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

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

Analysis/Sign.agda

@@ -52,7 +52,6 @@ open import Lattice.AboveBelow Sign _≡_ (record { ≈-refl = refl; ≈-sym = s
     using ()
     renaming
         ( AboveBelow to SignLattice
-        ; ≈-Decidable to ≈ᵍ-Decidable
         ; ⊥ to ⊥ᵍ
         ; ⊤ to ⊤ᵍ
         ; [_] to [_]ᵍ
@@ -72,10 +71,7 @@ open AB.Plain 0ˢ using ()
         ; _⊓_ to _⊓ᵍ_
         )
 
-open IsLattice isLatticeᵍ using ()
-    renaming
-        ( ≼-trans to ≼ᵍ-trans
-        )
+open IsLattice isLatticeᵍ using () renaming (≼-trans to ≼ᵍ-trans)
 
 plus : SignLattice → SignLattice → SignLattice
 plus ⊥ᵍ _ = ⊥ᵍ
@@ -175,9 +171,9 @@ instance
 module WithProg (prog : Program) where
     open Program prog
 
-    open import Analysis.Forward.Lattices isFiniteHeightLatticeᵍ ≈ᵍ-Decidable prog
-    open import Analysis.Forward.Evaluation isFiniteHeightLatticeᵍ ≈ᵍ-Decidable prog
-    open import Analysis.Forward.Adapters isFiniteHeightLatticeᵍ ≈ᵍ-Decidable prog
+    open import Analysis.Forward.Lattices SignLattice prog
+    open import Analysis.Forward.Evaluation SignLattice prog
+    open import Analysis.Forward.Adapters SignLattice prog
 
     eval : ∀ (e : Expr) → VariableValues → SignLattice
     eval (e₁ + e₂) vs = plus (eval e₁ vs) (eval e₂ vs)
@@ -233,7 +229,7 @@ module WithProg (prog : Program) where
         SignEval = record { eval = eval; eval-Monoʳ = eval-Monoʳ }
 
     -- For debugging purposes, print out the result.
-    output = show (Analysis.Forward.WithProg.result isFiniteHeightLatticeᵍ ≈ᵍ-Decidable prog)
+    output = show (Analysis.Forward.WithProg.result SignLattice prog)
 
     -- This should have fewer cases -- the same number as the actual 'plus' above.
     -- But agda only simplifies on first argument, apparently, so we are stuck