[Agda] Overloaded constructor trouble

[Thorsten Altenkirch]

Ok, let’s say I want to show that suc is injective:

open import Relation.Binary.PropositionalEquality
open import Data.Nat

inj-suc : {m n : ℕ} → suc m ≡ suc n → m ≡ n
inj-suc = {!!}

So far so good but at some point I decide to use Fin as well.

open import Relation.Binary.PropositionalEquality
open import Data.Nat
open import Data.Fin

inj-suc : {m n : ℕ} → suc m ≡ suc n → m ≡ n
inj-suc = {!!}

But now things get yellow ☹ Ok agda cannot infer which suc I want to use, even though only one actually works.

This is annoying, especially if you are writing a book and are reluctant to write

inj-suc : {m n : ℕ} → _≡_ {A = ℕ} (suc m) (suc n) → m ≡ n
inj-suc = {!!}

instead (this is ugly).

I have two questions: are there any good workarounds? And is there a way to fix it?

Cheers,
Thorsten



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