diff options
author | Greg Brown <greg.brown@cl.cam.ac.uk> | 2022-02-02 14:18:34 +0000 |
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committer | Greg Brown <greg.brown@cl.cam.ac.uk> | 2022-02-02 14:18:34 +0000 |
commit | e947c8ef6c844b612e7aec9670f67d00008661e3 (patch) | |
tree | 1775714cb127f1df61e98ded8a84699ecdd33f2e /src/Helium/Semantics/Denotational | |
parent | 66fa99f84c918ad3a7680a6df141367c291ceaee (diff) |
Define pseudocode for a number of instructions.
Diffstat (limited to 'src/Helium/Semantics/Denotational')
-rw-r--r-- | src/Helium/Semantics/Denotational/Core.agda | 128 |
1 files changed, 0 insertions, 128 deletions
diff --git a/src/Helium/Semantics/Denotational/Core.agda b/src/Helium/Semantics/Denotational/Core.agda deleted file mode 100644 index 9b6a3c8..0000000 --- a/src/Helium/Semantics/Denotational/Core.agda +++ /dev/null @@ -1,128 +0,0 @@ ------------------------------------------------------------------------- --- Agda Helium --- --- Base definitions for the denotational semantics. ------------------------------------------------------------------------- - -{-# OPTIONS --safe --without-K #-} - -module Helium.Semantics.Denotational.Core - {ℓ′} - (State : Set ℓ′) - where - -open import Algebra.Core -open import Data.Bool as Bool using (Bool) -open import Data.Fin hiding (lift) -open import Data.Nat using (ℕ; zero; suc) -import Data.Nat.Properties as ℕₚ -open import Data.Product hiding (_<*>_; _,′_) -open import Data.Product.Nary.NonDependent -open import Data.Sum using (_⊎_; inj₁; inj₂; fromInj₂; [_,_]′) -open import Data.Unit using (⊤) -open import Level renaming (suc to ℓsuc) hiding (zero) -open import Function using (_∘_; _∘₂_; _|>_) -open import Function.Nary.NonDependent.Base -open import Relation.Nullary.Decidable using (True) - -private - variable - ℓ ℓ₁ ℓ₂ : Level - τ τ′ : Set ℓ - - update : ∀ {n ls} {Γ : Sets n ls} i → Projₙ Γ i → Product⊤ n Γ → Product⊤ n Γ - update zero y (_ , xs) = y , xs - update (suc i) y (x , xs) = x , update i y xs - -Expr : ∀ n {ls} → Sets n ls → Set ℓ → Set (ℓ ⊔ ⨆ n ls ⊔ ℓ′) -Expr n Γ τ = (σ : State) → (ρ : Product⊤ n Γ) → τ - -record Reference n {ls} (Γ : Sets n ls) (τ : Set ℓ) : Set (ℓ ⊔ ⨆ n ls ⊔ ℓ′) where - field - get : Expr n Γ τ - set : τ → Expr n Γ (State × Product⊤ n Γ) - -Function : ∀ n {ls} → Sets n ls → Set ℓ → Set (ℓ ⊔ ⨆ n ls ⊔ ℓ′) -Function n Γ τ = Expr n Γ τ - -Procedure : ∀ n {ls} → Sets n ls → Set (⨆ n ls ⊔ ℓ′) -Procedure n Γ = Expr n Γ State - -Statement : ∀ n {ls} → Sets n ls → Set ℓ → Set (ℓ ⊔ ⨆ n ls ⊔ ℓ′) -Statement n Γ τ = Expr n Γ (State × (Product⊤ n Γ ⊎ τ)) - --- Expressions - -pure : ∀ {n ls} {Γ : Sets n ls} → τ → Expr n Γ τ -pure v σ ρ = v - -_<*>_ : ∀ {n ls} {Γ : Sets n ls} → Expr n Γ (τ → τ′) → Expr n Γ τ → Expr n Γ τ′ -_<*>_ f e σ ρ = f σ ρ |> λ f → f (e σ ρ) - -!_ : ∀ {n ls} {Γ : Sets n ls} → Reference n Γ τ → Expr n Γ τ -! r = Reference.get r - -call : ∀ {m n ls₁ ls₂} {Γ : Sets m ls₁} {Δ : Sets n ls₂} → Function m Γ τ → Expr n Δ (Product m Γ) → Expr n Δ τ -call f e σ ρ = e σ ρ |> toProduct⊤ _ |> f σ - -declare : ∀ {n ls} {Γ : Sets n ls} → Expr n Γ τ → Expr (suc n) (τ , Γ) τ′ → Expr n Γ τ′ -declare e s σ ρ = e σ ρ |> _, ρ |> s σ - --- References - -var : ∀ {n ls} {Γ : Sets n ls} i → Reference n Γ (Projₙ Γ i) -var i = record - { get = λ σ ρ → projₙ _ i (toProduct _ ρ) - ; set = λ v → curry (map₂ (update i v)) - } - -!#_ : ∀ {n ls} {Γ : Sets n ls} m {m<n : True (suc m ℕₚ.≤? n)} → Expr n Γ (Projₙ Γ (#_ m {n} {m<n})) -(!# m) {m<n} = ! var (#_ m {m<n = m<n}) - -_,′_ : ∀ {n ls} {Γ : Sets n ls} → Reference n Γ τ → Reference n Γ τ′ → Reference n Γ (τ × τ′) -&x ,′ &y = record - { get = λ σ ρ → Reference.get &x σ ρ , Reference.get &y σ ρ - ; set = λ (x , y) σ ρ → uncurry (Reference.set &y y) (Reference.set &x x σ ρ) - } - --- Statements - -infixl 1 _∙_ _∙return_ -infix 1 _∙end -infixl 2 if_then_else_ -infix 4 _≔_ _⟵_ - -skip : ∀ {n ls} {Γ : Sets n ls} → Statement n Γ τ -skip σ ρ = σ , inj₁ ρ - -invoke : ∀ {m n ls₁ ls₂} {Γ : Sets m ls₁} {Δ : Sets n ls₂} → Procedure m Γ → Expr n Δ (Product m Γ) → Statement n Δ τ -invoke f e σ ρ = call f e σ ρ |> _, inj₁ ρ - -_≔_ : ∀ {n ls} {Γ : Sets n ls} → Reference n Γ τ → Expr n Γ τ → Statement n Γ τ′ -(&x ≔ e) σ ρ = e σ ρ |> λ x → Reference.set &x x σ ρ |> map₂ inj₁ - -_⟵_ : ∀ {n ls} {Γ : Sets n ls} → Reference n Γ τ → Op₁ τ → Statement n Γ τ′ -&x ⟵ e = &x ≔ ⦇ e (! &x) ⦈ - -if_then_else_ : ∀ {n ls} {Γ : Sets n ls} → Expr n Γ Bool → Statement n Γ τ → Statement n Γ τ → Statement n Γ τ -(if e then b₁ else b₂) σ ρ = e σ ρ |> (Bool.if_then b₁ σ ρ else b₂ σ ρ) - -for : ∀ {n ls} {Γ : Sets n ls} m → Statement (suc n) (Fin m , Γ) τ → Statement n Γ τ -for zero b σ ρ = σ , inj₁ ρ -for (suc m) b σ ρ with b σ (zero , ρ) -... | σ′ , inj₂ x = σ′ , inj₂ x -... | σ′ , inj₁ (_ , ρ′) = for m b′ σ′ ρ′ - where - b′ : Statement (suc _) (Fin m , _) _ - b′ σ (i , ρ) with b σ (suc i , ρ) - ... | σ′ , inj₂ x = σ′ , inj₂ x - ... | σ′ , inj₁ (_ , ρ′) = σ′ , inj₁ (i , ρ′) - -_∙_ : ∀ {n ls} {Γ : Sets n ls} → Statement n Γ τ → Statement n Γ τ → Statement n Γ τ -(b₁ ∙ b₂) σ ρ = b₁ σ ρ |> λ (σ , ρ⊎x) → [ b₂ σ , (σ ,_) ∘ inj₂ ]′ ρ⊎x - -_∙end : ∀ {n ls} {Γ : Sets n ls} → Statement n Γ ⊤ → Procedure n Γ -_∙end s σ ρ = s σ ρ |> proj₁ - -_∙return_ : ∀ {n ls} {Γ : Sets n ls} → Statement n Γ τ → Expr n Γ τ → Function n Γ τ -(s ∙return e) σ ρ = s σ ρ |> λ (σ , ρ⊎x) → fromInj₂ (e σ) ρ⊎x |