[Agda] type of []

[Sergei Meshveliani]

People,

In the proof

take-n-[] : {n : ℕ} → take n [] ≡ []
take-n-[] {0} = refl
take-n-[] {suc _} = refl

Agda cannot derive the type of [].
I can fix the signature in two ways.

(I)
take-n-[] : ∀ {α} {A : Set α} {n} → let []A : List A -- lenghty
[]A = []
in
take n []A ≡ []

(II)
El : ∀ {a} (A : Set a) → A → A -- for common usage
El A x = x --
--
syntax El A x = x ∈: A --

take-n-[] : ∀ {α} {A : Set α} {n} → take n ([] ∈: List A) ≡ []

What is a regular approach, please?

------
Sergei

[Thorsten Altenkirch]

Not sure what is the "regular" way but could you not just supply the implicit argument to [] (or to take)?

take-n-[] : ∀ {α} {A : Set α} {n} → take n ([] {A}) ≡ []

or

take-n-[] : ∀ {α} {A : Set α} {n} → take {A} n [] ≡ []


On 17/04/2018, 13:45, "Agda on behalf of Sergei Meshveliani" <agda-***@lists.chalmers.se on behalf of ***@botik.ru> wrote:

People,

In the proof

take-n-[] : {n : ℕ} → take n [] ≡ []
take-n-[] {0} = refl
take-n-[] {suc _} = refl

Agda cannot derive the type of [].
I can fix the signature in two ways.

(I)
take-n-[] : ∀ {α} {A : Set α} {n} → let []A : List A -- lenghty
[]A = []
in
take n []A ≡ []

(II)
El : ∀ {a} (A : Set a) → A → A -- for common usage
El A x = x --
--
syntax El A x = x ∈: A --

take-n-[] : ∀ {α} {A : Set α} {n} → take n ([] ∈: List A) ≡ []

What is a regular approach, please?

------
Sergei

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[Sergei Meshveliani]

Post by Thorsten Altenkirch
Not sure what is the "regular" way but could you not just supply the implicit argument to [] (or to take)?
take-n-[] : ∀ {α} {A : Set α} {n} → take n ([] {A}) ≡ []
or
take-n-[] : ∀ {α} {A : Set α} {n} → take {A} n [] ≡ []

Thank you.
This is exactly what is needed.
I knew that I was missing some simple point, but just did not recall
that `take' or [] can be given implicit argument!

------
Sergei

Post by Thorsten Altenkirch
People,
In the proof
take-n-[] : {n : ℕ} → take n [] ≡ []
take-n-[] {0} = refl
take-n-[] {suc _} = refl
Agda cannot derive the type of [].
I can fix the signature in two ways.
[..]