[Agda] Agda patterns

[Ulf Norell]

The difference is that you are not allowed to pattern match on datatype
parameters, since they
are not stored in the constructor. In a right-hand side you can give the
parameters to guide the
type checker, but they are thrown out during elaboration.

/ Ulf

On Fri, May 1, 2020 at 10:56 PM Martin Escardo <m.escardo at cs.bham.ac.uk>
wrote:

> Thanks, that works. (https://github.com/agda/agda/issues/4632)
>
> I still wonder why refl {x} and refl {_} {_} {x} behave differently
> according to context.
>
> Best,
> Martin
>
> On 01/05/2020 21:16, ulf.norell at gmail.com wrote:
> > pattern reflpv x = refl {x = x}
> >
> > / Ulf
> >
> >
> > On Fri, May 1, 2020 at 6:39 PM Martin Escardo <m.escardo at cs.bham.ac.uk
> > <mailto:m.escardo at cs.bham.ac.uk>> wrote:
> >
> >     Consider the following, which works:
> >
> >     data _≡_ {ℓ} {X : Set ℓ} : X → X → Set ℓ where
> >         refl : {x : X} → x ≡ x
> >
> >     pattern reflp x = refl {x}
> >     pattern reflv x = refl {_} {_} {x}
> >
> >     J : ∀ {i j} (X : Set i) (A : (x y : X) → x ≡ y → Set j)
> >         → ((x : X) → A x x (reflv x))
> >         → (x y : X) (p : x ≡ y) → A x y p
> >     J X A f x x (reflp x) = f x
> >
> >     The idea is to make the argument of refl explicit if we wish, via the
> >     pattern definition.
> >
> >     However, the patterns behave differently "as patterns" and "as
> values".
> >     For instance, the following doesn't work:
> >
> >     J : ∀ {i j} (X : Set i) (A : (x y : X) → x ≡ y → Set j)
> >         → ((x : X) → A x x (reflp x))  -- error here
> >         → (x y : X) (p : x ≡ y) → A x y p
> >     J X A f x x (reflp x) = f x
> >
> >     This doesn't work either:
> >
> >     J : ∀ {i j} (X : Set i) (A : (x y : X) → x ≡ y → Set j)
> >         → ((x : X) → A x x (reflv x))
> >         → (x y : X) (p : x ≡ y) → A x y p
> >     J X A f x x (reflv x) = f x -- error here
> >
> >     It would be desirable to have a definition that works both as a
> pattern
> >     and as a value. Is that possible?
> >
> >     Thanks,
> >     Martin
> >     _______________________________________________
> >     Agda mailing list
> >     Agda at lists.chalmers.se <mailto:Agda at lists.chalmers.se>
> >     https://lists.chalmers.se/mailman/listinfo/agda
> >
>
> --
> Martin Escardo
> http://www.cs.bham.ac.uk/~mhe
>
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