Stop using modules in 'Sign' analysis

Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>

Analysis/Sign.agda

@@ -12,9 +12,7 @@ open import Data.Unit using (⊤)
 open import Language
 open import Lattice
 open import Utils using (Pairwise)
-import Lattice.Bundles.FiniteValueMap
+import Lattice.FiniteValueMap
-
-private module FixedHeightFiniteMap = Lattice.Bundles.FiniteValueMap.FromFiniteHeightLattice
 
 data Sign : Set where
     + : Sign
@@ -52,6 +50,8 @@ open import Lattice.AboveBelow Sign _≡_ (record { ≈-refl = refl; ≈-sym = s
 open AB.Plain 0ˢ using ()
     renaming
         ( finiteHeightLattice to finiteHeightLatticeᵍ
+        ; isLattice to isLatticeᵍ
+        ; fixedHeight to fixedHeightᵍ
         ; _≼_ to _≼ᵍ_
         ; _⊔_ to _⊔ᵍ_
         )
@@ -98,45 +98,54 @@ module _ (prog : Program) where
     open Program prog
 
     -- The variable -> sign map is a finite value-map with keys strings. Use a bundle to avoid explicitly specifying operators.
-    open FixedHeightFiniteMap String SignLattice _≟ˢ_ finiteHeightLatticeᵍ vars-Unique ≈ᵍ-dec
+    open Lattice.FiniteValueMap.WithKeys _≟ˢ_ isLatticeᵍ vars
         using ()
         renaming
-            ( finiteHeightLattice to finiteHeightLatticeᵛ
+            ( FiniteMap to VariableSigns
-            ; FiniteMap to VariableSigns
+            ; isLattice to isLatticeᵛ
             ; _≈_ to _≈ᵛ_
             ; _⊔_ to _⊔ᵛ_
-            ; ≈-dec to ≈ᵛ-dec
+            ; _≼_ to _≼ᵛ_
+            ; ≈₂-dec⇒≈-dec to ≈ᵍ-dec⇒≈ᵛ-dec
             ; _∈_ to _∈ᵛ_
             ; _∈k_ to _∈kᵛ_
             ; _updating_via_ to _updatingᵛ_via_
             ; locate to locateᵛ
             )
-    open FiniteHeightLattice finiteHeightLatticeᵛ
+    open IsLattice isLatticeᵛ
         using ()
         renaming
             ( ⊔-Monotonicˡ to ⊔ᵛ-Monotonicˡ
             ; ⊔-Monotonicʳ to ⊔ᵛ-Monotonicʳ
-            ; _≼_ to _≼ᵛ_
-            ; joinSemilattice to joinSemilatticeᵛ
             ; ⊔-idemp to ⊔ᵛ-idemp
             )
+    open Lattice.FiniteValueMap.IterProdIsomorphism.WithUniqueKeysAndFixedHeight _≟ˢ_ isLatticeᵍ vars-Unique ≈ᵍ-dec _ fixedHeightᵍ
+        using ()
+        renaming
+            ( isFiniteHeightLattice to isFiniteHeightLatticeᵛ
+            )
 
-    ⊥ᵛ = proj₁ (proj₁ (proj₁ (FiniteHeightLattice.fixedHeight finiteHeightLatticeᵛ)))
+    ≈ᵛ-dec = ≈ᵍ-dec⇒≈ᵛ-dec ≈ᵍ-dec
+    joinSemilatticeᵛ = IsFiniteHeightLattice.joinSemilattice isFiniteHeightLatticeᵛ
+    fixedHeightᵛ = IsFiniteHeightLattice.fixedHeight isFiniteHeightLatticeᵛ
+    ⊥ᵛ = proj₁ (proj₁ (proj₁ fixedHeightᵛ))
 
     -- Finally, the map we care about is (state -> (variables -> sign)). Bring that in.
-    module StateVariablesFiniteMap = FixedHeightFiniteMap State VariableSigns _≟_ finiteHeightLatticeᵛ states-Unique ≈ᵛ-dec
+    module StateVariablesFiniteMap = Lattice.FiniteValueMap.WithKeys _≟_ isLatticeᵛ states
     open StateVariablesFiniteMap
         using (_[_]; m₁≼m₂⇒m₁[ks]≼m₂[ks])
         renaming
-            ( finiteHeightLattice to finiteHeightLatticeᵐ
+            ( FiniteMap to StateVariables
-            ; FiniteMap to StateVariables
             ; isLattice to isLatticeᵐ
             ; _∈k_ to _∈kᵐ_
             ; locate to locateᵐ
+            ; _≼_ to _≼ᵐ_
             )
-    open FiniteHeightLattice finiteHeightLatticeᵐ
+    open Lattice.FiniteValueMap.IterProdIsomorphism.WithUniqueKeysAndFixedHeight _≟_ isLatticeᵛ states-Unique ≈ᵛ-dec _ fixedHeightᵛ
         using ()
-        renaming (_≼_ to _≼ᵐ_)
+        renaming
+            ( isFiniteHeightLattice to isFiniteHeightLatticeᵛ
+            )
 
     -- build up the 'join' function, which follows from Exercise 4.26's
     --
@@ -195,4 +204,8 @@ module _ (prog : Program) where
             in
                 vs updatingᵛ (k ∷ []) via (λ _ → eval e k∈e⇒k∈vars vs)
 
-    -- module Test = StateVariablesFiniteMap.GeneralizedUpdate states isLatticeᵐ joinAll joinAll-Mono
+    open StateVariablesFiniteMap.GeneralizedUpdate states isLatticeᵐ (λ x → x) (λ a₁≼a₂ → a₁≼a₂) updateForState {!!} states
+        renaming
+            ( f' to updateAll
+            ; f'-Monotonic to updateAll-Mono
+            )

Lattice/AboveBelow.agda

@@ -299,7 +299,7 @@ module Plain (x : A) where
         ; isLattice = isLattice
         }
 
-    open IsLattice isLattice using (_≼_; _≺_) public
+    open IsLattice isLattice using (_≼_; _≺_; ⊔-Monotonicˡ; ⊔-Monotonicʳ) public
 
     ⊥≺[x] : ∀ (x : A) → ⊥ ≺ [ x ]
     ⊥≺[x] x = (≈-refl , λ ())
@@ -343,10 +343,13 @@ module Plain (x : A) where
     isLongest {⊥} (step {_} {[ x ]} _ (≈-lift _) (step [x]≺y y≈z c@(step _ _ _)))
         rewrite [x]≺y⇒y≡⊤ _ _ [x]≺y with ≈-⊤-⊤ ← y≈z = ⊥-elim (¬-Chain-⊤ c)
 
+    fixedHeight : IsLattice.FixedHeight isLattice 2
+    fixedHeight = (((⊥ , ⊤) , longestChain) , isLongest)
+
     isFiniteHeightLattice : IsFiniteHeightLattice AboveBelow 2 _≈_ _⊔_ _⊓_
     isFiniteHeightLattice = record
         { isLattice = isLattice
-        ; fixedHeight = (((⊥ , ⊤) , longestChain) , isLongest)
+        ; fixedHeight = fixedHeight
         }
 
     finiteHeightLattice : FiniteHeightLattice AboveBelow

Lattice/FiniteMap.agda

@@ -128,7 +128,7 @@ module WithKeys (ks : List A) where
         ; absorb-⊓-⊔ = λ (m₁ , _) (m₂ , _) → absorb-⊓ᵐ-⊔ᵐ m₁ m₂
         }
 
-    open IsLattice isLattice using (_≼_) public
+    open IsLattice isLattice using (_≼_; ⊔-Monotonicˡ; ⊔-Monotonicʳ) public
 
     lattice : Lattice FiniteMap
     lattice = record