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Start working on proving 'sufficiency'

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
This commit is contained in:
Danila Fedorin 2024-04-20 21:37:28 -07:00
parent e218d1b7a3
commit b134c143ca
2 changed files with 25 additions and 4 deletions
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25
Language/Properties.agda
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@ -3,15 +3,17 @@ module Language.Properties where
open import Language.Base open import Language.Base
open import Language.Semantics open import Language.Semantics
open import Language.Graphs open import Language.Graphs
open import Language.Traces
open import MonotonicState _⊆_ ⊆-trans renaming (MonotonicState to MonotonicGraphFunction) open import MonotonicState _⊆_ ⊆-trans renaming (MonotonicState to MonotonicGraphFunction)
open import Utils using (_⊗_; _,_)
open Relaxable {{...}} open Relaxable {{...}}
open import Data.Fin using (zero) open import Data.Fin using (zero)
open import Data.List using (List) open import Data.List using (List; _∷_; [])
open import Data.Vec using (_∷_; []) open import Data.Vec using (_∷_; [])
open import Data.Vec.Properties using (cast-is-id; lookup-++ˡ; lookup-++ʳ) open import Data.Vec.Properties using (cast-is-id; lookup-++ˡ; lookup-++ʳ)
open import Relation.Binary.PropositionalEquality as Eq using (_≡_; refl; sym; trans) open import Relation.Binary.PropositionalEquality as Eq using (_≡_; refl; sym; trans; subst)
relax-preserves-[]≡ : ∀ (g₁ g₂ : Graph) (g₁⊆g₂ : g₁ ⊆ g₂) (idx : Graph.Index g₁) → relax-preserves-[]≡ : ∀ (g₁ g₂ : Graph) (g₁⊆g₂ : g₁ ⊆ g₂) (idx : Graph.Index g₁) →
g₁ [ idx ] ≡ g₂ [ relax g₁⊆g₂ idx ] g₁ [ idx ] ≡ g₂ [ relax g₁⊆g₂ idx ]
@ -29,3 +31,22 @@ instance
pushBasicBlock-works : ∀ (bss : List BasicStmt) → Always (λ g idx → g [ idx ] ≡ bss) (pushBasicBlock 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) pushBasicBlock-works bss = MkAlways (λ g → lookup-++ʳ (Graph.nodes g) (bss ∷ []) zero)
TransformsEnv : ∀ (ρ₁ ρ₂ : Env) → DependentPredicate (Graph.Index ⊗ Graph.Index)
TransformsEnv ρ₁ ρ₂ g (idx₁ , idx₂) = Trace {g} idx₁ idx₂ ρ₁ ρ₂
instance
TransformsEnvMonotonic : ∀ {ρ₁ ρ₂ : Env} → MonotonicPredicate (TransformsEnv ρ₁ ρ₂)
TransformsEnvMonotonic = {!!}
buildCfg-sufficient : ∀ {ρ₁ ρ₂ : Env} {s : Stmt} → ρ₁ , s ⇒ˢ ρ₂ → Always (TransformsEnv ρ₁ ρ₂) (buildCfg s)
buildCfg-sufficient {ρ₁} {ρ₂} {⟨ bs ⟩} (⇒ˢ-⟨⟩ ρ₁ ρ₂ bs ρ₁,bs⇒ρ₂) =
pushBasicBlock-works (bs ∷ [])
map-reason
(λ g idx g[idx]≡[bs] → Trace-single (subst (ρ₁ ,_⇒ᵇˢ ρ₂)
(sym g[idx]≡[bs])
(ρ₁,bs⇒ρ₂ ∷ [])))
buildCfg-sufficient {ρ₁} {ρ₂} {s₁ then s₂} (⇒ˢ-then ρ₁ ρ ρ₂ s₁ s₂ ρ₁,s₁⇒ρ₂ ρ₂,s₂⇒ρ₃) =
(buildCfg-sufficient ρ₁,s₁⇒ρ₂ ⟨⊗⟩-reason buildCfg-sufficient ρ₂,s₂⇒ρ₃)
update-reason {!!}
map-reason {!!}

4
MonotonicState.agda
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@ -173,7 +173,7 @@ _map-reason_ : ∀ {T₁ T₂ : S → Set s}
{P : DependentPredicate T₁} {Q : DependentPredicate T₂} {P : DependentPredicate T₁} {Q : DependentPredicate T₂}
{m : MonotonicState T₁} {m : MonotonicState T₁}
{f : ∀ (s : S) → T₁ s → T₂ s} → {f : ∀ (s : S) → T₁ s → T₂ s} →
Always P m → (∀ (s : S) (t₁ : T₁ s) (t₂ : T₂ s) → P s t₁ → Q s t₂) → Always P m → (∀ (s : S) (t₁ : T₁ s) → P s t₁ → Q s (f s t₁)) →
Always Q (m map f) Always Q (m map f)
_map-reason_ {P = P} {Q = Q} {m = m} {f = f} (MkAlways aP) P⇒Q = _map-reason_ {P = P} {Q = Q} {m = m} {f = f} (MkAlways aP) P⇒Q =
MkAlways impl MkAlways impl
@ -181,4 +181,4 @@ _map-reason_ {P = P} {Q = Q} {m = m} {f = f} (MkAlways aP) P⇒Q =
impl : ∀ s₁ → let (s₂ , t , _) = (m map f) s₁ in Q s₂ t impl : ∀ s₁ → let (s₂ , t , _) = (m map f) s₁ in Q s₂ t
impl s impl s
with p ← aP s with p ← aP s
with (s' , (t₁ , s≼s')) ← m s = P⇒Q s' t₁ (f s' t₁) p with (s' , (t₁ , s≼s')) ← m s = P⇒Q s' t₁ p