Start working on proving facts about graph construction
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
This commit is contained in:
parent
f3e0d5f2e3
commit
54b11d21b0
|
@ -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
|
||||
|
|
Loading…
Reference in New Issue
Block a user