool
> test _ = Bool
>
> -- Moderate fix: retain the index in harmless (pattern case).
>
> module PatternFamily where
>
> -- Version with index,
> -- but using equality when non-pattern index would be needed.
>
> data Term : (i : Bool) → Set where
> I : Term false
> App : (i a b : Bool) → i ≡ a ∨ b → Term a → Term b → Term i
>
> test : Term false → Set
> test (App .false false false refl I x) = Bool
> test _ = Bool
>
> Hope that helps,
> Andreas
>
>
>
> On 05.12.2014 22:47, Dmytro Starosud wrote:
>
> Hello guys,
>
> I am trying to write a function on indexed types:
> https://gist.github.com/dima-__starosud/7100947b0e243ea6a034
> <https://gist.github.com/dima-starosud/7100947b0e243ea6a034>
> But I cannot understand the reason of the error messages
> shown, and how
> to solve issues arisen.
>
> Please see a gist (link above).
> Ideally I wanted "reduce₁". But that didn't compile.
> (And I think I can
> imagine the reason why)
>
> Next attempt was "reduce₂". But this would involve a lot
> of unnecessary
> code on RHSs.
>
> Than I decided to improve it and got "reduce₃", but it
> gave me
> completely puzzling error message.
>
> Please help me to understand all that stuff Agda
> communicates to me.
>
> I would like something really simple (like "reduce₁"),
> probably with
> help of *pattern*s.
>
> Thanks in advance,
> Dmytro
>
>
>
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> --
> Andreas Abel <>< Du bist der geliebte Mensch.
>
> Department of Computer Science and Engineering
> Chalmers and Gothenburg University, Sweden
>
> andreas.abel at gu.se <mailto:andreas.abel at gu.se>
> http://www2.tcs.ifi.lmu.de/~__abel/
> <http://www2.tcs.ifi.lmu.de/~abel/>
>
>
>
>
--
Andreas Abel <>< Du bist der geliebte Mensch.
Department of Computer Science and Engineering
Chalmers and Gothenburg University, Sweden
andreas.abel at gu.se
http://www2.tcs.ifi.lmu.de/~abel/
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