53 lines
2.6 KiB
Plaintext
53 lines
2.6 KiB
Plaintext
module Language.Properties where
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open import Language.Base
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open import Language.Semantics
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open import Language.Graphs
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open import Language.Traces
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open import MonotonicState _⊆_ ⊆-trans renaming (MonotonicState to MonotonicGraphFunction)
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open import Utils using (_⊗_; _,_)
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open Relaxable {{...}}
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open import Data.Fin using (zero)
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open import Data.List using (List; _∷_; [])
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open import Data.Vec using (_∷_; [])
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open import Data.Vec.Properties using (cast-is-id; lookup-++ˡ; lookup-++ʳ)
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open import Relation.Binary.PropositionalEquality as Eq using (_≡_; refl; sym; trans; subst)
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relax-preserves-[]≡ : ∀ (g₁ g₂ : Graph) (g₁⊆g₂ : g₁ ⊆ g₂) (idx : Graph.Index g₁) →
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g₁ [ idx ] ≡ g₂ [ relax g₁⊆g₂ idx ]
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relax-preserves-[]≡ g₁ g₂ (Mk-⊆ n refl newNodes nsg₂≡nsg₁++newNodes _) idx
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rewrite cast-is-id refl (Graph.nodes g₂)
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with refl ← nsg₂≡nsg₁++newNodes = sym (lookup-++ˡ (Graph.nodes g₁) _ _)
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instance
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NodeEqualsMonotonic : ∀ {bss : List BasicStmt} →
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MonotonicPredicate (λ g n → g [ n ] ≡ bss)
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NodeEqualsMonotonic = record
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{ relaxPredicate = λ g₁ g₂ idx g₁⊆g₂ g₁[idx]≡bss →
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trans (sym (relax-preserves-[]≡ g₁ g₂ g₁⊆g₂ idx)) g₁[idx]≡bss
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}
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pushBasicBlock-works : ∀ (bss : List BasicStmt) → Always (λ g idx → g [ idx ] ≡ bss) (pushBasicBlock bss)
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pushBasicBlock-works bss = MkAlways (λ g → lookup-++ʳ (Graph.nodes g) (bss ∷ []) zero)
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TransformsEnv : ∀ (ρ₁ ρ₂ : Env) → DependentPredicate (Graph.Index ⊗ Graph.Index)
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TransformsEnv ρ₁ ρ₂ g (idx₁ , idx₂) = Trace {g} idx₁ idx₂ ρ₁ ρ₂
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instance
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TransformsEnvMonotonic : ∀ {ρ₁ ρ₂ : Env} → MonotonicPredicate (TransformsEnv ρ₁ ρ₂)
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TransformsEnvMonotonic = {!!}
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buildCfg-sufficient : ∀ {ρ₁ ρ₂ : Env} {s : Stmt} → ρ₁ , s ⇒ˢ ρ₂ → Always (TransformsEnv ρ₁ ρ₂) (buildCfg s)
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buildCfg-sufficient {ρ₁} {ρ₂} {⟨ bs ⟩} (⇒ˢ-⟨⟩ ρ₁ ρ₂ bs ρ₁,bs⇒ρ₂) =
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pushBasicBlock-works (bs ∷ [])
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map-reason
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(λ g idx g[idx]≡[bs] → Trace-single (subst (ρ₁ ,_⇒ᵇˢ ρ₂)
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(sym g[idx]≡[bs])
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(ρ₁,bs⇒ρ₂ ∷ [])))
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buildCfg-sufficient {ρ₁} {ρ₂} {s₁ then s₂} (⇒ˢ-then ρ₁ ρ ρ₂ s₁ s₂ ρ₁,s₁⇒ρ₂ ρ₂,s₂⇒ρ₃) =
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(buildCfg-sufficient ρ₁,s₁⇒ρ₂ ⟨⊗⟩-reason buildCfg-sufficient ρ₂,s₂⇒ρ₃)
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update-reason {!!}
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map-reason {!!}
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