diff options
Diffstat (limited to 'src/Helium/Semantics/Axiomatic/Core.agda')
-rw-r--r-- | src/Helium/Semantics/Axiomatic/Core.agda | 85 |
1 files changed, 0 insertions, 85 deletions
diff --git a/src/Helium/Semantics/Axiomatic/Core.agda b/src/Helium/Semantics/Axiomatic/Core.agda deleted file mode 100644 index a65a6d0..0000000 --- a/src/Helium/Semantics/Axiomatic/Core.agda +++ /dev/null @@ -1,85 +0,0 @@ ------------------------------------------------------------------------- --- Agda Helium --- --- Base definitions for the axiomatic semantics ------------------------------------------------------------------------- - -{-# OPTIONS --safe --without-K #-} - -open import Helium.Data.Pseudocode.Algebra using (RawPseudocode) - -module Helium.Semantics.Axiomatic.Core - {b₁ b₂ i₁ i₂ i₃ r₁ r₂ r₃} - (rawPseudocode : RawPseudocode b₁ b₂ i₁ i₂ i₃ r₁ r₂ r₃) - where - -private - open module C = RawPseudocode rawPseudocode - -open import Data.Bool as Bool using (Bool) -open import Data.Fin as Fin using (Fin; zero; suc) -open import Data.Fin.Patterns -open import Data.Nat as ℕ using (ℕ; suc) -import Data.Nat.Induction as Natᵢ -import Data.Nat.Properties as ℕₚ -open import Data.Product as × using (_×_; _,_; uncurry) -open import Data.Sum using (_⊎_) -open import Data.Unit using (⊤) -open import Data.Vec as Vec using (Vec; []; _∷_; _++_; lookup) -open import Data.Vec.Relation.Unary.All as All using (All; []; _∷_) -open import Function using (_on_) -open import Helium.Data.Pseudocode.Core -open import Helium.Data.Pseudocode.Properties -import Induction.WellFounded as Wf -open import Level using (_⊔_; Lift; lift) -import Relation.Binary.Construct.On as On -open import Relation.Binary.PropositionalEquality using (_≡_; refl; cong; cong₂) -open import Relation.Nullary using (Dec; does; yes; no) -open import Relation.Nullary.Decidable.Core using (True; toWitness; map′) -open import Relation.Nullary.Product using (_×-dec_) -open import Relation.Unary using (_⊆_) - -private - variable - t t′ : Type - m n : ℕ - Γ Δ Σ ts : Vec Type m - -⟦_⟧ₜ : Type → Set (b₁ ⊔ i₁ ⊔ r₁) -⟦_⟧ₜ′ : Vec Type n → Set (b₁ ⊔ i₁ ⊔ r₁) - -⟦ bool ⟧ₜ = Lift (b₁ ⊔ i₁ ⊔ r₁) Bool -⟦ int ⟧ₜ = Lift (b₁ ⊔ r₁) ℤ -⟦ fin n ⟧ₜ = Lift (b₁ ⊔ i₁ ⊔ r₁) (Fin n) -⟦ real ⟧ₜ = Lift (b₁ ⊔ i₁) ℝ -⟦ bit ⟧ₜ = Lift (i₁ ⊔ r₁) Bit -⟦ bits n ⟧ₜ = Vec ⟦ bit ⟧ₜ n -⟦ tuple n ts ⟧ₜ = ⟦ ts ⟧ₜ′ -⟦ array t n ⟧ₜ = Vec ⟦ t ⟧ₜ n - -⟦ [] ⟧ₜ′ = Lift (b₁ ⊔ i₁ ⊔ r₁) ⊤ -⟦ t ∷ ts ⟧ₜ′ = ⟦ t ⟧ₜ × ⟦ ts ⟧ₜ′ - -fetch : ∀ i → ⟦ Γ ⟧ₜ′ → ⟦ lookup Γ i ⟧ₜ -fetch {Γ = _ ∷ _} 0F (x , _) = x -fetch {Γ = _ ∷ _} (suc i) (_ , xs) = fetch i xs - -Transform : Vec Type m → Type → Set (b₁ ⊔ i₁ ⊔ r₁) -Transform ts t = ⟦ ts ⟧ₜ′ → ⟦ t ⟧ₜ - -Predicate : Vec Type m → Set (b₁ ⊔ i₁ ⊔ r₁) -Predicate ts = ⟦ ts ⟧ₜ′ → Bool - --- data HoareTriple {n Γ m Δ} : Assertion Σ {n} Γ {m} Δ → Statement Γ → Assertion Σ Γ Δ → Set (b₁ ⊔ i₁ ⊔ r₁) where --- _∙_ : ∀ {P Q R s₁ s₂} → HoareTriple P s₁ Q → HoareTriple Q s₂ R → HoareTriple P (s₁ ∙ s₂) R --- skip : ∀ {P} → HoareTriple P skip P - --- assign : ∀ {P t ref canAssign e} → HoareTriple (asrtSubst P (toWitness canAssign) (ℰ e)) (_≔_ {t = t} ref {canAssign} e) P --- declare : ∀ {t P Q e s} → HoareTriple (P ∧ equal (var 0F) (termWknVar (ℰ e))) s (asrtWknVar Q) → HoareTriple (asrtElimVar P (ℰ e)) (declare {t = t} e s) Q --- invoke : ∀ {m ts P Q s e} → HoareTriple (assignMetas Δ ts (All.tabulate var) (asrtAddVars P)) s (asrtAddVars Q) → HoareTriple (assignMetas Δ ts (All.tabulate (λ i → ℰ (All.lookup i e))) (asrtAddVars P)) (invoke {m = m} {ts} (s ∙end) e) (asrtAddVars Q) --- if : ∀ {P Q e s₁ s₂} → HoareTriple (P ∧ equal (ℰ e) (𝒦 (Bool.true ′b))) s₁ Q → HoareTriple (P ∧ equal (ℰ e) (𝒦 (Bool.false ′b))) s₂ Q → HoareTriple P (if e then s₁ else s₂) Q --- for : ∀ {m} {I : Assertion Σ Γ (fin (suc m) ∷ Δ)} {s} → HoareTriple (some (asrtWknVar (asrtWknMetaAt 1F I) ∧ equal (meta 1F) (var 0F) ∧ equal (meta 0F) (func (λ { _ (lift x ∷ []) → lift (Fin.inject₁ x) }) (meta 1F ∷ [])))) s (some (asrtWknVar (asrtWknMetaAt 1F I) ∧ equal (meta 0F) (func (λ { _ (lift x ∷ []) → lift (Fin.suc x) }) (meta 1F ∷ [])))) → HoareTriple (some (I ∧ equal (meta 0F) (func (λ _ _ → lift 0F) []))) (for m s) (some (I ∧ equal (meta 0F) (func (λ _ _ → lift (Fin.fromℕ m)) []))) - --- consequence : ∀ {P₁ P₂ Q₁ Q₂ s} → ⟦ P₁ ⟧ₐ ⊆ ⟦ P₂ ⟧ₐ → HoareTriple P₂ s Q₂ → ⟦ Q₂ ⟧ₐ ⊆ ⟦ Q₁ ⟧ₐ → HoareTriple P₁ s Q₁ --- some : ∀ {t P Q s} → HoareTriple P s Q → HoareTriple (some {t = t} P) s (some Q) --- frame : ∀ {P Q R s} → HoareTriple P s Q → HoareTriple (P * R) s (Q * R) |