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
( FiniteMap to StateVariables
; isLattice to isLatticeᵐ
; _≈_ to _≈ᵐ_
; _∈k_ to _∈kᵐ_
; locate to locateᵐ
; _≼_ to _≼ᵐ_
@ -92,6 +93,11 @@ module WithProg (prog : Program) where
renaming
( isFiniteHeightLattice to isFiniteHeightLatticeᵐ
)
open IsFiniteHeightLattice isFiniteHeightLatticeᵐ
using ()
renaming
( ≈-sym to ≈ᵐ-sym
)
≈ᵐ-dec = ≈ᵛ-dec⇒≈ᵐ-dec ≈ᵛ-dec
fixedHeightᵐ = IsFiniteHeightLattice.fixedHeight isFiniteHeightLatticeᵐ
@ -107,6 +113,9 @@ module WithProg (prog : Program) where
variablesAt : State StateVariables VariableValues
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
--
-- 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,bss⇒ρ ⟦vs⟧ρ rewrite variablesAt-updateAll s sv =
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.Semantics public
open import Language.Traces public
open import Language.Graphs public
open import Language.Properties public