[Agda] list equality decision procedure fails termination check
with Agda 2.4.0.1?
Jesper Cockx
Jesper at sikanda.be
Sun Jul 13 15:35:55 CEST 2014
Maxime: To be honest, I'm not sure what the intuition behind my fix is
either. However, it is exactly what I need in order to apply structural
recursion in my translation of pattern matching to eliminators (see
http://people.cs.kuleuven.be/~jesper.cockx/Without-K/Pattern-matching-without-K.pdf).
I'm afraid I don't really understand your criterion for Coq either. I
thought univalence was only proven sound in combination with the standard
eliminators, and not with sized types?
Dan: Your examples are instances of issue 59 (
https://code.google.com/p/agda/issues/detail?id=59), which was fixed by
inlining "with" and "rewrite" for the purpose of termination checking.
However, at least for "rewrite" this inlining actually did bad things when
--without-K was enabled. For example, the following was accepted in 2.3.2:
==================================================
{-# OPTIONS --without-K #-}
open import Relation.Binary.PropositionalEquality
data Zero : Set where
data WOne : Set where wrap : (Zero → WOne) → WOne
FOne = Zero → WOne
postulate
iso : WOne ≡ FOne
foo : WOne → Zero
foo (wrap f) rewrite (sym iso) = foo f
BOOM : Zero
BOOM = foo (wrap (λ ()))
==================================================
I'm not sure if the inlining of "with" also causes problems, but on the
other hand I don't have a proof that it is sound either. So I decided to
disable the inlining entirely (when --without-K is enabled). It would be
interesting to take a look at the desuraging of "with" by Agda to see how
they differ from your manual desugaring. Does anyone know if this is
possible?
Jesper
On Wed, Jul 9, 2014 at 11:43 PM, Dan Licata <drl at cs.cmu.edu> wrote:
> Hi Jesper,
>
> Today I got the development version of Agda. There are some examples that
> I think should work. They termination-check with without-K turned off but
> not with it on.
>
> See the functions tagged with
> NO_TERMINATION_CHECK
>
> in
>
> https://github.com/dlicata335/hott-agda/blob/master/lib/Int.agda
>
> https://github.com/dlicata335/hott-agda/blob/master/lib/loopspace/Truncation.agda
>
> One issue seems to have to do with absurd patterns; for example, if I do
> something like this (TLevel's are like natural numbers, with -2 being like
> 0, so S - is not less than it)
>
> foo : {C : _} (x y : TLevel) -> x <tl y -> C
> foo (S x) (S y) lt = foo x y {!!}
> foo (S y) -2 lt with lt
> foo (S y) -2 lt | ()
> foo _ _ _ = {!!}
>
> then the clause with the absurd pattern fails the termination checker (?).
>
> Another seems to have something to do with 'with'; e.g. a function
>
> 1<=pos : (p : Positive) → tl 1 <=tl (tlp p)
> 1<=pos One = Inr id
> 1<=pos (S n) with 1<=pos n
> ... | Inl lt = Inl (ltSR lt)
> ... | Inr eq = transport (λ x → tl 1 <=tl S x) eq (Inl ltS)
>
> which is clearly structural recursive on p fails. But if I write out the
> 'with' explicitly it's fine.
>
> I think I could get all of these to pass by writing out the 'with's
> explicitly, but perhaps there is a way to change the termination checker so
> that it accepts them?
>
> -Dan
>
> On Jul 1, 2014, at 12:59 PM, Dan Licata <dlicata at wesleyan.edu> wrote:
>
> > Hi Jesper,
> >
> > Thanks for the nice explanation! I don't think this restriction should
> be much of an issue for HoTT, because we tend to stick closer to the
> eliminators (e.g. for higher inductives that's all we know how to do), so
> in the examples I can think of ftrue/ffalse are already applications of
> eliminators, rather than direct recursive calls.
> >
> > I'll try my library on it next time I have a chance to upgrade agda.
> >
> > -Dan
> >
> >
> > On Jul 1, 2014, at 12:00 AM, Jesper Cockx <Jesper at sikanda.be> wrote:
> >
> >> The current restriction is quite simple: for a function to be
> >> structurally recursive on an argument x of type T, the type T must be
> >> a data type *before* any matching has been done. In particular, this
> >> prohibits structural recursion on 'deep' arguments and universe-like
> >> constructions such as the one in my previous mail. I don't know what
> >> the current situation is on the Coq side of things, maybe someone else
> >> can clarify?
> >>
> >> Jesper
> >>
> >> On 6/30/14, Dan Licata <dlicata at wesleyan.edu> wrote:
> >>> 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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> >>>>>
> >>>>>
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> >>>>
> >>>>
> >>>
> >>>
> >
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