[Agda] list equality decision procedure fails termination check with Agda 2.4.0.1?

[Dan Licata]

great! is there a way to explain what the restriction is?  Has Coq fixed this bug yet, and if so, how does your solution compare to theirs?

-Dan

On Jun 27, 2014, at 12:26 PM, Jesper Cockx <Jesper at sikanda.be> wrote:

> Yes, this restriction is to address the incompatibility of the termination checker with univalence. As a side-effect, many functions on universes no longer pass the termination check, for example (by Andreas):
> T : Bool -> Set
> T true = Nat
> T false = List Nat
> 
> f : (x : Bool) -> T x -> Set
> f true zero = Nat
> f true (suc x) = f true x
> f false nil = Nat
> f false (x :: xs) = f false xs
> For the moment, such definitions have to be unfolded manually:
> f : (x : Bool) -> T x -> Set
> f true = ftrue
>   where
>     ftrue : Nat -> Set
>     ftrue zero = Nat
>     ftrue (suc x) = ftrue x
> f false = ffalse
>   where
>     ffalse : List Nat -> Set
>     ffalse nil = Nat
>     ffalse (x :: xs) = ffalse xs
> However, due to a mistake I made in the fix, the termination checker a complains much more than necessary when --without-K is enabled. This has now been fixed in the development version: https://code.google.com/p/agda/issues/detail?id=1214&can=1. I'll check the other errors in Nils' library later. If you have any specific examples that you think should be accepted, please send them to me and I'll see what I can do.
> 
> Jesper
> 
> 
> On Fri, Jun 27, 2014 at 6:52 AM, Dan Licata <dlicata at wesleyan.edu> wrote:
> Is this restriction addressing the "termination checker + propositional univalence inconsistency" issue, or something else?
> 
> -Dan
> 
> On Jun 21, 2014, at 1:44 PM, Jesper Cockx <Jesper at sikanda.be> wrote:
> 
>> I suppose by 'people working on this issue', you mean Andreas and me? I'm not currently working on this problem, but I could be convinced to if the current hack turns out to be too inconvenient. However, I have two problems before I can start working on a fix:
>> 
>> - The current theory of pattern matching doesn't allow induction on 'deep' arguments, i.e. ones that only get an inductive type after pattern matching on some other arguments. So the theory would have to be extended.
>> 
>> - I don't have a lot of experience with the termination checker, so I'm not confident to mess with it. It seems that in order to fix this problem, the termination checker would need some type information, as well as information about the substitutions performed by the previous case splits.
>> 
>> If anyone can help me with (one of) these problems, I'd like to work together on it. Otherwise I'll try to get a better understanding by myself, but then it might take a long time.
>> 
>> Jesper
>> 
>> 
>> On Fri, Jun 20, 2014 at 7:13 PM, Andrés Sicard-Ramírez <asr at eafit.edu.co> wrote:
>> 
>> On 20 June 2014 09:07, Brent Yorgey <byorgey at seas.upenn.edu> wrote:
>> but is the code I linked now expected to
>> fail termination checking?
>> 
>> Using the --without-K option? I don't know. This is an open issue and
>> people working on this issue know that the current behaviour is too
>> restrictive. I don't know if they are working in a better solution
>> right now.
>> 
>> -- 
>> Andrés
>> 
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