Use instance search to avoid multiply-nested modules
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
This commit is contained in:
parent
9131214880
commit
10332351ea
@ -38,6 +38,8 @@ module WithProg (prog : Program) where
|
||||
|
||||
-- The variable -> abstract value (e.g. sign) map is a finite value-map
|
||||
-- with keys strings. Use a bundle to avoid explicitly specifying operators.
|
||||
-- It's helpful to export these via 'public' since consumers tend to
|
||||
-- use various variable lattice operations.
|
||||
module VariableValuesFiniteMap = Lattice.FiniteValueMap.WithKeys _≟ˢ_ isLatticeˡ vars
|
||||
open VariableValuesFiniteMap
|
||||
using ()
|
||||
@ -96,7 +98,6 @@ module WithProg (prog : Program) where
|
||||
; ≈₂-dec⇒≈-dec to ≈ᵛ-dec⇒≈ᵐ-dec
|
||||
; m₁≼m₂⇒m₁[k]≼m₂[k] to m₁≼m₂⇒m₁[k]ᵐ≼m₂[k]ᵐ
|
||||
)
|
||||
public
|
||||
open Lattice.FiniteValueMap.IterProdIsomorphism.WithUniqueKeysAndFixedHeight _≟_ isLatticeᵛ states-Unique ≈ᵛ-dec _ fixedHeightᵛ
|
||||
using ()
|
||||
renaming
|
||||
@ -150,6 +151,7 @@ module WithProg (prog : Program) where
|
||||
|
||||
-- The name f' comes from the formulation of Exercise 4.26.
|
||||
open StateVariablesFiniteMap.GeneralizedUpdate states isLatticeᵐ (λ x → x) (λ a₁≼a₂ → a₁≼a₂) joinForKey joinForKey-Mono states
|
||||
using ()
|
||||
renaming
|
||||
( f' to joinAll
|
||||
; f'-Monotonic to joinAll-Mono
|
||||
@ -162,16 +164,22 @@ module WithProg (prog : Program) where
|
||||
with (vs , s,vs∈usv) ← locateᵐ {s} {joinAll sv} (states-in-Map s (joinAll sv)) =
|
||||
joinAll-k∈ks-≡ {l = sv} (states-complete s) s,vs∈usv
|
||||
|
||||
record Evaluator : Set where
|
||||
field
|
||||
eval : Expr → VariableValues → L
|
||||
eval-Mono : ∀ (e : Expr) → Monotonic _≼ᵛ_ _≼ˡ_ (eval e)
|
||||
|
||||
-- With 'join' in hand, we need to perform abstract evaluation.
|
||||
module WithEvaluator (eval : Expr → VariableValues → L)
|
||||
(eval-Mono : ∀ (e : Expr) → Monotonic _≼ᵛ_ _≼ˡ_ (eval e)) where
|
||||
module _ {{evaluator : Evaluator}} where
|
||||
open Evaluator evaluator
|
||||
|
||||
-- For a particular evaluation function, we need to perform an evaluation
|
||||
-- for an assignment, and update the corresponding key. Use Exercise 4.26's
|
||||
-- generalized update to set the single key's value.
|
||||
|
||||
private module _ (k : String) (e : Expr) where
|
||||
module _ (k : String) (e : Expr) where
|
||||
open VariableValuesFiniteMap.GeneralizedUpdate vars isLatticeᵛ (λ x → x) (λ a₁≼a₂ → a₁≼a₂) (λ _ → eval e) (λ _ {vs₁} {vs₂} vs₁≼vs₂ → eval-Mono e {vs₁} {vs₂} vs₁≼vs₂) (k ∷ [])
|
||||
using ()
|
||||
renaming
|
||||
( f' to updateVariablesFromExpression
|
||||
; f'-Monotonic to updateVariablesFromExpression-Mono
|
||||
@ -213,11 +221,13 @@ module WithProg (prog : Program) where
|
||||
vs₁≼vs₂
|
||||
|
||||
open StateVariablesFiniteMap.GeneralizedUpdate states isLatticeᵐ (λ x → x) (λ a₁≼a₂ → a₁≼a₂) updateVariablesForState updateVariablesForState-Monoʳ states
|
||||
using ()
|
||||
renaming
|
||||
( f' to updateAll
|
||||
; f'-Monotonic to updateAll-Mono
|
||||
; f'-k∈ks-≡ to updateAll-k∈ks-≡
|
||||
)
|
||||
public
|
||||
|
||||
-- Finally, the whole analysis consists of getting the 'join'
|
||||
-- of all incoming states, then applying the per-state evaluation
|
||||
@ -243,7 +253,7 @@ module WithProg (prog : Program) where
|
||||
with (vs , s,vs∈usv) ← locateᵐ {s} {updateAll sv} (states-in-Map s (updateAll sv)) =
|
||||
updateAll-k∈ks-≡ {l = sv} (states-complete s) s,vs∈usv
|
||||
|
||||
module WithInterpretation (latticeInterpretationˡ : LatticeInterpretation isLatticeˡ) where
|
||||
module _ {{latticeInterpretationˡ : LatticeInterpretation isLatticeˡ}} where
|
||||
open LatticeInterpretation latticeInterpretationˡ
|
||||
using ()
|
||||
renaming
|
||||
@ -251,6 +261,7 @@ module WithProg (prog : Program) where
|
||||
; ⟦⟧-respects-≈ to ⟦⟧ˡ-respects-≈ˡ
|
||||
; ⟦⟧-⊔-∨ to ⟦⟧ˡ-⊔ˡ-∨
|
||||
)
|
||||
public
|
||||
|
||||
⟦_⟧ᵛ : VariableValues → Env → Set
|
||||
⟦_⟧ᵛ vs ρ = ∀ {k l} → (k , l) ∈ᵛ vs → ∀ {v} → (k , v) Language.∈ ρ → ⟦ l ⟧ˡ v
|
||||
@ -283,10 +294,26 @@ module WithProg (prog : Program) where
|
||||
⟦⟧ᵛ-⊔ᵛ-∨ {vs₁ = vs'} {vs₂ = foldr _⊔ᵛ_ ⊥ᵛ vss'} ρ
|
||||
(inj₂ (⟦⟧ᵛ-foldr ⟦vs⟧ρ vs∈vss'))
|
||||
|
||||
InterpretationValid : Set
|
||||
InterpretationValid = ∀ {vs ρ e v} → ρ , e ⇒ᵉ v → ⟦ vs ⟧ᵛ ρ → ⟦ eval e vs ⟧ˡ v
|
||||
module _ {{evaluator : Evaluator}} {{interpretation : LatticeInterpretation isLatticeˡ}} where
|
||||
open Evaluator evaluator
|
||||
open LatticeInterpretation interpretation
|
||||
|
||||
module WithValidity (interpretationValidˡ : InterpretationValid) where
|
||||
IsValid : Set
|
||||
IsValid = ∀ {vs ρ e v} → ρ , e ⇒ᵉ v → ⟦ vs ⟧ᵛ ρ → ⟦ eval e vs ⟧ˡ v
|
||||
|
||||
record ValidInterpretation : Set₁ where
|
||||
field
|
||||
{{evaluator}} : Evaluator
|
||||
{{interpretation}} : LatticeInterpretation isLatticeˡ
|
||||
|
||||
open Evaluator evaluator
|
||||
open LatticeInterpretation interpretation
|
||||
|
||||
field
|
||||
valid : IsValid
|
||||
|
||||
module _ {{validInterpretation : ValidInterpretation}} where
|
||||
open ValidInterpretation validInterpretation
|
||||
|
||||
updateVariablesFromStmt-matches : ∀ {bs vs ρ₁ ρ₂} → ρ₁ , bs ⇒ᵇ ρ₂ → ⟦ vs ⟧ᵛ ρ₁ → ⟦ updateVariablesFromStmt bs vs ⟧ᵛ ρ₂
|
||||
updateVariablesFromStmt-matches {_} {vs} {ρ₁} {ρ₁} (⇒ᵇ-noop ρ₁) ⟦vs⟧ρ₁ = ⟦vs⟧ρ₁
|
||||
@ -294,7 +321,7 @@ module WithProg (prog : Program) where
|
||||
with k ≟ˢ k' | k',v'∈ρ₂
|
||||
... | yes refl | here _ v _
|
||||
rewrite updateVariablesFromExpression-k∈ks-≡ k e {l = vs} (Any.here refl) k',l∈vs' =
|
||||
interpretationValidˡ ρ,e⇒v ⟦vs⟧ρ₁
|
||||
valid ρ,e⇒v ⟦vs⟧ρ₁
|
||||
... | yes k≡k' | there _ _ _ _ _ k'≢k _ = ⊥-elim (k'≢k (sym k≡k'))
|
||||
... | no k≢k' | here _ _ _ = ⊥-elim (k≢k' refl)
|
||||
... | no k≢k' | there _ _ _ _ _ _ k',v'∈ρ₁ =
|
||||
|
||||
@ -159,6 +159,7 @@ s₁≢s₂⇒¬s₁∧s₂ { - } { - } +≢+ _ = ⊥-elim (+≢+ refl)
|
||||
⟦⟧ᵍ-⊓ᵍ-∧ {[ g₁ ]ᵍ} {⊥ᵍ} x (_ , bot) = bot
|
||||
⟦⟧ᵍ-⊓ᵍ-∧ {[ g₁ ]ᵍ} {⊤ᵍ} x (px₁ , _) = px₁
|
||||
|
||||
instance
|
||||
latticeInterpretationᵍ : LatticeInterpretation isLatticeᵍ
|
||||
latticeInterpretationᵍ = record
|
||||
{ ⟦_⟧ = ⟦_⟧ᵍ
|
||||
@ -171,7 +172,7 @@ module WithProg (prog : Program) where
|
||||
open Program prog
|
||||
|
||||
module ForwardWithProg = Analysis.Forward.WithProg (record { isLattice = isLatticeᵍ; fixedHeight = fixedHeightᵍ }) ≈ᵍ-dec prog
|
||||
open ForwardWithProg
|
||||
open ForwardWithProg hiding (analyze-correct)
|
||||
|
||||
eval : ∀ (e : Expr) → VariableValues → SignLattice
|
||||
eval (e₁ + e₂) vs = plus (eval e₁ vs) (eval e₂ vs)
|
||||
@ -222,15 +223,13 @@ module WithProg (prog : Program) where
|
||||
eval-Mono (# 0) _ = ≈ᵍ-refl
|
||||
eval-Mono (# (suc n')) _ = ≈ᵍ-refl
|
||||
|
||||
module ForwardWithEval = ForwardWithProg.WithEvaluator eval eval-Mono
|
||||
open ForwardWithEval using (result)
|
||||
instance
|
||||
SignEval : Evaluator
|
||||
SignEval = record { eval = eval; eval-Mono = eval-Mono }
|
||||
|
||||
-- For debugging purposes, print out the result.
|
||||
output = show result
|
||||
|
||||
module ForwardWithInterp = ForwardWithEval.WithInterpretation latticeInterpretationᵍ
|
||||
open ForwardWithInterp using (⟦_⟧ᵛ; InterpretationValid)
|
||||
|
||||
-- This should have fewer cases -- the same number as the actual 'plus' above.
|
||||
-- But agda only simplifies on first argument, apparently, so we are stuck
|
||||
-- listing them all.
|
||||
@ -281,16 +280,16 @@ module WithProg (prog : Program) where
|
||||
minus-valid {[ 0ˢ ]ᵍ} {[ 0ˢ ]ᵍ} refl refl = refl
|
||||
minus-valid {[ 0ˢ ]ᵍ} {⊤ᵍ} _ _ = tt
|
||||
|
||||
eval-Valid : InterpretationValid
|
||||
eval-Valid (⇒ᵉ-+ ρ e₁ e₂ z₁ z₂ ρ,e₁⇒z₁ ρ,e₂⇒z₂) ⟦vs⟧ρ =
|
||||
plus-valid (eval-Valid ρ,e₁⇒z₁ ⟦vs⟧ρ) (eval-Valid ρ,e₂⇒z₂ ⟦vs⟧ρ)
|
||||
eval-Valid (⇒ᵉ-- ρ e₁ e₂ z₁ z₂ ρ,e₁⇒z₁ ρ,e₂⇒z₂) ⟦vs⟧ρ =
|
||||
minus-valid (eval-Valid ρ,e₁⇒z₁ ⟦vs⟧ρ) (eval-Valid ρ,e₂⇒z₂ ⟦vs⟧ρ)
|
||||
eval-Valid {vs} (⇒ᵉ-Var ρ x v x,v∈ρ) ⟦vs⟧ρ
|
||||
eval-valid : IsValid
|
||||
eval-valid (⇒ᵉ-+ ρ e₁ e₂ z₁ z₂ ρ,e₁⇒z₁ ρ,e₂⇒z₂) ⟦vs⟧ρ =
|
||||
plus-valid (eval-valid ρ,e₁⇒z₁ ⟦vs⟧ρ) (eval-valid ρ,e₂⇒z₂ ⟦vs⟧ρ)
|
||||
eval-valid (⇒ᵉ-- ρ e₁ e₂ z₁ z₂ ρ,e₁⇒z₁ ρ,e₂⇒z₂) ⟦vs⟧ρ =
|
||||
minus-valid (eval-valid ρ,e₁⇒z₁ ⟦vs⟧ρ) (eval-valid ρ,e₂⇒z₂ ⟦vs⟧ρ)
|
||||
eval-valid {vs} (⇒ᵉ-Var ρ x v x,v∈ρ) ⟦vs⟧ρ
|
||||
with ∈k-decᵛ x (proj₁ (proj₁ vs))
|
||||
... | yes x∈kvs = ⟦vs⟧ρ (proj₂ (locateᵛ {x} {vs} x∈kvs)) x,v∈ρ
|
||||
... | no x∉kvs = tt
|
||||
eval-Valid (⇒ᵉ-ℕ ρ 0) _ = refl
|
||||
eval-Valid (⇒ᵉ-ℕ ρ (suc n')) _ = (n' , refl)
|
||||
eval-valid (⇒ᵉ-ℕ ρ 0) _ = refl
|
||||
eval-valid (⇒ᵉ-ℕ ρ (suc n')) _ = (n' , refl)
|
||||
|
||||
open ForwardWithInterp.WithValidity eval-Valid using (analyze-correct) public
|
||||
analyze-correct = ForwardWithProg.analyze-correct
|
||||
|
||||
Loading…
Reference in New Issue
Block a user