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author | Helmut Grohne <grohne@cs.uni-bonn.de> | 2014-02-04 10:52:49 +0100 |
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committer | Helmut Grohne <grohne@cs.uni-bonn.de> | 2014-02-04 10:52:49 +0100 |
commit | 20c176d383e59a0345f7425c5f14679906159a59 (patch) | |
tree | a2874cac4922670c6d8e8229c24b56a725c11dda /Bidir.agda | |
parent | 257665f2910296c6e87113d2f7a418e1f83b33f6 (diff) | |
download | bidiragda-20c176d383e59a0345f7425c5f14679906159a59.tar.gz |
add convenience members to PartialVecVec.Get
Diffstat (limited to 'Bidir.agda')
-rw-r--r-- | Bidir.agda | 6 |
1 files changed, 3 insertions, 3 deletions
@@ -128,7 +128,7 @@ lemma-map-denumerate-enumerate (a ∷ as) = cong (_∷_ a) (begin as ∎) where open ≡-Reasoning -theorem-1 : (G : Get) → {i : Setoid.Carrier (Get.I G)} → (s : Vec Carrier (to (Get.gl₁ G) ⟨$⟩ i)) → bff G s (Get.get G s) ≡ just s +theorem-1 : (G : Get) → {i : Get.|I| G} → (s : Vec Carrier (Get.|gl₁| G i)) → bff G s (Get.get G s) ≡ just s theorem-1 G s = begin bff G s (get s) ≡⟨ cong (bff G s ∘ get) (sym (lemma-map-denumerate-enumerate s)) ⟩ @@ -192,7 +192,7 @@ lemma-mapM-successful (x ∷ xs) () | just y | nothing | _ lemma-mapM-successful (x ∷ xs) p | just y | just ys | [ p′ ] with lemma-mapM-successful xs p′ lemma-mapM-successful (x ∷ xs) p | just y | just ys | [ p′ ] | w , pw = y ∷ w , cong (_∷_ (just y)) pw -lemma-get-mapMV : {A B : Set} {f : A → Maybe B} → (G : Get) → {i : Setoid.Carrier (Get.I G)} {v : Vec A (to (Get.gl₁ G) ⟨$⟩ i)} {r : Vec B (to (Get.gl₁ G) ⟨$⟩ i)} → mapMV f v ≡ just r → Get.get G <$> mapMV f v ≡ mapMV f (Get.get G v) +lemma-get-mapMV : {A B : Set} {f : A → Maybe B} → (G : Get) → {i : Get.|I| G} {v : Vec A (Get.|gl₁| G i)} {r : Vec B (Get.|gl₁| G i)} → mapMV f v ≡ just r → Get.get G <$> mapMV f v ≡ mapMV f (Get.get G v) lemma-get-mapMV {f = f} G {v = v} p = let w , pw = lemma-mapM-successful v p in begin get <$> mapMV f v ≡⟨ cong (_<$>_ get) (sym (sequence-map f v)) ⟩ @@ -221,7 +221,7 @@ sequence-cong {S} {m₁ = just x ∷ xs} {m₂ = just y ∷ ys} (just x≈y VecE sequence-cong {S} {m₁ = just x ∷ xs} {m₂ = just y ∷ ys} (just x≈y VecEq.∷-cong xs≈ys) | nothing | nothing | nothing = Setoid.refl (MaybeSetoid (VecISetoid S at _)) sequence-cong {S} (nothing VecEq.∷-cong xs≈ys) = Setoid.refl (MaybeSetoid (VecISetoid S at _)) -theorem-2 : (G : Get) → {i : Setoid.Carrier (Get.I G)} → (v : Vec Carrier (Get.gl₂ G ⟨$⟩ i)) → (s u : Vec Carrier (to (Get.gl₁ G) ⟨$⟩ i)) → bff G s v ≡ just u → VecISetoid A.setoid at _ ∋ Get.get G u ≈ v +theorem-2 : (G : Get) → {i : Get.|I| G} → (v : Vec Carrier (Get.|gl₂| G i)) → (s u : Vec Carrier (Get.|gl₁| G i)) → bff G s v ≡ just u → VecISetoid A.setoid at _ ∋ Get.get G u ≈ v theorem-2 G v s u p with (lemma->>=-just ((flip union (delete-many (Get.get G (enumerate s)) (fromFunc (denumerate s)))) <$> (assoc (Get.get G (enumerate s)) v)) p) theorem-2 G v s u p | h′ , ph′ with (lemma-<$>-just (assoc (Get.get G (enumerate s)) v) ph′) theorem-2 G v s u p | h′ , ph′ | h , ph = drop-just (begin⟨ MaybeSetoid (VecISetoid A.setoid at _) ⟩ |