Language/Graphs.agda

@@ -124,6 +124,28 @@ buildCfg (s₁ then s₂) = buildCfg s₁ ↦ buildCfg s₂
 buildCfg (if _ then s₁ else s₂) = buildCfg s₁ ∙ buildCfg s₂
 buildCfg (while _ repeat s) = loop (buildCfg s)
 
+private
+    z≢sf : ∀ {n : ℕ} (f : Fin n) → ¬ (zero ≡ suc f)
+    z≢sf f ()
+
+    z≢mapsfs : ∀ {n : ℕ} (fs : List (Fin n)) → All (λ sf → ¬ zero ≡ sf) (List.map suc fs)
+    z≢mapsfs [] = []
+    z≢mapsfs (f ∷ fs') = z≢sf f ∷ z≢mapsfs fs'
+
+    finValues : ∀ (n : ℕ) → Σ (List (Fin n)) Unique
+    finValues 0 = ([] , Utils.empty)
+    finValues (suc n') =
+        let
+            (inds' , unids') = finValues n'
+        in
+            ( zero ∷ List.map suc inds'
+            , push (z≢mapsfs inds') (Unique-map suc suc-injective unids')
+            )
+
+    finValues-complete : ∀ (n : ℕ) (f : Fin n) → f ListMem.∈ (proj₁ (finValues n))
+    finValues-complete (suc n') zero = RelAny.here refl
+    finValues-complete (suc n') (suc f') = RelAny.there (x∈xs⇒fx∈fxs suc (finValues-complete n' f'))
+
 module _ (g : Graph) where
     open import Data.Product.Properties as ProdProp using ()
     private _≟_ = ProdProp.≡-dec (FinProp._≟_ {Graph.size g})
@@ -132,13 +154,13 @@ module _ (g : Graph) where
     open import Data.List.Membership.DecPropositional (_≟_) using (_∈?_)
 
     indices : List (Graph.Index g)
-    indices = proj₁ (fins (Graph.size g))
+    indices = proj₁ (finValues (Graph.size g))
 
     indices-complete : ∀ (idx : (Graph.Index g)) → idx ListMem.∈ indices
-    indices-complete = fins-complete (Graph.size g)
+    indices-complete = finValues-complete (Graph.size g)
 
     indices-Unique : Unique indices
-    indices-Unique = proj₂ (fins (Graph.size g))
+    indices-Unique = proj₂ (finValues (Graph.size g))
 
     predecessors : (Graph.Index g) → List (Graph.Index g)
     predecessors idx = List.filter (λ idx' → (idx' , idx) ∈? (Graph.edges g)) indices

Utils.agda

@@ -1,10 +1,8 @@
 module Utils where
 
 open import Agda.Primitive using () renaming (_⊔_ to _⊔ℓ_)
-open import Data.Product as Prod using (Σ; _×_; _,_; proj₁; proj₂)
+open import Data.Product as Prod using (_×_)
 open import Data.Nat using (ℕ; suc)
-open import Data.Fin as Fin using (Fin; suc; zero)
-open import Data.Fin.Properties using (suc-injective)
 open import Data.List using (List; cartesianProduct; []; _∷_; _++_; foldr; filter) renaming (map to mapˡ)
 open import Data.List.Membership.Propositional using (_∈_)
 open import Data.List.Membership.Propositional.Properties as ListMemProp using ()
@@ -108,24 +106,3 @@ _∧_ P Q a = P a × Q a
 
 it : ∀ {a} {A : Set a} {{_ : A}} → A
 it {{x}} = x
-
-z≢sf : ∀ {n : ℕ} (f : Fin n) → ¬ (Fin.zero ≡ Fin.suc f)
-z≢sf f ()
-
-z≢mapsfs : ∀ {n : ℕ} (fs : List (Fin n)) → All (λ sf → ¬ zero ≡ sf) (mapˡ suc fs)
-z≢mapsfs [] = []
-z≢mapsfs (f ∷ fs') = z≢sf f ∷ z≢mapsfs fs'
-
-fins : ∀ (n : ℕ) → Σ (List (Fin n)) Unique
-fins 0 = ([] , empty)
-fins (suc n') =
-    let
-        (inds' , unids') = fins n'
-    in
-        ( zero ∷ mapˡ suc inds'
-        , push (z≢mapsfs inds') (Unique-map suc suc-injective unids')
-        )
-
-fins-complete : ∀ (n : ℕ) (f : Fin n) → f ∈ (proj₁ (fins n))
-fins-complete (suc n') zero = here refl
-fins-complete (suc n') (suc f') = there (x∈xs⇒fx∈fxs suc (fins-complete n' f'))