Switch maps (and consequently most of the code) to using instances

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

Analysis/Forward/Adapters.agda

@@ -2,14 +2,14 @@ open import Language hiding (_[_])
 open import Lattice
 
 module Analysis.Forward.Adapters
-    {L : Set} {h}
+    (L : Set) {h}
     {_≈ˡ_ : L → L → Set} {_⊔ˡ_ : L → L → L} {_⊓ˡ_ : L → L → L}
-    (isFiniteHeightLatticeˡ : IsFiniteHeightLattice L h _≈ˡ_ _⊔ˡ_ _⊓ˡ_)
-    (≈ˡ-dec : IsDecidable _≈ˡ_)
+    {{isFiniteHeightLatticeˡ : IsFiniteHeightLattice L h _≈ˡ_ _⊔ˡ_ _⊓ˡ_}}
+    {{≈ˡ-dec : IsDecidable _≈ˡ_}}
     (prog : Program) where
 
-open import Analysis.Forward.Lattices isFiniteHeightLatticeˡ ≈ˡ-dec prog
-open import Analysis.Forward.Evaluation isFiniteHeightLatticeˡ ≈ˡ-dec prog
+open import Analysis.Forward.Lattices L prog
+open import Analysis.Forward.Evaluation L prog
 
 open import Data.Empty using (⊥-elim)
 open import Data.String using (String) renaming (_≟_ to _≟ˢ_)
@@ -41,7 +41,7 @@ module ExprToStmtAdapter {{ exprEvaluator : ExprEvaluator }} where
     -- for an assignment, and update the corresponding key. Use Exercise 4.26's
     -- generalized update to set the single key's value.
     private module _ (k : String) (e : Expr) where
-        open VariableValuesFiniteMap.GeneralizedUpdate isLatticeᵛ (λ x → x) (λ a₁≼a₂ → a₁≼a₂) (λ _ → evalᵉ e) (λ _ {vs₁} {vs₂} vs₁≼vs₂ → evalᵉ-Monoʳ e {vs₁} {vs₂} vs₁≼vs₂) (k ∷ [])
+        open VariableValuesFiniteMap.GeneralizedUpdate {{isLatticeᵛ}} (λ x → x) (λ a₁≼a₂ → a₁≼a₂) (λ _ → evalᵉ e) (λ _ {vs₁} {vs₂} vs₁≼vs₂ → evalᵉ-Monoʳ e {vs₁} {vs₂} vs₁≼vs₂) (k ∷ [])
             using ()
             renaming
                 ( f' to updateVariablesFromExpression