Make 'IsDecidable' into a record to aid instance search

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

Analysis/Sign.agda

@@ -7,6 +7,7 @@ open import Data.Sum using (inj₁; inj₂)
 open import Data.Empty using (⊥; ⊥-elim)
 open import Data.Unit using (⊤; tt)
 open import Data.List.Membership.Propositional as MemProp using () renaming (_∈_ to _∈ˡ_)
+open import Relation.Binary.Definitions using (Decidable)
 open import Relation.Binary.PropositionalEquality using (_≡_; refl; sym; trans; subst)
 open import Relation.Nullary using (¬_; yes; no)
 
@@ -32,7 +33,7 @@ instance
         }
 
 -- g for siGn; s is used for strings and i is not very descriptive.
-_≟ᵍ_ : IsDecidable (_≡_ {_} {Sign})
+_≟ᵍ_ : Decidable (_≡_ {_} {Sign})
 _≟ᵍ_ + + = yes refl
 _≟ᵍ_ + - = no (λ ())
 _≟ᵍ_ + 0ˢ = no (λ ())
@@ -43,12 +44,15 @@ _≟ᵍ_ 0ˢ + = no (λ ())
 _≟ᵍ_ 0ˢ - = no (λ ())
 _≟ᵍ_ 0ˢ 0ˢ = yes refl
 
+≡-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 }) _≟ᵍ_ as AB
+open import Lattice.AboveBelow Sign _≡_ (record { ≈-refl = refl; ≈-sym = sym; ≈-trans = trans }) ≡-Decidable-Sign as AB
     using ()
     renaming
         ( AboveBelow to SignLattice
-        ; ≈-dec to ≈ᵍ-dec
+        ; ≈-Decidable to ≈ᵍ-Decidable
         ; ⊥ to ⊥ᵍ
         ; ⊤ to ⊤ᵍ
         ; [_] to [_]ᵍ
@@ -171,9 +175,9 @@ instance
 module WithProg (prog : Program) where
     open Program prog
 
-    open import Analysis.Forward.Lattices isFiniteHeightLatticeᵍ ≈ᵍ-dec prog
-    open import Analysis.Forward.Evaluation isFiniteHeightLatticeᵍ ≈ᵍ-dec prog
-    open import Analysis.Forward.Adapters isFiniteHeightLatticeᵍ ≈ᵍ-dec 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
 
     eval : ∀ (e : Expr) → VariableValues → SignLattice
     eval (e₁ + e₂) vs = plus (eval e₁ vs) (eval e₂ vs)
@@ -229,7 +233,7 @@ 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-dec prog)
+    output = show (Analysis.Forward.WithProg.result isFiniteHeightLatticeᵍ ≈ᵍ-Decidable 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