diff options
Diffstat (limited to 'src')
| -rw-r--r-- | src/Helium/Data/BitVec/Properties.agda | 32 |
1 files changed, 32 insertions, 0 deletions
diff --git a/src/Helium/Data/BitVec/Properties.agda b/src/Helium/Data/BitVec/Properties.agda index 53d6228..8094f97 100644 --- a/src/Helium/Data/BitVec/Properties.agda +++ b/src/Helium/Data/BitVec/Properties.agda @@ -384,3 +384,35 @@ xor-distribʳ-not (x ∷ xs) (y ∷ ys) = cong₂ _∷_ (bxor-distribʳ-not x y) { 0# → refl ; 1# → refl }) + + +-- Conversions + +-- bitToFin and finToBit + +bitToFin-finToBit : ∀ x → bitToFin (finToBit x) ≡ x +bitToFin-finToBit zero = refl +bitToFin-finToBit (suc zero) = refl + +finToBit-bitToFin : ∀ x → finToBit (bitToFin x) ≡ x +finToBit-bitToFin 0# = refl +finToBit-bitToFin 1# = refl + +-- toFin and fromFin + +fromFin-toFin : ∀ xs → fromFin {n} (toFin {n} xs) ≡ xs +fromFin-toFin [] = refl +fromFin-toFin {suc n} (x ∷ xs) with quotRem {2} (2 ^ n) (combine (bitToFin x) (toFin xs)) | remQuot-combine (bitToFin x) (toFin xs) +... | .(toFin xs) , .(bitToFin x) | refl = cong₂ _∷_ (finToBit-bitToFin x) (fromFin-toFin xs) + +toFin-fromFin : ∀ x → toFin {n} (fromFin x) ≡ x +toFin-fromFin {zero} zero = refl +toFin-fromFin {suc n} x = begin + combine (bitToFin (finToBit (proj₁ rq))) (toFin (fromFin {n} (proj₂ rq))) ≡⟨ eq₁ ⟩ + combine (proj₁ rq) (proj₂ rq) ≡⟨ combine-remQuot (2 ^ n) x ⟩ + x ∎ + where + open ≡-Reasoning + rq = remQuot {2} (2 ^ n) x + eq₁ = cong₂ combine (bitToFin-finToBit (proj₁ rq)) (toFin-fromFin {n} (proj₂ rq)) + |