Start end-to-end proof of correctness

Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
This commit is contained in:
Danila Fedorin 2024-05-08 23:30:03 -07:00
parent 4ac9dffa9b
commit 838aaf9c58
2 changed files with 21 additions and 0 deletions

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@ -80,6 +80,7 @@ module WithProg (prog : Program) where
renaming renaming
( FiniteMap to StateVariables ( FiniteMap to StateVariables
; isLattice to isLatticeᵐ ; isLattice to isLatticeᵐ
; _≈_ to _≈ᵐ_
; _∈k_ to _∈kᵐ_ ; _∈k_ to _∈kᵐ_
; locate to locateᵐ ; locate to locateᵐ
; _≼_ to _≼ᵐ_ ; _≼_ to _≼ᵐ_
@ -92,6 +93,11 @@ module WithProg (prog : Program) where
renaming renaming
( isFiniteHeightLattice to isFiniteHeightLatticeᵐ ( isFiniteHeightLattice to isFiniteHeightLatticeᵐ
) )
open IsFiniteHeightLattice isFiniteHeightLatticeᵐ
using ()
renaming
( ≈-sym to ≈ᵐ-sym
)
≈ᵐ-dec = ≈ᵛ-dec⇒≈ᵐ-dec ≈ᵛ-dec ≈ᵐ-dec = ≈ᵛ-dec⇒≈ᵐ-dec ≈ᵛ-dec
fixedHeightᵐ = IsFiniteHeightLattice.fixedHeight isFiniteHeightLatticeᵐ fixedHeightᵐ = IsFiniteHeightLattice.fixedHeight isFiniteHeightLatticeᵐ
@ -107,6 +113,9 @@ module WithProg (prog : Program) where
variablesAt : State StateVariables VariableValues variablesAt : State StateVariables VariableValues
variablesAt s sv = proj₁ (locateᵐ {s} {sv} (states-in-Map s sv)) variablesAt s sv = proj₁ (locateᵐ {s} {sv} (states-in-Map s sv))
variablesAt-≈ : s sv₁ sv₂ sv₁ ≈ᵐ sv₂ variablesAt s sv₁ ≈ᵛ variablesAt s sv₂
variablesAt-≈ = {!!}
-- build up the 'join' function, which follows from Exercise 4.26's -- build up the 'join' function, which follows from Exercise 4.26's
-- --
-- L₁ → (A → L₂) -- L₁ → (A → L₂)
@ -270,3 +279,14 @@ module WithProg (prog : Program) where
updateAll-matches : {s sv ρ₁ ρ₂} ρ₁ , (code s) ⇒ᵇˢ ρ₂ variablesAt s sv ⟧ᵛ ρ₁ variablesAt s (updateAll sv) ⟧ᵛ ρ₂ updateAll-matches : {s sv ρ₁ ρ₂} ρ₁ , (code s) ⇒ᵇˢ ρ₂ variablesAt s sv ⟧ᵛ ρ₁ variablesAt s (updateAll sv) ⟧ᵛ ρ₂
updateAll-matches {s} {sv} ρ₁,bss⇒ρ ⟦vs⟧ρ rewrite variablesAt-updateAll s sv = updateAll-matches {s} {sv} ρ₁,bss⇒ρ ⟦vs⟧ρ rewrite variablesAt-updateAll s sv =
updateVariablesForState-matches {s} {sv} ρ₁,bss⇒ρ ⟦vs⟧ρ updateVariablesForState-matches {s} {sv} ρ₁,bss⇒ρ ⟦vs⟧ρ
walkTrace : {s₁ s₂ ρ₁ ρ₂} joinForKey s₁ result ⟧ᵛ ρ₁ Trace {graph} s₁ s₂ ρ₁ ρ₂ variablesAt s₂ result ⟧ᵛ ρ₂
walkTrace {s₁} {s₁} {ρ₁} {ρ₂} ⟦joinForKey-s₁⟧ρ (Trace-single ρ₁,bss⇒ρ) =
let
-- I'd use rewrite, but Agda gets a memory overflow (?!).
⟦joinAll-result⟧ρ = subst (λ vs vs ⟧ᵛ ρ₁) (sym (variablesAt-joinAll s₁ result)) ⟦joinForKey-s₁⟧ρ
⟦analyze-result⟧ρ = updateAll-matches {sv = joinAll result} ρ₁,bss⇒ρ ⟦joinAll-result⟧ρ
analyze-result≈result = ≈ᵐ-sym {result} {updateAll (joinAll result)} result≈analyze-result
analyze-s₁≈s₁ = variablesAt-≈ s₁ (updateAll (joinAll result)) result (analyze-result≈result)
in
⟦⟧ᵛ-respects-≈ᵛ {variablesAt s₁ (updateAll (joinAll result))} {variablesAt s₁ result} (analyze-s₁≈s₁) ρ₂ ⟦analyze-result⟧ρ

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@ -2,6 +2,7 @@ module Language where
open import Language.Base public open import Language.Base public
open import Language.Semantics public open import Language.Semantics public
open import Language.Traces public
open import Language.Graphs public open import Language.Graphs public
open import Language.Properties public open import Language.Properties public