Termination check on unionWith

Question

I\'m having a problem with termination checking, very similar to the one described in this question and also this Agda bug report/feature request.

The problem is convinc

Answer 1

It seems the first solution proposed for the earlier list-merge question does indeed work here, but only under Agda version 2.3.3+. Here's the full version, with a slightly nicer syntax for ∷.

data FiniteMap (l : Key) : Set (k ⊔ v ⊔ ℓ) where
   [] : FiniteMap l
   _∷[_]_ : (kv : KV) → let k = proj₁ kv in l < k → (m : FiniteMap k) → FiniteMap l

-- Split into two definitions to help the termination checker.
unionWith : ∀ {l} → Op₂ Value → Op₂ (FiniteMap l)
unionWith′ : ∀ {l} → Op₂ Value → (kv : KV) → let k = proj₁ kv in l < k → FiniteMap k → Op₁ (FiniteMap l)

unionWith _ [] [] = []
unionWith _ [] m = m
unionWith _ m [] = m
unionWith _⊕_ ((k , v) ∷[ k _ _ k′ _ _ k′