Rewrite Forward analysis to use statement-based evaluators.

To keep old (expression-based) analyses working, switch to using
instance search and provide "adapters" that auto-construct statement
analyzers from expression analyzers.

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

Analysis/Sign.agda

@@ -62,7 +62,7 @@ open import Lattice.AboveBelow Sign _≡_ (record { ≈-refl = refl; ≈-sym = s
 open AB.Plain 0ˢ using ()
     renaming
         ( isLattice to isLatticeᵍ
-        ; fixedHeight to fixedHeightᵍ
+        ; isFiniteHeightLattice to isFiniteHeightLatticeᵍ
         ; _≼_ to _≼ᵍ_
         ; _⊔_ to _⊔ᵍ_
         ; _⊓_ to _⊓ᵍ_
@@ -171,8 +171,9 @@ instance
 module WithProg (prog : Program) where
     open Program prog
 
-    module ForwardWithProg = Analysis.Forward.WithProg (record { isLattice = isLatticeᵍ; fixedHeight = fixedHeightᵍ }) ≈ᵍ-dec prog
-    open ForwardWithProg hiding (analyze-correct)
+    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
 
     eval : ∀ (e : Expr) → VariableValues → SignLattice
     eval (e₁ + e₂) vs = plus (eval e₁ vs) (eval e₂ vs)
@@ -184,8 +185,8 @@ module WithProg (prog : Program) where
     eval (# 0) _ = [ 0ˢ ]ᵍ
     eval (# (suc n')) _ = [ + ]ᵍ
 
-    eval-Mono : ∀ (e : Expr) → Monotonic _≼ᵛ_ _≼ᵍ_ (eval e)
-    eval-Mono (e₁ + e₂) {vs₁} {vs₂} vs₁≼vs₂ =
+    eval-Monoʳ : ∀ (e : Expr) → Monotonic _≼ᵛ_ _≼ᵍ_ (eval e)
+    eval-Monoʳ (e₁ + e₂) {vs₁} {vs₂} vs₁≼vs₂ =
         let
             -- TODO: can this be done with less boilerplate?
             g₁vs₁ = eval e₁ vs₁
@@ -195,9 +196,9 @@ module WithProg (prog : Program) where
         in
             ≼ᵍ-trans
                 {plus g₁vs₁ g₂vs₁} {plus g₁vs₂ g₂vs₁} {plus g₁vs₂ g₂vs₂}
-                (plus-Monoˡ g₂vs₁ {g₁vs₁} {g₁vs₂} (eval-Mono e₁ {vs₁} {vs₂} vs₁≼vs₂))
-                (plus-Monoʳ g₁vs₂ {g₂vs₁} {g₂vs₂} (eval-Mono e₂ {vs₁} {vs₂} vs₁≼vs₂))
-    eval-Mono (e₁ - e₂) {vs₁} {vs₂} vs₁≼vs₂ =
+                (plus-Monoˡ g₂vs₁ {g₁vs₁} {g₁vs₂} (eval-Monoʳ e₁ {vs₁} {vs₂} vs₁≼vs₂))
+                (plus-Monoʳ g₁vs₂ {g₂vs₁} {g₂vs₂} (eval-Monoʳ e₂ {vs₁} {vs₂} vs₁≼vs₂))
+    eval-Monoʳ (e₁ - e₂) {vs₁} {vs₂} vs₁≼vs₂ =
         let
             -- TODO: here too -- can this be done with less boilerplate?
             g₁vs₁ = eval e₁ vs₁
@@ -207,9 +208,9 @@ module WithProg (prog : Program) where
         in
             ≼ᵍ-trans
                 {minus g₁vs₁ g₂vs₁} {minus g₁vs₂ g₂vs₁} {minus g₁vs₂ g₂vs₂}
-                (minus-Monoˡ g₂vs₁ {g₁vs₁} {g₁vs₂} (eval-Mono e₁ {vs₁} {vs₂} vs₁≼vs₂))
-                (minus-Monoʳ g₁vs₂ {g₂vs₁} {g₂vs₂} (eval-Mono e₂ {vs₁} {vs₂} vs₁≼vs₂))
-    eval-Mono (` k) {vs₁@((kvs₁ , _) , _)} {vs₂@((kvs₂ , _), _)} vs₁≼vs₂
+                (minus-Monoˡ g₂vs₁ {g₁vs₁} {g₁vs₂} (eval-Monoʳ e₁ {vs₁} {vs₂} vs₁≼vs₂))
+                (minus-Monoʳ g₁vs₂ {g₂vs₁} {g₂vs₂} (eval-Monoʳ e₂ {vs₁} {vs₂} vs₁≼vs₂))
+    eval-Monoʳ (` k) {vs₁@((kvs₁ , _) , _)} {vs₂@((kvs₂ , _), _)} vs₁≼vs₂
         with ∈k-decᵛ k kvs₁ | ∈k-decᵛ k kvs₂
     ...   | yes k∈kvs₁ | yes k∈kvs₂ =
             let
@@ -220,15 +221,15 @@ module WithProg (prog : Program) where
     ...   | yes k∈kvs₁ | no k∉kvs₂ = ⊥-elim (k∉kvs₂ (subst (λ l → k ∈ˡ l) (all-equal-keysᵛ vs₁ vs₂) k∈kvs₁))
     ...   | no k∉kvs₁ | yes k∈kvs₂ = ⊥-elim (k∉kvs₁ (subst (λ l → k ∈ˡ l) (all-equal-keysᵛ vs₂ vs₁) k∈kvs₂))
     ...   | no k∉kvs₁ | no k∉kvs₂ = IsLattice.≈-refl isLatticeᵍ
-    eval-Mono (# 0) _ = ≈ᵍ-refl
-    eval-Mono (# (suc n')) _ = ≈ᵍ-refl
+    eval-Monoʳ (# 0) _ = ≈ᵍ-refl
+    eval-Monoʳ (# (suc n')) _ = ≈ᵍ-refl
 
     instance
-        SignEval : Evaluator
-        SignEval = record { eval = eval; eval-Mono = eval-Mono }
+        SignEval : ExprEvaluator
+        SignEval = record { eval = eval; eval-Monoʳ = eval-Monoʳ }
 
     -- For debugging purposes, print out the result.
-    output = show result
+    output = show (Analysis.Forward.WithProg.result isFiniteHeightLatticeᵍ ≈ᵍ-dec 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
@@ -280,7 +281,7 @@ module WithProg (prog : Program) where
     minus-valid {[ 0ˢ ]ᵍ} {[ 0ˢ ]ᵍ} refl refl = refl
     minus-valid {[ 0ˢ ]ᵍ} {⊤ᵍ} _ _ = tt
 
-    eval-valid : IsValid
+    eval-valid : IsValidExprEvaluator
     eval-valid (⇒ᵉ-+ ρ e₁ e₂ z₁ z₂ ρ,e₁⇒z₁ ρ,e₂⇒z₂) ⟦vs⟧ρ =
         plus-valid (eval-valid ρ,e₁⇒z₁ ⟦vs⟧ρ) (eval-valid ρ,e₂⇒z₂ ⟦vs⟧ρ)
     eval-valid (⇒ᵉ-- ρ e₁ e₂ z₁ z₂ ρ,e₁⇒z₁ ρ,e₂⇒z₂) ⟦vs⟧ρ =
@@ -292,4 +293,4 @@ module WithProg (prog : Program) where
     eval-valid (⇒ᵉ-ℕ ρ 0) _ = refl
     eval-valid (⇒ᵉ-ℕ ρ (suc n')) _ = (n' , refl)
 
-    analyze-correct = ForwardWithProg.analyze-correct
+    analyze-correct = Analysis.Forward.WithProg.analyze-correct