Agda: rewrite subexpression

Question

I'm trying to prove:

AddTodoSetsNewCompletedToFalse :
  ∀ {n : ℕ} (todos : Vec Todo (1 + n)) (text : String) →
    Todo.completed (last (AddTodo todos text)) ≡ false
AddTodoSetsNewCompletedToFalse todos text = ?

where

AddTodoLastAddedElementIsTodo :
  ∀ {a} {A : Set a} {n} (todos : Vec Todo n) (text : String) →
    last (AddTodo todos text) ≡ 
      record
        { id        = 1
        ; completed = false
        ; text      = text
        }
AddTodoLastAddedElementIsTodo todos text = vecLast todos

and

vecLast : ∀ {a} {A : Set a} {l n} (xs : Vec A n) → last (xs ∷ʳ l) ≡ l
vecLast []       = refl
vecLast (_ ∷ xs) = P.trans (prop (xs ∷ʳ _)) (vecLast xs)
  where
    prop : ∀ {a} {A : Set a} {n x} (xs : Vec A (suc n)) → last (x ∷ xs) ≡ last xs
    prop xs with initLast xs
    ...        | _ , _ , refl = refl

I tried using rewrite and got:

AddTodoSetsNewCompletedToFalse :
  ∀ {a} {A : Set a} {n} (todos : Vec Todo n) (text : String) →
    Todo.completed (last (AddTodo todos text)) ≡ false
AddTodoSetsNewCompletedToFalse todos text rewrite AddTodoLastAddedElementIsTodo todos text = refl

but the error:

_a_100 : Agda.Primitive.Level

showed up.

I'm not sure how to resolve this. from here I understand that this is related to the implicit argument. But not sure how to fix it

This sort of error indicates an unsolved metavariable, which means that Agda has failed to infer an implicit argument

Thanks!

score 0 · Accepted Answer · answered Oct 23 '20 at 13:14

You do not use A for anything in the type of AddTodoSetsNewCompletedToFalse. Also, that is not an error, but an unsolved meta.

So what happens is that wherever you use AddTodoSetsNewCompletedToFalse, nothing in the arguments or the result type constrains the choice of A (and, subsequently, a) so the unifier has no way of solving these metavariables. You can make explicit what happens by writing AddTodoSetsNewCompletedToFalse {a = _} {A = _} and observing that these two metas are unsolved.

You should simply remove the first two parameters (a and A) from AddTodoSetsNewCompletedToFalse's type.

Agda: rewrite subexpression

1 Answers1