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Positivity checker
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| module Foo where | |
| open import Level using ( Lift ) | |
| data ℕ : Set where | |
| zero : ℕ | |
| suc : ℕ → ℕ | |
| elimℕ : ∀{ℓ} (P : ℕ → Set ℓ) | |
| (pzero : P zero) | |
| (psuc : (n : ℕ) → P n → P (suc n)) | |
| (n : ℕ) → P n | |
| elimℕ P pzero psuc zero = pzero | |
| elimℕ P pzero psuc (suc n) = psuc n (elimℕ P pzero psuc n) | |
| ℕ∨Xpred₁ : ∀{ℓ} (X : ℕ → Set ℓ) (n : ℕ) → Set ℓ | |
| ℕ∨Xpred₁ X zero = Lift ℕ | |
| ℕ∨Xpred₁ X (suc n) = X n | |
| ℕ∨Xpred₂ : ∀{ℓ} (X : ℕ → Set ℓ) (n : ℕ) → Set ℓ | |
| ℕ∨Xpred₂ {ℓ = ℓ} X = elimℕ (λ _ → Set ℓ) (Lift ℕ) (λ (m : ℕ) (ih : Set ℓ) → X m) | |
| data Foo {ℓ} (n : ℕ) : Set ℓ where | |
| foo₁ : ℕ∨Xpred₁ Foo n → Foo n | |
| foo₂ : ℕ∨Xpred₂ Foo n → Foo n | |
| -- elimℕ (λ _ → Set ℓ) (Lift ℕ) (λ m ih → Foo m) n → Foo n | |
| {- | |
| Foo is not strictly positive, because it occurs in the 4th argument | |
| to elimℕ in the type of the constructor foo₂ in the definition of | |
| Foo. | |
| -} | |
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