Merge branch feature-get-record into feature-partial-getlen

These two features heavily interconnect. As such it makes sense to
integrate them properly. This non-trivial merge does that work. Compared
to feature-partial-getlen a few definitions moved from FreeTheorems.agda
to GetTypes.agda. Many types changed compared to both branches.

Conflicts:
	BFF.agda
	Bidir.agda
	FreeTheorems.agda
	Precond.agda
        conflict in GetTypes.agda not detected by merge

1 files changed, 8 insertions, 6 deletions

diff --git a/Precond.agda b/Precond.agda
index a6f2871..787f010 100644
--- a/Precond.agda
+++ b/Precond.agda
@@ -34,8 +34,9 @@ import CheckInsert
 open CheckInsert (decSetoid deq) using (checkInsert ; lemma-checkInsert-new ; lemma-lookupM-checkInsert-other)
 import BFF
 open import Bidir (decSetoid deq) using (_in-domain-of_ ; lemma-assoc-domain ; lemma-just-sequence)
-
-open BFF.PartialVecBFF (decSetoid deq) using (get-type ; assoc ; enumerate ; denumerate ; bff)
+import GetTypes
+open GetTypes.PartialVecVec using (Get ; module Get)
+open BFF.PartialVecBFF (decSetoid deq) using (assoc ; enumerate ; denumerate ; bff)
 
 lemma-lookup-map-just : {n : ℕ} (f : Fin n) {A : Set} (v : Vec A n) → lookup f (map Maybe.just v) ≡ Maybe.just (lookup f v)
 lemma-lookup-map-just zero    (x ∷ xs) = refl
@@ -73,9 +74,9 @@ lemma-union-delete-fromFunc {n = n} {is = i ∷ is} {h = h} {g = g} ((x , px) Da
           maybe′ just (lookupM i (delete-many is (map just g))) (lookup i h) ∎
         inner f | no f≢i = cong (flip (maybe′ just) (lookup f h)) (lemma-lookupM-delete (delete-many is (map just g)) f≢i)
 
-assoc-enough : {I : Setoid ℓ₀ ℓ₀} → (gl₁ : I ↪ EqSetoid ℕ) → (gl₂ : I ⟶ EqSetoid ℕ) → (get : get-type gl₁ gl₂) → {i : Setoid.Carrier I} → (s : Vec Carrier (to gl₁ ⟨$⟩ i)) → (v : Vec Carrier (gl₂ ⟨$⟩ i)) → ∃ (λ h → assoc (get (enumerate s)) v ≡ just h) → ∃ λ u → bff gl₁ gl₂ get s v ≡ just u
-assoc-enough gl₁ gl₂ get s v (h , p) = let w , pw = lemma-union-delete-fromFunc (lemma-assoc-domain (get s′) v h p) in _ , (begin
-  bff gl₁ gl₂ get s v
+assoc-enough : (G : Get) → {i : Setoid.Carrier (Get.I G)} → (s : Vec Carrier (to (Get.gl₁ G) ⟨$⟩ i)) → (v : Vec Carrier (Get.gl₂ G ⟨$⟩ i)) → ∃ (λ h → assoc (Get.get G (enumerate s)) v ≡ just h) → ∃ λ u → bff G s v ≡ just u
+assoc-enough G s v (h , p) = let w , pw = lemma-union-delete-fromFunc (lemma-assoc-domain (get s′) v h p) in _ , (begin
+  bff G s v
     ≡⟨ cong (flip _>>=_ (flip mapMV s′ ∘ flip lookupM) ∘ _<$>_ (flip union g′)) p ⟩
   mapMV (flip lookupM (union h g′)) s′
     ≡⟨ sym (sequence-map (flip lookupM (union h g′)) s′) ⟩
@@ -88,7 +89,8 @@ assoc-enough gl₁ gl₂ get s v (h , p) = let w , pw = lemma-union-delete-fromF
   sequenceV (map Maybe.just (map (flip lookup w) s′))
     ≡⟨ lemma-just-sequence (map (flip lookup w) s′) ⟩
   just (map (flip lookup w) s′) ∎)
-  where s′ = enumerate s
+  where open Get G
+        s′ = enumerate s
         g  = fromFunc (denumerate s)
         g′ = delete-many (get s′) g