jozefg 2014-07-02 03:07:59.388021 UTC
| 1 | module teaching where |
| 2 | open import Data.Nat |
| 3 | open import Data.Empty |
| 4 | open import Data.Product |
| 5 | open import Relation.Binary.PropositionalEquality |
| 6 | open import Relation.Nullary |
| 7 | |
| 8 | postulate unsafeDiv : ℕ → ℕ → ℕ |
| 9 | |
| 10 | div : (top bot : ℕ) → ¬ (bot ≡ 0) → ℕ |
| 11 | div top zero p = ⊥-elim (p refl) -- The absurd case |
| 12 | div top (suc bot) p = unsafeDiv top (suc bot) -- The normal case |
| 13 | |
| 14 | |
| 15 | -- Some example usages |
| 16 | |
| 17 | obviously-not-zero : {n : ℕ} → ¬ (suc n ≡ 0) |
| 18 | obviously-not-zero () -- The proof is trivial |
| 19 | |
| 20 | test : ℕ |
| 21 | test = div 5 2 obviously-not-zero |
| 22 | |
| 23 | test2 : ℕ |
| 24 | test2 = div 0 2 obviously-not-zero |
| 25 | |
| 26 | test3 : ℕ |
| 27 | test3 = div 1 6 obviously-not-zero |