Separate out Hoare logic terms.

1 files changed, 26 insertions, 68 deletions

diff --git a/src/Helium/Semantics/Axiomatic/Core.agda b/src/Helium/Semantics/Axiomatic/Core.agda
index 176dbdd..de4f411 100644
--- a/src/Helium/Semantics/Axiomatic/Core.agda
+++ b/src/Helium/Semantics/Axiomatic/Core.agda
@@ -22,7 +22,7 @@ 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.Product as × using (_×_; _,_; uncurry)
 open import Data.Sum using (_⊎_)
 open import Data.Unit using (⊤)
 open import Data.Vec as Vec using (Vec; []; _∷_; _++_; lookup)
@@ -45,79 +45,37 @@ private
     m n      : ℕ
     Γ Δ Σ ts : Vec Type m
 
-sizeOf : Type → Sliced → ℕ
-sizeOf bool s = 0
-sizeOf int s = 0
-sizeOf (fin n) s = 0
-sizeOf real s = 0
-sizeOf bit s = 0
-sizeOf (bits n) s = Bool.if does (s ≟ˢ bits) then n else 0
-sizeOf (tuple _ []) s = 0
-sizeOf (tuple _ (t ∷ ts)) s = sizeOf t s ℕ.+ sizeOf (tuple _ ts) s
-sizeOf (array t n) s = Bool.if does (s ≟ˢ array t) then n else sizeOf t s
+⟦_⟧ₜ  : Type → Set (b₁ ⊔ i₁ ⊔ r₁)
+⟦_⟧ₜ′ : Vec Type n → Set (b₁ ⊔ i₁ ⊔ r₁)
 
-allocateSpace : Vec Type n → Sliced → ℕ
-allocateSpace []       s = 0
-allocateSpace (t ∷ ts) s = sizeOf t s ℕ.+ allocateSpace ts s
+⟦ 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
 
-private
-  getSliced : ∀ {t} → True (sliced? t) → Sliced
-  getSliced t = ×.proj₁ (toWitness t)
-
-  getCount : ∀ {t} → True (sliced? t) → ℕ
-  getCount t = ×.proj₁ (×.proj₂ (toWitness t))
-
-data ⟦_；_⟧ₜ (counts : Sliced → ℕ) : (τ : Type) → Set (b₁ ⊔ i₁ ⊔ r₁) where
-  bool   : Bool → ⟦ counts ； bool ⟧ₜ
-  int    : ℤ → ⟦ counts ； int ⟧ₜ
-  fin    : ∀ {n} → Fin n → ⟦ counts ； fin n ⟧ₜ
-  real   : ℝ → ⟦ counts ； real ⟧ₜ
-  bit    : Bit → ⟦ counts ； bit ⟧ₜ
-  bits   : ∀ {n} → Vec (⟦ counts ； bit ⟧ₜ ⊎ Fin (counts bits)) n → ⟦ counts ； bits n ⟧ₜ
-  array  : ∀ {t n} → Vec (⟦ counts ； t ⟧ₜ ⊎ Fin (counts (array t))) n → ⟦ counts ； array t n ⟧ₜ
-  tuple  : ∀ {n ts} → All ⟦ counts ；_⟧ₜ  ts → ⟦ counts ； tuple n ts ⟧ₜ
-
-Stack : (counts : Sliced → ℕ) → Vec Type n → Set (b₁ ⊔ i₁ ⊔ r₁)
-Stack counts Γ = ⟦ counts ； tuple _ Γ ⟧ₜ
-
-Heap : (counts : Sliced → ℕ) → Set (b₁ ⊔ i₁ ⊔ r₁)
-Heap counts = ∀ t → Vec ⟦ counts ； elemType t ⟧ₜ (counts t)
-
-record State (Γ : Vec Type n) : Set (b₁ ⊔ i₁ ⊔ r₁) where
-  private
-    counts = allocateSpace Γ
-  field
-    stack   : Stack counts Γ
-    heap    : Heap counts
+⟦ [] ⟧ₜ′     = Lift (b₁ ⊔ i₁ ⊔ r₁) ⊤
+⟦ t ∷ ts ⟧ₜ′ = ⟦ t ⟧ₜ × ⟦ ts ⟧ₜ′
 
 Transform : Vec Type m → Type → Set (b₁ ⊔ i₁ ⊔ r₁)
-Transform ts t = ∀ counts → Heap counts → ⟦ counts ； tuple _ ts ⟧ₜ → ⟦ counts ； t ⟧ₜ
+Transform ts t = ⟦ ts ⟧ₜ′ → ⟦ t ⟧ₜ
 
 Predicate : Vec Type m → Set (b₁ ⊔ i₁ ⊔ r₁)
-Predicate ts = ∀ counts → ⟦ counts ； tuple _ ts ⟧ₜ → Bool
-
--- --   ⟦_⟧ₐ : ∀ {m Δ} → Assertion Σ Γ {m} Δ → State (Σ ++ Γ ++ Δ) → Set (b₁ ⊔ i₁ ⊔ r₁)
--- --   ⟦_⟧ₐ = {!!}
-
--- -- module _ {o} {Σ : Vec Type o} where
--- --   open Code Σ
-
--- --   𝒦 : ∀ {n Γ m Δ t} → Literal t → Term Σ {n} Γ {m} Δ t
--- --   𝒦 = {!!}
-
--- --   ℰ : ∀ {n Γ m Δ t} → Expression {n} Γ t → Term Σ Γ {m} Δ t
--- --   ℰ = {!!}
+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
+--   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)) [])))
+--     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)
+--     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)