32 lines
1.4 KiB
Agda
32 lines
1.4 KiB
Agda
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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 MonotonicState _⊆_ ⊆-trans renaming (MonotonicState to MonotonicGraphFunction)
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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)
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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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