From fb32315f58ae2c68d372e490672833dab9ba2dd7 Mon Sep 17 00:00:00 2001 From: Danila Fedorin Date: Sat, 27 Apr 2024 14:18:16 -0700 Subject: [PATCH] Allow traces to be promoted through graph overlaying Signed-off-by: Danila Fedorin --- Language/Properties.agda | 28 +++++++++++++++++++++++++++- 1 file changed, 27 insertions(+), 1 deletion(-) diff --git a/Language/Properties.agda b/Language/Properties.agda index 15b11ab..70c56a5 100644 --- a/Language/Properties.agda +++ b/Language/Properties.agda @@ -7,9 +7,13 @@ open import Language.Traces open import Data.Fin as Fin using (zero) open import Data.List using (_∷_; []) +open import Data.List.Membership.Propositional.Properties as ListMemProp using () open import Data.Product using (Σ; _,_) +open import Data.Vec.Properties using (lookup-++ˡ; ++-identityʳ; lookup-++ʳ) +open import Relation.Binary.PropositionalEquality as Eq using (_≡_; refl; sym) + +open import Utils using (x∈xs⇒fx∈fxs) -open import Relation.Binary.PropositionalEquality as Eq using (_≡_; refl) buildCfg-input : ∀ (s : Stmt) → let g = buildCfg s in Σ (Graph.Index g) (λ idx → Graph.inputs g ≡ idx ∷ []) buildCfg-input ⟨ bs₁ ⟩ = (zero , refl) @@ -26,3 +30,25 @@ buildCfg-output (s₁ then s₂) buildCfg-output (if _ then s₁ else s₂) = (_ , refl) buildCfg-output (while _ repeat s) with (idx , p) ← buildCfg-output s rewrite p = (_ , refl) + +Trace-∙ˡ : ∀ (g₁ g₂ : Graph) {idx₁ idx₂ : Graph.Index g₁} {ρ₁ ρ₂ : Env} → + Trace {g₁} idx₁ idx₂ ρ₁ ρ₂ → + Trace {g₁ ∙ g₂} (idx₁ Fin.↑ˡ Graph.size g₂) (idx₂ Fin.↑ˡ Graph.size g₂) ρ₁ ρ₂ +Trace-∙ˡ g₁ g₂ {idx₁} {idx₁} (Trace-single ρ₁⇒ρ₂) + rewrite sym (lookup-++ˡ (Graph.nodes g₁) (Graph.nodes g₂) idx₁) = + Trace-single ρ₁⇒ρ₂ +Trace-∙ˡ g₁ g₂ {idx₁} (Trace-edge ρ₁⇒ρ idx₁→idx tr') + rewrite sym (lookup-++ˡ (Graph.nodes g₁) (Graph.nodes g₂) idx₁) = + Trace-edge ρ₁⇒ρ (ListMemProp.∈-++⁺ˡ (x∈xs⇒fx∈fxs (_↑ˡ Graph.size g₂) idx₁→idx)) + (Trace-∙ˡ g₁ g₂ tr') + +Trace-∙ʳ : ∀ (g₁ g₂ : Graph) {idx₁ idx₂ : Graph.Index g₂} {ρ₁ ρ₂ : Env} → + Trace {g₂} idx₁ idx₂ ρ₁ ρ₂ → + Trace {g₁ ∙ g₂} (Graph.size g₁ Fin.↑ʳ idx₁) (Graph.size g₁ Fin.↑ʳ idx₂) ρ₁ ρ₂ +Trace-∙ʳ g₁ g₂ {idx₁} {idx₁} (Trace-single ρ₁⇒ρ₂) + rewrite sym (lookup-++ʳ (Graph.nodes g₁) (Graph.nodes g₂) idx₁) = + Trace-single ρ₁⇒ρ₂ +Trace-∙ʳ g₁ g₂ {idx₁} (Trace-edge ρ₁⇒ρ idx₁→idx tr') + rewrite sym (lookup-++ʳ (Graph.nodes g₁) (Graph.nodes g₂) idx₁) = + Trace-edge ρ₁⇒ρ (ListMemProp.∈-++⁺ʳ _ (x∈xs⇒fx∈fxs (Graph.size g₁ ↑ʳ_) idx₁→idx)) + (Trace-∙ʳ g₁ g₂ tr')