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Get forward analysis working again

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
This commit is contained in:
Danila Fedorin 2024-04-13 14:08:40 -07:00
parent 4fe0d147fa
commit 44f04e4020
3 changed files with 42 additions and 19 deletions
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40
Analysis/Forward.agda
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@ -145,25 +145,33 @@ module WithProg (prog : Program) where
-- also monotonically; we derive the for-each-state update from -- also monotonically; we derive the for-each-state update from
-- the Exercise 4.26 again. -- the Exercise 4.26 again.
updateVariablesFromStmt : BasicStmt → VariableValues → VariableValues
updateVariablesFromStmt (k ← e) vs = updateVariablesFromExpression k e vs
updateVariablesFromStmt noop vs = vs
updateVariablesFromStmt-Monoʳ : ∀ (bs : BasicStmt) → Monotonic _≼ᵛ_ _≼ᵛ_ (updateVariablesFromStmt bs)
updateVariablesFromStmt-Monoʳ (k ← e) {vs₁} {vs₂} vs₁≼vs₂ = updateVariablesFromExpression-Mono k e {vs₁} {vs₂} vs₁≼vs₂
updateVariablesFromStmt-Monoʳ noop vs₁≼vs₂ = vs₁≼vs₂
updateVariablesForState : State → StateVariables → VariableValues updateVariablesForState : State → StateVariables → VariableValues
updateVariablesForState s sv updateVariablesForState s sv =
with code s let
... | k ← e = bss = code s
let (vs , s,vs∈sv) = locateᵐ {s} {sv} (states-in-Map s sv)
(vs , s,vs∈sv) = locateᵐ {s} {sv} (states-in-Map s sv) in
in foldr updateVariablesFromStmt vs bss
updateVariablesFromExpression k e vs
updateVariablesForState-Monoʳ : ∀ (s : State) → Monotonic _≼ᵐ_ _≼ᵛ_ (updateVariablesForState s) updateVariablesForState-Monoʳ : ∀ (s : State) → Monotonic _≼ᵐ_ _≼ᵛ_ (updateVariablesForState s)
updateVariablesForState-Monoʳ s {sv₁} {sv₂} sv₁≼sv₂ updateVariablesForState-Monoʳ s {sv₁} {sv₂} sv₁≼sv₂ =
with code s let
... | k ← e = bss = code s
let (vs₁ , s,vs₁∈sv₁) = locateᵐ {s} {sv₁} (states-in-Map s sv₁)
(vs₁ , s,vs₁∈sv₁) = locateᵐ {s} {sv₁} (states-in-Map s sv₁) (vs₂ , s,vs₂∈sv₂) = locateᵐ {s} {sv₂} (states-in-Map s sv₂)
(vs₂ , s,vs₂∈sv₂) = locateᵐ {s} {sv₂} (states-in-Map s sv₂) vs₁≼vs₂ = m₁≼m₂⇒m₁[k]ᵐ≼m₂[k]ᵐ sv₁ sv₂ sv₁≼sv₂ s,vs₁∈sv₁ s,vs₂∈sv₂
vs₁≼vs₂ = m₁≼m₂⇒m₁[k]ᵐ≼m₂[k]ᵐ sv₁ sv₂ sv₁≼sv₂ s,vs₁∈sv₁ s,vs₂∈sv₂ in
in foldr-Mono' (IsLattice.joinSemilattice isLatticeᵛ) bss
updateVariablesFromExpression-Mono k e {vs₁} {vs₂} vs₁≼vs₂ updateVariablesFromStmt updateVariablesFromStmt-Monoʳ
vs₁≼vs₂
open StateVariablesFiniteMap.GeneralizedUpdate states isLatticeᵐ (λ x → x) (λ a₁≼a₂ → a₁≼a₂) updateVariablesForState updateVariablesForState-Monoʳ states open StateVariablesFiniteMap.GeneralizedUpdate states isLatticeᵐ (λ x → x) (λ a₁≼a₂ → a₁≼a₂) updateVariablesForState updateVariablesForState-Monoʳ states
renaming renaming

6
Language.agda
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@ -499,10 +499,10 @@ record Program : Set where
open Graphs open Graphs
field field
prog : Stmt rootStmt : Stmt
private private
buildResult = Construction.buildCfg prog empty buildResult = Construction.buildCfg rootStmt empty
graph : Graph graph : Graph
graph = proj₁ buildResult graph = proj₁ buildResult
@ -518,7 +518,7 @@ record Program : Set where
private private
vars-Set : StringSet vars-Set : StringSet
vars-Set = Stmt-vars prog vars-Set = Stmt-vars rootStmt
vars : List String vars : List String
vars = to-Listˢ vars-Set vars = to-Listˢ vars-Set

15
Lattice.agda
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@ -150,6 +150,21 @@ module _ {a b} {A : Set a} {B : Set b}
≼₂-trans (f-Mono₁ (foldr f b₁ xs) x≼y) ≼₂-trans (f-Mono₁ (foldr f b₁ xs) x≼y)
(f-Mono₂ y (foldr-Mono xs ys f b₁ b₂ xs≼ys b₁≼b₂ f-Mono₁ f-Mono₂)) (f-Mono₂ y (foldr-Mono xs ys f b₁ b₂ xs≼ys b₁≼b₂ f-Mono₁ f-Mono₂))
module _ {a b} {A : Set a} {B : Set b}
{_≈₂_ : B → B → Set b} {_⊔₂_ : B → B → B}
(lB : IsSemilattice B _≈₂_ _⊔₂_) where
open IsSemilattice lB using () renaming (_≼_ to _≼₂_; ⊔-idemp to ⊔₂-idemp; ≼-trans to ≼₂-trans)
open import Data.List as List using (List; foldr; _∷_)
open import Utils using (Pairwise; _∷_)
foldr-Mono' : ∀ (l : List A) (f : A → B → B) →
(∀ a → Monotonic _≼₂_ _≼₂_ (f a)) →
Monotonic _≼₂_ _≼₂_ (λ b → foldr f b l)
foldr-Mono' List.[] f _ b₁≼b₂ = b₁≼b₂
foldr-Mono' (x ∷ xs) f f-Mono₂ b₁≼b₂ = f-Mono₂ x (foldr-Mono' xs f f-Mono₂ b₁≼b₂)
record IsLattice {a} (A : Set a) record IsLattice {a} (A : Set a)
(_≈_ : A → A → Set a) (_≈_ : A → A → Set a)
(_⊔_ : A → A → A) (_⊔_ : A → A → A)