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AST.agda
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AST.agda
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module Print.AST where
open import C
open import Data.Nat as ℕ using (ℕ)
open import Data.Integer as ℤ using (ℤ)
open import Data.String
open import Data.List using (List ; _∷_ ; [])
open import Data.Product
open import Relation.Nullary
open import Relation.Binary
open import Relation.Binary.PropositionalEquality
data IExpr : c_type → Set
IRef : c_type → Set
IRef _ = ℕ × List (IExpr Int)
data IExpr where
lit : ℤ → IExpr Int
add : IExpr Int → IExpr Int → IExpr Int
mul : IExpr Int → IExpr Int → IExpr Int
sub : IExpr Int → IExpr Int → IExpr Int
div : IExpr Int → IExpr Int → IExpr Int
lt : IExpr Int → IExpr Int → IExpr Bool
lte : IExpr Int → IExpr Int → IExpr Bool
gt : IExpr Int → IExpr Int → IExpr Bool
gte : IExpr Int → IExpr Int → IExpr Bool
eq : IExpr Int → IExpr Int → IExpr Bool
true : IExpr Bool
false : IExpr Bool
or : IExpr Bool → IExpr Bool → IExpr Bool
and : IExpr Bool → IExpr Bool → IExpr Bool
not : IExpr Bool → IExpr Bool
deref : ∀ { α } → IRef α → IExpr α
tenary : ∀ { α } → IExpr Bool → IExpr α → IExpr α → IExpr α
data IStatement : Set where
ifthenelse : IExpr Bool → IStatement → IStatement → IStatement
assignment : ∀ { α } → IRef α → IExpr α → IStatement
sequence : IStatement → IStatement → IStatement
declaration : (α : c_type) → ℕ → IStatement → IStatement
for : IRef Int → IExpr Int → IExpr Int → IStatement → IStatement
while : IExpr Bool → IStatement → IStatement
nop : IStatement
putchar : IExpr Int → IStatement
AST-C : Lang
Lang.Expr AST-C α = IExpr α
Lang.Ref AST-C α = IRef α
Lang.Statement AST-C = ℕ → ℕ × IStatement
Lang.⟪_⟫ AST-C x = lit x
Lang._+_ AST-C x y = add x y
Lang._*_ AST-C x y = mul x y
Lang._-_ AST-C x y = sub x y
Lang._/_ AST-C x y = div x y
Lang._<_ AST-C x y = lt x y
Lang._<=_ AST-C x y = lte x y
Lang._>_ AST-C x y = gt x y
Lang._>=_ AST-C x y = gte x y
Lang._==_ AST-C x y = eq x y
Lang.true AST-C = true
Lang.false AST-C = false
Lang._||_ AST-C x y = or x y
Lang._&&_ AST-C x y = and x y
Lang.!_ AST-C x = not x
Lang._[_] AST-C (r , l) i = r , i ∷ l
Lang.★_ AST-C x = deref x
Lang._⁇_∷_ AST-C c x y = tenary c x y
Lang._≔_ AST-C x y n = n , assignment x y
Lang.if_then_else_ AST-C e x y n =
let n , x = x n in
let n , y = y n in
n , ifthenelse e x y
Lang._；_ AST-C x y n =
let n , x = x n in
let n , y = y n in
n , sequence x y
Lang.decl AST-C α f n =
let ref = n in
let n , f = f (ref , []) (ℕ.suc n) in
n , declaration α ref f
Lang.nop AST-C n = n , nop
Lang.for_to_then_ AST-C l u f n =
let ref = (n , []) in
let n , f = f ref (ℕ.suc n) in
n , for ref l u f
Lang.while_then_ AST-C e f n =
let n , f = f n in
n , while e f
Lang.putchar AST-C x n = n , putchar x
toAST : (∀ ⦃ ℐ ⦄ → Lang.Statement ℐ) → IStatement
toAST s = proj₂ ((s ⦃ AST-C ⦄) 0)
≟-List : ∀ { a } { A : Set a }
→ Decidable (λ (a b : A) → a ≡ b) → Decidable (λ (a b : List A) → a ≡ b)
≟-List ≟-A [] [] = yes refl
≟-List ≟-A [] (x ∷ b) = no λ ()
≟-List ≟-A (x ∷ a) [] = no λ ()
≟-List ≟-A (x ∷ a) (y ∷ b) with ≟-A x y
... | no ¬p = no λ { refl → ¬p refl }
... | yes refl with ≟-List ≟-A a b
... | no ¬p = no λ { refl → ¬p refl }
... | yes refl = yes refl
≟-IExpr : ∀ { α } → Decidable (λ (a b : IExpr α) → a ≡ b)
≟-IRef : ∀ { α } → Decidable (λ ( a b : IRef α ) → a ≡ b)
≟-IRef (n , a) (m , b) with n ℕ.≟ m | ≟-List ≟-IExpr a b
... | yes refl | yes refl = yes refl
... | yes refl | no ¬q = no λ { refl → ¬q refl }
... | no ¬p | _ = no λ { refl → ¬p refl }
≟-IExpr (lit x) (lit y) with x ℤ.≟ y
... | yes refl = yes refl
... | no ¬p = no λ { refl → ¬p refl }
≟-IExpr (lit _) (add _ _) = no λ ()
≟-IExpr (lit _) (mul _ _) = no λ ()
≟-IExpr (lit _) (sub _ _) = no λ ()
≟-IExpr (lit _) (div _ _) = no λ ()
≟-IExpr (lit _) (deref x₁) = no λ ()
≟-IExpr (lit _) (tenary _ _ _) = no λ ()
≟-IExpr (add _ _) (lit _) = no λ ()
≟-IExpr (add a b) (add x y) with ≟-IExpr a x | ≟-IExpr b y
... | yes refl | yes refl = yes refl
... | yes refl | no ¬p = no λ { refl → ¬p refl }
... | no ¬p | _ = no λ { refl → ¬p refl }
≟-IExpr (add _ _) (mul _ _) = no λ ()
≟-IExpr (add _ _) (sub _ _) = no λ ()
≟-IExpr (add _ _) (div _ _) = no λ ()
≟-IExpr (add _ _) (deref _) = no λ ()
≟-IExpr (add _ _) (tenary _ _ _) = no λ ()
≟-IExpr (mul _ _) (lit _) = no λ ()
≟-IExpr (mul _ _) (add _ _) = no λ ()
≟-IExpr (mul a b) (mul x y) with ≟-IExpr a x | ≟-IExpr b y
... | yes refl | yes refl = yes refl
... | yes refl | no ¬p = no λ { refl → ¬p refl }
... | no ¬p | _ = no λ { refl → ¬p refl }
≟-IExpr (mul _ _) (sub _ _) = no λ ()
≟-IExpr (mul _ _) (div _ _) = no λ ()
≟-IExpr (mul _ _) (deref _) = no λ ()
≟-IExpr (mul _ _) (tenary _ _ _) = no λ ()
≟-IExpr (sub _ _) (lit _) = no λ ()
≟-IExpr (sub _ _) (add _ _) = no λ ()
≟-IExpr (sub _ _) (mul _ _) = no λ ()
≟-IExpr (sub x y) (sub a b) with ≟-IExpr a x | ≟-IExpr b y
... | yes refl | yes refl = yes refl
... | yes refl | no ¬p = no λ { refl → ¬p refl }
... | no ¬p | _ = no λ { refl → ¬p refl }
≟-IExpr (sub _ _) (div _ _) = no λ ()
≟-IExpr (sub _ _) (deref _) = no λ ()
≟-IExpr (sub _ _) (tenary _ _ _) = no λ ()
≟-IExpr (div _ _) (lit _) = no λ ()
≟-IExpr (div _ _) (add _ _) = no λ ()
≟-IExpr (div _ _) (mul _ _) = no λ ()
≟-IExpr (div _ _) (sub _ _) = no λ ()
≟-IExpr (div a b) (div x y) with ≟-IExpr a x | ≟-IExpr b y
... | yes refl | yes refl = yes refl
... | yes refl | no ¬p = no λ { refl → ¬p refl }
... | no ¬p | _ = no λ { refl → ¬p refl }
≟-IExpr (div _ _) (deref _) = no λ ()
≟-IExpr (div _ _) (tenary _ _ _) = no λ ()
≟-IExpr (lt a b) (lt x y) with ≟-IExpr a x | ≟-IExpr b y
... | yes refl | yes refl = yes refl
... | yes refl | no ¬p = no λ { refl → ¬p refl }
... | no ¬p | _ = no λ { refl → ¬p refl }
≟-IExpr (lt _ _) (lte _ _) = no λ ()
≟-IExpr (lt _ _) (gt _ _) = no λ ()
≟-IExpr (lt _ _) (gte _ _) = no λ ()
≟-IExpr (lt _ _) (eq _ _) = no λ ()
≟-IExpr (lt _ _) true = no λ ()
≟-IExpr (lt _ _) false = no λ ()
≟-IExpr (lt _ _) (or _ _) = no λ ()
≟-IExpr (lt _ _) (and _ _) = no λ ()
≟-IExpr (lt _ _) (not _) = no λ ()
≟-IExpr (lt _ _) (deref _) = no λ ()
≟-IExpr (lt _ _) (tenary _ _ _) = no λ ()
≟-IExpr (lte _ _) (lt _ _) = no λ ()
≟-IExpr (lte a b) (lte x y) with ≟-IExpr a x | ≟-IExpr b y
... | yes refl | yes refl = yes refl
... | yes refl | no ¬p = no λ { refl → ¬p refl }
... | no ¬p | _ = no λ { refl → ¬p refl }
≟-IExpr (lte _ _) (gt _ _) = no λ ()
≟-IExpr (lte _ _) (gte _ _) = no λ ()
≟-IExpr (lte _ _) (eq _ _) = no λ ()
≟-IExpr (lte _ _) true = no λ ()
≟-IExpr (lte _ _) false = no λ ()
≟-IExpr (lte _ _) (or _ _) = no λ ()
≟-IExpr (lte _ _) (and _ _) = no λ ()
≟-IExpr (lte _ _) (not _) = no λ ()
≟-IExpr (lte _ _) (deref _) = no λ ()
≟-IExpr (lte _ _) (tenary _ _ _) = no λ ()
≟-IExpr (gt _ _) (lt _ _) = no λ ()
≟-IExpr (gt _ _) (lte _ _) = no λ ()
≟-IExpr (gt a b) (gt x y) with ≟-IExpr a x | ≟-IExpr b y
... | yes refl | yes refl = yes refl
... | yes refl | no ¬p = no λ { refl → ¬p refl }
... | no ¬p | _ = no λ { refl → ¬p refl }
≟-IExpr (gt _ _) (gte _ _) = no λ ()
≟-IExpr (gt _ _) (eq _ _) = no λ ()
≟-IExpr (gt _ _) true = no λ ()
≟-IExpr (gt _ _) false = no λ ()
≟-IExpr (gt _ _) (or _ _) = no λ ()
≟-IExpr (gt _ _) (and _ _) = no λ ()
≟-IExpr (gt _ _) (not _) = no λ ()
≟-IExpr (gt _ _) (deref _) = no λ ()
≟-IExpr (gt _ _) (tenary _ _ _) = no λ ()
≟-IExpr (gte _ _) (lt _ _) = no λ ()
≟-IExpr (gte _ _) (lte _ _) = no λ ()
≟-IExpr (gte _ _) (gt _ _) = no λ ()
≟-IExpr (gte a b) (gte x y) with ≟-IExpr a x | ≟-IExpr b y
... | yes refl | yes refl = yes refl
... | yes refl | no ¬p = no λ { refl → ¬p refl }
... | no ¬p | _ = no λ { refl → ¬p refl }
≟-IExpr (gte _ _) (eq _ _) = no λ ()
≟-IExpr (gte _ _) true = no λ ()
≟-IExpr (gte _ _) false = no λ ()
≟-IExpr (gte _ _) (or _ _) = no λ ()
≟-IExpr (gte _ _) (and _ _) = no λ ()
≟-IExpr (gte _ _) (not _) = no λ ()
≟-IExpr (gte _ _) (deref _) = no λ ()
≟-IExpr (gte _ _) (tenary _ _ _) = no λ ()
≟-IExpr (eq _ _) (lt _ _) = no λ ()
≟-IExpr (eq _ _) (lte _ _) = no λ ()
≟-IExpr (eq _ _) (gt _ _) = no λ ()
≟-IExpr (eq _ _) (gte _ _) = no (λ ())
≟-IExpr (eq a b) (eq x y) with ≟-IExpr a x | ≟-IExpr b y
... | yes refl | yes refl = yes refl
... | yes refl | no ¬p = no λ { refl → ¬p refl }
... | no ¬p | _ = no λ { refl → ¬p refl }
≟-IExpr (eq _ _) true = no (λ ())
≟-IExpr (eq _ _) false = no (λ ())
≟-IExpr (eq _ _) (or _ _) = no (λ ())
≟-IExpr (eq _ _) (and _ _) = no (λ ())
≟-IExpr (eq _ _) (not _) = no (λ ())
≟-IExpr (eq _ _) (deref _) = no (λ ())
≟-IExpr (eq _ _) (tenary _ _ _) = no (λ ())
≟-IExpr true (lt _ _) = no (λ ())
≟-IExpr true (lte _ _) = no (λ ())
≟-IExpr true (gt _ _) = no (λ ())
≟-IExpr true (gte _ _) = no (λ ())
≟-IExpr true (eq _ _) = no (λ ())
≟-IExpr true true = yes refl
≟-IExpr true false = no (λ ())
≟-IExpr true (or _ _) = no (λ ())
≟-IExpr true (and _ _) = no (λ ())
≟-IExpr true (not _) = no (λ ())
≟-IExpr true (deref _) = no (λ ())
≟-IExpr true (tenary _ _ _) = no (λ ())
≟-IExpr false (lt _ _) = no (λ ())
≟-IExpr false (lte _ _) = no (λ ())
≟-IExpr false (gt _ _) = no (λ ())
≟-IExpr false (gte _ _) = no (λ ())
≟-IExpr false (eq _ _) = no (λ ())
≟-IExpr false true = no (λ ())
≟-IExpr false false = yes refl
≟-IExpr false (or _ _) = no (λ ())
≟-IExpr false (and _ _) = no (λ ())
≟-IExpr false (not _) = no (λ ())
≟-IExpr false (deref _) = no (λ ())
≟-IExpr false (tenary _ _ _) = no (λ ())
≟-IExpr (or _ _) (lt _ _) = no (λ ())
≟-IExpr (or _ _) (lte _ _) = no (λ ())
≟-IExpr (or _ _) (gt _ _) = no (λ ())
≟-IExpr (or _ _) (gte _ _) = no (λ ())
≟-IExpr (or _ _) (eq _ _) = no (λ ())
≟-IExpr (or _ _) true = no (λ ())
≟-IExpr (or _ _) false = no (λ ())
≟-IExpr (or a b) (or x y) with ≟-IExpr a x | ≟-IExpr b y
... | yes refl | yes refl = yes refl
... | yes refl | no ¬p = no λ { refl → ¬p refl }
... | no ¬p | _ = no λ { refl → ¬p refl }
≟-IExpr (or _ _) (and _ _) = no (λ ())
≟-IExpr (or _ _) (not _) = no (λ ())
≟-IExpr (or _ _) (deref _) = no (λ ())
≟-IExpr (or _ _) (tenary _ _ _) = no (λ ())
≟-IExpr (and _ _) (lt _ _) = no (λ ())
≟-IExpr (and _ _) (lte _ _) = no (λ ())
≟-IExpr (and _ _) (gt _ _) = no (λ ())
≟-IExpr (and _ _) (gte _ _) = no (λ ())
≟-IExpr (and _ _) (eq _ _) = no (λ ())
≟-IExpr (and _ _) true = no (λ ())
≟-IExpr (and _ _) false = no (λ ())
≟-IExpr (and _ _) (or _ _) = no (λ ())
≟-IExpr (and a b) (and x y) with ≟-IExpr a x | ≟-IExpr b y
... | yes refl | yes refl = yes refl
... | yes refl | no ¬p = no λ { refl → ¬p refl }
... | no ¬p | _ = no λ { refl → ¬p refl }
≟-IExpr (and _ _) (not _) = no (λ ())
≟-IExpr (and _ _) (deref _) = no (λ ())
≟-IExpr (and _ _) (tenary _ _ _) = no (λ ())
≟-IExpr (not _) (lt _ _) = no (λ ())
≟-IExpr (not _) (lte _ _) = no (λ ())
≟-IExpr (not _) (gt _ _) = no (λ ())
≟-IExpr (not _) (gte _ _) = no (λ ())
≟-IExpr (not _) (eq _ _) = no (λ ())
≟-IExpr (not _) true = no (λ ())
≟-IExpr (not _) false = no (λ ())
≟-IExpr (not _) (or _ _) = no (λ ())
≟-IExpr (not _) (and _ _) = no (λ ())
≟-IExpr (not a) (not b) with ≟-IExpr a b
... | yes refl = yes refl
... | no ¬p = no λ { refl → ¬p refl }
≟-IExpr (not _) (deref _) = no (λ ())
≟-IExpr (not _) (tenary _ _ _) = no (λ ())
≟-IExpr (deref _) (lit _) = no (λ ())
≟-IExpr (deref _) (add _ _) = no (λ ())
≟-IExpr (deref _) (mul _ _) = no (λ ())
≟-IExpr (deref _) (sub _ _) = no (λ ())
≟-IExpr (deref _) (div _ _) = no (λ ())
≟-IExpr (deref _) (lt _ _) = no (λ ())
≟-IExpr (deref _) (lte _ _) = no (λ ())
≟-IExpr (deref _) (gt _ _) = no (λ ())
≟-IExpr (deref _) (gte _ _) = no (λ ())
≟-IExpr (deref _) (eq _ _) = no (λ ())
≟-IExpr (deref _) true = no (λ ())
≟-IExpr (deref _) false = no (λ ())
≟-IExpr (deref _) (or _ _) = no (λ ())
≟-IExpr (deref _) (and _ _) = no (λ ())
≟-IExpr (deref _) (not _) = no (λ ())
≟-IExpr {α} (deref a) (deref b) =
∨-dec (helper a b)
where
helper : Decidable (λ (a b : IRef α) → a ≡ b)
helper (n , a) (m , b) with n ℕ.≟ m
... | no ¬p = no λ { refl → ¬p refl }
... | yes refl with check-list a b
where
check-list : Decidable (λ (x y : List (IExpr Int)) → x ≡ y)
check-list [] [] = yes refl
check-list [] (x ∷ y) = no λ ()
check-list (x ∷ x₁) [] = no λ ()
check-list (x ∷ xs) (y ∷ ys) with ≟-IExpr x y
... | no ¬q = no λ { refl → ¬q refl }
... | yes refl with check-list xs ys
... | no ¬q = no λ { refl → ¬q refl }
... | yes refl = yes refl
... | yes refl = yes refl
... | no ¬q = no λ { refl → ¬q refl }
∨-dec : ∀ { a b : IRef α } → Dec (a ≡ b) → Dec (deref a ≡ deref b)
∨-dec (yes refl) = yes refl
∨-dec (no ¬p) = no λ { refl → ¬p refl }
≟-IExpr (deref _) (tenary _ _ _) = no (λ ())
≟-IExpr (tenary _ _ _) (lit _) = no (λ ())
≟-IExpr (tenary _ _ _) (add _ _) = no (λ ())
≟-IExpr (tenary _ _ _) (mul _ _) = no (λ ())
≟-IExpr (tenary _ _ _) (sub _ _) = no (λ ())
≟-IExpr (tenary _ _ _) (div _ _) = no (λ ())
≟-IExpr (tenary _ _ _) (lt _ _) = no (λ ())
≟-IExpr (tenary _ _ _) (lte _ _) = no (λ ())
≟-IExpr (tenary _ _ _) (gt _ _) = no (λ ())
≟-IExpr (tenary _ _ _) (gte _ _) = no (λ ())
≟-IExpr (tenary _ _ _) (eq _ _) = no (λ ())
≟-IExpr (tenary _ _ _) true = no (λ ())
≟-IExpr (tenary _ _ _) false = no (λ ())
≟-IExpr (tenary _ _ _) (or _ _) = no (λ ())
≟-IExpr (tenary _ _ _) (and _ _) = no (λ ())
≟-IExpr (tenary _ _ _) (not _) = no (λ ())
≟-IExpr (tenary _ _ _) (deref _) = no (λ ())
≟-IExpr (tenary a b c) (tenary x y z) with ≟-IExpr a x | ≟-IExpr b y | ≟-IExpr c z
... | yes refl | yes refl | yes refl = yes refl
... | yes refl | yes refl | no ¬p = no λ { refl → ¬p refl }
... | yes refl | no ¬p | _ = no λ { refl → ¬p refl }
... | no ¬p | _ | _ = no λ { refl → ¬p refl }