[Agda] Agda patterns

[Ulf Norell]

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>
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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