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Semiring solver (#50)

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Patrick Stevens
2019-10-12 11:14:27 +01:00
committed by GitHub
parent 5af4030361
commit 96d15c6017
7 changed files with 306 additions and 25 deletions
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25
Numbers/Integers/Definition.agda
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@@ -8,28 +8,3 @@ module Numbers.Integers.Definition where
data ℤ : Set where
nonneg : ℕ → ℤ
negSucc : ℕ → ℤ
data ℤSimple : Set where
negativeSucc : (a : ℕ) → ℤSimple
positiveSucc : (a : ℕ) → ℤSimple
zZero : ℤSimple
convertZ : ℤ → ℤSimple
convertZ (nonneg zero) = zZero
convertZ (nonneg (succ x)) = positiveSucc x
convertZ (negSucc x) = negativeSucc x
convertZ' : ℤSimple → ℤ
convertZ' (negativeSucc a) = negSucc a
convertZ' (positiveSucc a) = nonneg (succ a)
convertZ' zZero = nonneg 0
zIsZ : (a : ℤ) → convertZ' (convertZ a) ≡ a
zIsZ (nonneg zero) = refl
zIsZ (nonneg (succ x)) = refl
zIsZ (negSucc x) = refl
zIsZ' : (a : ℤSimple) → convertZ (convertZ' a) ≡ a
zIsZ' (negativeSucc a) = refl
zIsZ' (positiveSucc a) = refl
zIsZ' zZero = refl