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Start working on proving facts about graph construction 

Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
This commit is contained in:
Danila Fedorin 2024-04-20 19:31:47 -07:00
parent f3e0d5f2e3
commit 54b11d21b0
1 changed files with 13 additions and 2 deletions
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15
Language/Graphs.agda
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@ -12,8 +12,8 @@ open import Data.Nat as Nat using (ℕ; suc)
open import Data.Nat.Properties using (+-assoc; +-comm)
open import Data.Product using (_×_; Σ; _,_)
open import Data.Vec using (Vec; []; _∷_; lookup; cast; _++_)
open import Data.Vec.Properties using (cast-is-id; ++-assoc; lookup-++ˡ; cast-sym; ++-identityʳ)
open import Relation.Binary.PropositionalEquality as Eq using (_≡_; sym; refl; subst)
open import Data.Vec.Properties using (cast-is-id; ++-assoc; lookup-++ˡ; cast-sym; ++-identityʳ; lookup-++ʳ)
open import Relation.Binary.PropositionalEquality as Eq using (_≡_; sym; refl; subst; trans)
open import Lattice
open import Utils using (x∈xs⇒fx∈fxs; _⊗_; _,_)
@ -134,6 +134,14 @@ relax-preserves-[]≡ g₁ g₂ (Mk-⊆ n refl newNodes nsg₂≡nsg₁++newNode
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
@ -152,6 +160,9 @@ 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)
addEdges : ∀ (g : Graph) → List (Graph.Edge g) → Σ Graph (λ g' → g ⊆ g')
addEdges (MkGraph s ns es) es' =
( record