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Add a new 'properties' module

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
This commit is contained in:
Danila Fedorin 2024-04-20 20:25:40 -07:00
parent 54b11d21b0
commit 6e3f06ca5d
3 changed files with 62 additions and 47 deletions
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1
Language.agda
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@ -3,6 +3,7 @@ module Language where
open import Language.Base public
open import Language.Semantics public
open import Language.Graphs public
open import Language.Properties public
open import Data.Fin using (Fin; suc; zero)
open import Data.Fin.Properties as FinProp using (suc-injective)

23
Language/Graphs.agda
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@ -1,7 +1,6 @@
module Language.Graphs where
open import Language.Base
open import Language.Semantics
open import Data.Fin as Fin using (Fin; suc; zero; _↑ˡ_; _↑ʳ_)
open import Data.Fin.Properties as FinProp using (suc-injective)
@ -57,6 +56,7 @@ record _⊆_ (g₁ g₂ : Graph) : Set where
e ListMem.∈ (Graph.edges g₁) →
(↑ˡ-Edge e n) ListMem.∈ (subst (λ m → List (Fin m × Fin m)) sg₂≡sg₁+n (Graph.edges g₂))
private
castᵉ : ∀ {n m : ℕ} .(p : n ≡ m) → (Fin n × Fin n) → (Fin m × Fin m)
castᵉ p (idx₁ , idx₂) = (Fin.cast p idx₁ , Fin.cast p idx₂)
@ -128,20 +128,6 @@ instance
open Relaxable {{...}}
relax-preserves-[]≡ : ∀ (g₁ g₂ : Graph) (g₁⊆g₂ : g₁ ⊆ g₂) (idx : Graph.Index g₁) →
g₁ [ idx ] ≡ g₂ [ relax g₁⊆g₂ idx ]
relax-preserves-[]≡ g₁ g₂ (Mk-⊆ n refl newNodes nsg₂≡nsg₁++newNodes _) idx
rewrite cast-is-id refl (Graph.nodes g₂)
with refl ← nsg₂≡nsg₁++newNodes = sym (lookup-++ˡ (Graph.nodes g₁) _ _)
instance
NodeEqualsMonotonic : ∀ {bss : List BasicStmt} →
MonotonicPredicate (λ g n → g [ n ] ≡ bss)
NodeEqualsMonotonic = record
{ relaxPredicate = λ g₁ g₂ idx g₁⊆g₂ g₁[idx]≡bss →
trans (sym (relax-preserves-[]≡ g₁ g₂ g₁⊆g₂ idx)) g₁[idx]≡bss
}
pushBasicBlock : List BasicStmt → MonotonicGraphFunction Graph.Index
pushBasicBlock bss g =
( record
@ -160,8 +146,8 @@ pushBasicBlock bss g =
)
)
pushBasicBlock-works : ∀ (bss : List BasicStmt) → Always (λ g idx → g [ idx ] ≡ bss) (pushBasicBlock bss)
pushBasicBlock-works bss = MkAlways (λ g → lookup-++ʳ (Graph.nodes g) (bss ∷ []) zero)
pushEmptyBlock : MonotonicGraphFunction Graph.Index
pushEmptyBlock = pushBasicBlock []
addEdges : ∀ (g : Graph) → List (Graph.Edge g) → Σ Graph (λ g' → g ⊆ g')
addEdges (MkGraph s ns es) es' =
@ -183,9 +169,6 @@ addEdges (MkGraph s ns es) es' =
}
)
pushEmptyBlock : MonotonicGraphFunction Graph.Index
pushEmptyBlock = pushBasicBlock []
buildCfg : Stmt → MonotonicGraphFunction (Graph.Index ⊗ Graph.Index)
buildCfg ⟨ bs₁ ⟩ = pushBasicBlock (bs₁ ∷ []) map (λ g idx → (idx , idx))
buildCfg (s₁ then s₂) =

31
Language/Properties.agda Normal file
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@ -0,0 +1,31 @@
module Language.Properties where
open import Language.Base
open import Language.Semantics
open import Language.Graphs
open import MonotonicState _⊆_ ⊆-trans renaming (MonotonicState to MonotonicGraphFunction)
open Relaxable {{...}}
open import Data.Fin using (zero)
open import Data.List using (List)
open import Data.Vec using (_∷_; [])
open import Data.Vec.Properties using (cast-is-id; lookup-++ˡ; lookup-++ʳ)
open import Relation.Binary.PropositionalEquality as Eq using (_≡_; refl; sym; trans)
relax-preserves-[]≡ : ∀ (g₁ g₂ : Graph) (g₁⊆g₂ : g₁ ⊆ g₂) (idx : Graph.Index g₁) →
g₁ [ idx ] ≡ g₂ [ relax g₁⊆g₂ idx ]
relax-preserves-[]≡ g₁ g₂ (Mk-⊆ n refl newNodes nsg₂≡nsg₁++newNodes _) idx
rewrite cast-is-id refl (Graph.nodes g₂)
with refl ← nsg₂≡nsg₁++newNodes = sym (lookup-++ˡ (Graph.nodes g₁) _ _)
instance
NodeEqualsMonotonic : ∀ {bss : List BasicStmt} →
MonotonicPredicate (λ g n → g [ n ] ≡ bss)
NodeEqualsMonotonic = record
{ relaxPredicate = λ g₁ g₂ idx g₁⊆g₂ g₁[idx]≡bss →
trans (sym (relax-preserves-[]≡ g₁ g₂ g₁⊆g₂ idx)) g₁[idx]≡bss
}
pushBasicBlock-works : ∀ (bss : List BasicStmt) → Always (λ g idx → g [ idx ] ≡ bss) (pushBasicBlock bss)
pushBasicBlock-works bss = MkAlways (λ g → lookup-++ʳ (Graph.nodes g) (bss ∷ []) zero)