Move predecessor computation into Graphs
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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@ -11,8 +11,6 @@ open import Data.Fin.Properties as FinProp using (suc-injective)
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open import Data.List as List using (List; []; _∷_)
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open import Data.List.Membership.Propositional as ListMem using ()
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open import Data.List.Membership.Propositional.Properties as ListMemProp using (∈-filter⁺)
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open import Data.List.Relation.Unary.All using (All; []; _∷_)
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open import Data.List.Relation.Unary.Any as RelAny using ()
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open import Data.Nat using (ℕ; suc)
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open import Data.Product using (_,_; Σ; proj₁; proj₂)
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open import Data.Product.Properties as ProdProp using ()
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@ -28,28 +26,6 @@ open import Lattice.MapSet _≟ˢ_ using ()
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; to-List to to-Listˢ
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)
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private
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z≢sf : ∀ {n : ℕ} (f : Fin n) → ¬ (zero ≡ suc f)
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z≢sf f ()
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z≢mapsfs : ∀ {n : ℕ} (fs : List (Fin n)) → All (λ sf → ¬ zero ≡ sf) (List.map suc fs)
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z≢mapsfs [] = []
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z≢mapsfs (f ∷ fs') = z≢sf f ∷ z≢mapsfs fs'
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indices : ∀ (n : ℕ) → Σ (List (Fin n)) Unique
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indices 0 = ([] , Utils.empty)
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indices (suc n') =
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let
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(inds' , unids') = indices n'
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in
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( zero ∷ List.map suc inds'
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, push (z≢mapsfs inds') (Unique-map suc suc-injective unids')
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)
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indices-complete : ∀ (n : ℕ) (f : Fin n) → f ListMem.∈ (proj₁ (indices n))
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indices-complete (suc n') zero = RelAny.here refl
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indices-complete (suc n') (suc f') = RelAny.there (x∈xs⇒fx∈fxs suc (indices-complete n' f'))
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record Program : Set where
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field
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rootStmt : Stmt
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@ -77,13 +53,13 @@ record Program : Set where
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vars-Unique = proj₂ vars-Set
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states : List State
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states = proj₁ (indices (Graph.size graph))
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states = indices graph
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states-complete : ∀ (s : State) → s ListMem.∈ states
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states-complete = indices-complete (Graph.size graph)
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states-complete = indices-complete graph
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states-Unique : Unique states
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states-Unique = proj₂ (indices (Graph.size graph))
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states-Unique = indices-Unique graph
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code : State → List BasicStmt
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code st = graph [ st ]
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@ -100,7 +76,7 @@ record Program : Set where
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open import Data.List.Membership.DecPropositional _≟ᵉ_ using (_∈?_)
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incoming : State → List State
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incoming idx = List.filter (λ idx' → (idx' , idx) ∈? (Graph.edges graph)) states
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incoming = predecessors graph
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edge⇒incoming : ∀ {s₁ s₂ : State} → (s₁ , s₂) ListMem.∈ (Graph.edges graph) →
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s₁ ListMem.∈ (incoming s₂)
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@ -7,15 +7,19 @@ open import Data.Fin.Properties as FinProp using (suc-injective)
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open import Data.List as List using (List; []; _∷_)
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open import Data.List.Membership.Propositional as ListMem using ()
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open import Data.List.Membership.Propositional.Properties as ListMemProp using ()
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open import Data.List.Relation.Unary.All using (All; []; _∷_)
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open import Data.List.Relation.Unary.Any as RelAny using ()
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open import Data.Nat as Nat using (ℕ; suc)
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open import Data.Nat.Properties using (+-assoc; +-comm)
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open import Data.Product using (_×_; Σ; _,_)
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open import Data.Product using (_×_; Σ; _,_; proj₁; proj₂)
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open import Data.Product.Properties as ProdProp using ()
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open import Data.Vec using (Vec; []; _∷_; lookup; cast; _++_)
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open import Data.Vec.Properties using (cast-is-id; ++-assoc; lookup-++ˡ; cast-sym; ++-identityʳ; lookup-++ʳ)
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open import Relation.Binary.PropositionalEquality as Eq using (_≡_; sym; refl; subst; trans)
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open import Relation.Nullary using (¬_)
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open import Lattice
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open import Utils using (x∈xs⇒fx∈fxs; ∈-cartesianProduct)
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open import Utils using (Unique; push; Unique-map; x∈xs⇒fx∈fxs; ∈-cartesianProduct)
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record Graph : Set where
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constructor MkGraph
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@ -120,3 +124,40 @@ buildCfg ⟨ bs₁ ⟩ = singleton (bs₁ ∷ [])
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buildCfg (s₁ then s₂) = buildCfg s₁ ↦ buildCfg s₂
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buildCfg (if _ then s₁ else s₂) = singleton [] ↦ (buildCfg s₁ ∙ buildCfg s₂) ↦ singleton []
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buildCfg (while _ repeat s) = loop (buildCfg s)
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private
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z≢sf : ∀ {n : ℕ} (f : Fin n) → ¬ (zero ≡ suc f)
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z≢sf f ()
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z≢mapsfs : ∀ {n : ℕ} (fs : List (Fin n)) → All (λ sf → ¬ zero ≡ sf) (List.map suc fs)
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z≢mapsfs [] = []
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z≢mapsfs (f ∷ fs') = z≢sf f ∷ z≢mapsfs fs'
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finValues : ∀ (n : ℕ) → Σ (List (Fin n)) Unique
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finValues 0 = ([] , Utils.empty)
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finValues (suc n') =
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let
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(inds' , unids') = finValues n'
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in
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( zero ∷ List.map suc inds'
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, push (z≢mapsfs inds') (Unique-map suc suc-injective unids')
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)
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finValues-complete : ∀ (n : ℕ) (f : Fin n) → f ListMem.∈ (proj₁ (finValues n))
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finValues-complete (suc n') zero = RelAny.here refl
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finValues-complete (suc n') (suc f') = RelAny.there (x∈xs⇒fx∈fxs suc (finValues-complete n' f'))
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module _ (g : Graph) where
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open import Data.List.Membership.DecPropositional (ProdProp.≡-dec (FinProp._≟_ {Graph.size g}) (FinProp._≟_ {Graph.size g})) using (_∈?_)
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indices : List (Graph.Index g)
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indices = proj₁ (finValues (Graph.size g))
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indices-complete : ∀ (idx : (Graph.Index g)) → idx ListMem.∈ indices
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indices-complete = finValues-complete (Graph.size g)
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indices-Unique : Unique indices
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indices-Unique = proj₂ (finValues (Graph.size g))
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predecessors : (Graph.Index g) → List (Graph.Index g)
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predecessors idx = List.filter (λ idx' → (idx' , idx) ∈? (Graph.edges g)) indices
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