Parameterize FiniteMap by its keys right away

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

Lattice/FiniteMap.agda

@@ -9,10 +9,10 @@ module Lattice.FiniteMap (A : Set) (B : Set)
     {_≈₂_ : B → B → Set}
     {_⊔₂_ : B → B → B} {_⊓₂_ : B → B → B}
     {{≡-Decidable-A : IsDecidable {_} {A} _≡_}}
-    {{lB : IsLattice B _≈₂_ _⊔₂_ _⊓₂_}} (dummy : ⊤) where
+    {{lB : IsLattice B _≈₂_ _⊔₂_ _⊓₂_}} (ks : List A) where
 
 open IsLattice lB using () renaming (_≼_ to _≼₂_)
-open import Lattice.Map A B dummy as Map
+open import Lattice.Map A B _ as Map
     using
         ( Map
         ; ⊔-equal-keys
@@ -74,7 +74,7 @@ open import Showable using (Showable; show)
 open import Isomorphism using (IsInverseˡ; IsInverseʳ)
 open import Chain using (Height)
 
-module WithKeys (ks : List A) where
+private module WithKeys (ks : List A) where
     FiniteMap : Set
     FiniteMap = Σ Map (λ m → Map.keys m ≡ ks)
 
@@ -131,7 +131,7 @@ module WithKeys (ks : List A) where
 
     []-∈ : ∀ {k : A} {v : B} {ks' : List A} (fm : FiniteMap) →
            k ∈ˡ ks' → (k , v) ∈ fm → v ∈ˡ (fm [ ks' ])
-    []-∈ {k} {v} {ks'} (m , _) k∈ks' k,v∈fm = []ᵐ-∈ m k,v∈fm k∈ks' 
+    []-∈ {k} {v} {ks'} (m , _) k∈ks' k,v∈fm = []ᵐ-∈ m k,v∈fm k∈ks'
 
     ≈-equiv : IsEquivalence FiniteMap _≈_
     ≈-equiv = record
@@ -253,9 +253,8 @@ module WithKeys (ks : List A) where
     ...   | yes k∈km₁ | no k∉km₂ = ⊥-elim (∈k-exclusive fm₁ fm₂ (k∈km₁ , k∉km₂))
     ...   | no k∉km₁ | yes k∈km₂ = ⊥-elim (∈k-exclusive fm₂ fm₁ (k∈km₂ , k∉km₁))
 
-open WithKeys public
-
 module IterProdIsomorphism where
+    open WithKeys
     open import Data.Unit using (tt)
     open import Lattice.Unit using ()
         renaming
@@ -267,7 +266,7 @@ module IterProdIsomorphism where
             ; ≈-equiv to ≈ᵘ-equiv
             ; fixedHeight to fixedHeightᵘ
             )
-    open import Lattice.IterProd B ⊤ dummy
+    open import Lattice.IterProd B ⊤ _
         as IP
         using (IterProd)
     open IsLattice lB using ()
@@ -631,3 +630,5 @@ module IterProdIsomorphism where
         ⊥-contains-bottoms {k} {v} k,v∈⊥
             rewrite IP.⊥-built {length ks} {{fhB = fixedHeightᵘ}} =
             to-build uks k v k,v∈⊥
+
+open WithKeys ks public