Start working on the evaluation operation.

Proving monotonicity is the main hurdle here.

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

Language.agda

@@ -15,7 +15,7 @@ open import Relation.Nullary using (¬_)
 open import Function using (_∘_)
 
 open import Lattice
-open import Utils using (Unique; Unique-map; empty; push)
+open import Utils using (Unique; Unique-map; empty; push; x∈xs⇒fx∈fxs)
 
 data Expr : Set where
     _+_ : Expr → Expr → Expr
@@ -156,6 +156,10 @@ private
             , push (z≢mapsfs inds') (Unique-map suc suc-injective unids')
             )
 
+    indices-complete : ∀ (n : ℕ) (f : Fin n) → f ∈ˡ (proj₁ (indices n))
+    indices-complete (suc n') zero = RelAny.here refl
+    indices-complete (suc n') (suc f') = RelAny.there (x∈xs⇒fx∈fxs suc (indices-complete n' f'))
+
 
 -- For now, just represent the program and CFG as one type, without branching.
 record Program : Set where
@@ -179,6 +183,9 @@ record Program : Set where
     states : List State
     states = proj₁ (indices length)
 
+    states-complete : ∀ (s : State) → s ∈ˡ states
+    states-complete = indices-complete length
+
     states-Unique : Unique states
     states-Unique = proj₂ (indices length)