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

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@ -12,8 +12,8 @@ open import Data.Nat as Nat using (; 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