Swich AboveBelow to using instances

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

Analysis/Sign.agda

@@ -13,6 +13,7 @@ open import Relation.Nullary using (¬_; yes; no)
 
 open import Language
 open import Lattice
+open import Equivalence
 open import Showable using (Showable; show)
 open import Utils using (_⇒_; _∧_; _∨_)
 import Analysis.Forward
@@ -44,11 +45,19 @@ _≟ᵍ_ 0ˢ + = no (λ ())
 _≟ᵍ_ 0ˢ - = no (λ ())
 _≟ᵍ_ 0ˢ 0ˢ = yes refl
 
-≡-Decidable-Sign : IsDecidable {_} {Sign} _≡_
+instance
-≡-Decidable-Sign = record { R-dec = _≟ᵍ_ }
+    ≡-equiv : IsEquivalence Sign _≡_
+    ≡-equiv = record
+        { ≈-refl = refl
+        ; ≈-sym = sym
+        ; ≈-trans = trans
+        }
+
+    ≡-Decidable-Sign : IsDecidable {_} {Sign} _≡_
+    ≡-Decidable-Sign = record { R-dec = _≟ᵍ_ }
 
 -- embelish 'sign' with a top and bottom element.
-open import Lattice.AboveBelow Sign _≡_ (record { ≈-refl = refl; ≈-sym = sym; ≈-trans = trans }) ≡-Decidable-Sign as AB
+open import Lattice.AboveBelow Sign _ as AB
     using ()
     renaming
         ( AboveBelow to SignLattice

Lattice/AboveBelow.agda

@@ -1,11 +1,12 @@
 open import Lattice
 open import Equivalence
 open import Relation.Nullary using (Dec; ¬_; yes; no)
+open import Data.Unit using () renaming (⊤ to ⊤ᵘ)
 
 module Lattice.AboveBelow {a} (A : Set a)
-                          (_≈₁_ : A → A → Set a)
+                          {_≈₁_ : A → A → Set a}
-                          (≈₁-equiv : IsEquivalence A _≈₁_)
+                          {{≈₁-equiv : IsEquivalence A _≈₁_}}
-                          (≈₁-Decidable : IsDecidable _≈₁_) where
+                          {{≈₁-Decidable : IsDecidable _≈₁_}} (dummy : ⊤ᵘ) where
 
 open import Data.Empty using (⊥-elim)
 open import Data.Product using (_,_)