[Agda] Agda patterns

[Martin Escardo]

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
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-- 
Martin Escardo
http://www.cs.bham.ac.uk/~mhe