DanilaFe/agda-spa
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Allow traces to be promoted through graph overlaying

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
This commit is contained in:
Danila Fedorin 2024-04-27 14:18:16 -07:00
parent 037358308f
commit fb32315f58
1 changed files with 27 additions and 1 deletions
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28
Language/Properties.agda
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@ -7,9 +7,13 @@ open import Language.Traces
open import Data.Fin as Fin using (zero) open import Data.Fin as Fin using (zero)
open import Data.List using (_∷_; []) open import Data.List using (_∷_; [])
open import Data.List.Membership.Propositional.Properties as ListMemProp using ()
open import Data.Product using (Σ; _,_) 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 : ∀ (s : Stmt) → let g = buildCfg s in Σ (Graph.Index g) (λ idx → Graph.inputs g ≡ idx ∷ [])
buildCfg-input ⟨ bs₁ ⟩ = (zero , refl) buildCfg-input ⟨ bs₁ ⟩ = (zero , refl)
@ -26,3 +30,25 @@ buildCfg-output (s₁ then s₂)
buildCfg-output (if _ then s₁ else s₂) = (_ , refl) buildCfg-output (if _ then s₁ else s₂) = (_ , refl)
buildCfg-output (while _ repeat s) buildCfg-output (while _ repeat s)
with (idx , p) ← buildCfg-output s rewrite p = (_ , refl) 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')