diff options
Diffstat (limited to 'src/Helium/Data/Pseudocode')
| -rw-r--r-- | src/Helium/Data/Pseudocode/Core.agda | 107 |
1 files changed, 61 insertions, 46 deletions
diff --git a/src/Helium/Data/Pseudocode/Core.agda b/src/Helium/Data/Pseudocode/Core.agda index 286b259..4e57f17 100644 --- a/src/Helium/Data/Pseudocode/Core.agda +++ b/src/Helium/Data/Pseudocode/Core.agda @@ -113,9 +113,8 @@ module Code {o} (Σ : Vec Type o) where data Expression {n} (Γ : Vec Type n) : Type → Set data CanAssign {n Γ} : ∀ {t} → Expression {n} Γ t → Set canAssign? : ∀ {n Γ t} → Decidable (CanAssign {n} {Γ} {t}) - data AssignsState {n Γ} : ∀ {t e} → CanAssign {n} {Γ} {t} e → Set - assignsState? : ∀ {n Γ t e} → Decidable (AssignsState {n} {Γ} {t} {e}) - assignsStateAny? : ∀ {n Γ m ts es} → Decidable {A = All (CanAssign ∘ proj₂) (reduce {P = Expression {n} Γ} (λ {x} e → x , e) {m} {ts} es)} (Any (AssignsState ∘ proj₂) ∘ reduce (λ {x} a → x , a)) + data ReferencesState {n Γ} : ∀ {t} → Expression {n} Γ t → Set + referencesState? : ∀ {n Γ t} → Decidable (ReferencesState {n} {Γ} {t}) data Statement {n} (Γ : Vec Type n) : Set data ChangesState {n Γ} : Statement {n} Γ → Set changesState? : ∀ {n Γ} → Decidable (ChangesState {n} {Γ}) @@ -126,7 +125,7 @@ module Code {o} (Σ : Vec Type o) where infixr 7 _^_ infixl 6 _*_ _and_ _>>_ -- infixl 6 _/_ - infixl 5 _+_ _or_ _&&_ _||_ _∶_ + infixl 5 _+_ _or_ _&&_ _||_ infix 4 _≟_ _<?_ data Expression {n} Γ where @@ -210,34 +209,50 @@ module Code {o} (Σ : Vec Type o) where canAssign? (call x e) = no λ () canAssign? (if e then e₁ else e₂) = no λ () - data AssignsState where - state : ∀ i → AssignsState (state i) - [_] : ∀ {t e a} → AssignsState a → AssignsState ([_] {t = t} {e} a) - unbox : ∀ {t e a} → AssignsState a → AssignsState (unbox {t = t} {e} a) - spliceˡ : ∀ {m n t e₁ e₂ a₁} → AssignsState a₁ → ∀ a₂ e₃ → AssignsState (splice {m = m} {n} {t} {e₁} {e₂} a₁ a₂ e₃) - spliceʳ : ∀ {m n t e₁ e₂} a₁ {a₂} → AssignsState a₂ → ∀ e₃ → AssignsState (splice {m = m} {n} {t} {e₁} {e₂} a₁ a₂ e₃) - cut : ∀ {m n t e₁ a₁} → AssignsState a₁ → ∀ e₂ → AssignsState (cut {m = m} {n} {t} {e₁} a₁ e₂) - cast : ∀ {i j t e} .(eq : i ≡ j) {a} → AssignsState a → AssignsState (cast {t = t} {e} eq a) - consˡ : ∀ {m t ts e₁ e₂ a₁} → AssignsState a₁ → ∀ a₂ → AssignsState (cons {m = m} {t} {ts} {e₁} {e₂} a₁ a₂) - consʳ : ∀ {m t ts e₁ e₂} a₁ {a₂} → AssignsState a₂ → AssignsState (cons {m = m} {t} {ts} {e₁} {e₂} a₁ a₂) - head : ∀ {m t ts e a} → AssignsState a → AssignsState (head {m = m} {t} {ts} {e} a) - tail : ∀ {m t ts e a} → AssignsState a → AssignsState (tail {m = m} {t} {ts} {e} a) - - assignsState? (state i) = yes (state i) - assignsState? (var i) = no λ () - assignsState? (abort e) = no λ () - assignsState? [ a ] = map′ [_] (λ { [ s ] → s }) (assignsState? a) - assignsState? (unbox a) = map′ unbox (λ { (unbox s) → s }) (assignsState? a) - assignsState? (splice a₁ a₂ e₃) = map′ [ (λ a₁ → spliceˡ a₁ a₂ e₃) , (λ a₂ → spliceʳ a₁ a₂ e₃) ]′ (λ { (spliceˡ a₁ _ _) → inj₁ a₁ ; (spliceʳ _ a₂ _) → inj₂ a₂ }) (assignsState? a₁ ⊎-dec assignsState? a₂) - assignsState? (cut a e₂) = map′ (λ s → cut s e₂ ) (λ { (cut s _) → s }) (assignsState? a) - assignsState? (cast eq a) = map′ (cast eq) (λ { (cast _ s) → s }) (assignsState? a) - assignsState? nil = no λ () - assignsState? (cons a₁ a₂) = map′ [ (λ a₁ → consˡ a₁ a₂) , (λ a₂ → consʳ a₁ a₂) ]′ (λ { (consˡ a₁ _) → inj₁ a₁ ; (consʳ _ a₂) → inj₂ a₂ }) (assignsState? a₁ ⊎-dec assignsState? a₂) - assignsState? (head a) = map′ head (λ { (head s) → s }) (assignsState? a) - assignsState? (tail a) = map′ tail (λ { (tail s) → s }) (assignsState? a) - - assignsStateAny? {es = []} [] = no λ () - assignsStateAny? {es = e ∷ es} (a ∷ as) = map′ [ here , there ]′ (λ { (here s) → inj₁ s ; (there ss) → inj₂ ss }) (assignsState? a ⊎-dec assignsStateAny? as) + data ReferencesState where + state : ∀ i → ReferencesState (state i) + [_] : ∀ {t e} → ReferencesState e → ReferencesState ([_] {t = t} e) + unbox : ∀ {t e} → ReferencesState e → ReferencesState (unbox {t = t} e) + spliceˡ : ∀ {m n t e} → ReferencesState e → ∀ e₁ e₂ → ReferencesState (splice {m = m} {n} {t} e e₁ e₂) + spliceʳ : ∀ {m n t} e {e₁} → ReferencesState e₁ → ∀ e₂ → ReferencesState (splice {m = m} {n} {t} e e₁ e₂) + cut : ∀ {m n t e} → ReferencesState e → ∀ e₁ → ReferencesState (cut {m = m} {n} {t} e e₁) + cast : ∀ {i j t} .(eq : i ≡ j) {e} → ReferencesState e → ReferencesState (cast {t = t} eq e) + consˡ : ∀ {m t ts e} → ReferencesState e → ∀ e₁ → ReferencesState (cons {m = m} {t} {ts} e e₁) + consʳ : ∀ {m t ts} e {e₁} → ReferencesState e₁ → ReferencesState (cons {m = m} {t} {ts} e e₁) + head : ∀ {m t ts e} → ReferencesState e → ReferencesState (head {m = m} {t} {ts} e) + tail : ∀ {m t ts e} → ReferencesState e → ReferencesState (tail {m = m} {t} {ts} e) + + referencesState? (lit x) = no λ () + referencesState? (state i) = yes (state i) + referencesState? (var i) = no λ () + referencesState? (abort e) = no λ () + referencesState? (e ≟ e₁) = no λ () + referencesState? (e <? e₁) = no λ () + referencesState? (inv e) = no λ () + referencesState? (e && e₁) = no λ () + referencesState? (e || e₁) = no λ () + referencesState? (not e) = no λ () + referencesState? (e and e₁) = no λ () + referencesState? (e or e₁) = no λ () + referencesState? [ e ] = map′ [_] (λ { [ e ] → e }) (referencesState? e) + referencesState? (unbox e) = map′ unbox (λ { (unbox e) → e }) (referencesState? e) + referencesState? (splice e e₁ e₂) = map′ [ (λ e → spliceˡ e e₁ e₂) , (λ e₁ → spliceʳ e e₁ e₂) ]′ (λ { (spliceˡ e e₁ e₂) → inj₁ e ; (spliceʳ e e₁ e₂) → inj₂ e₁ }) (referencesState? e ⊎-dec referencesState? e₁) + referencesState? (cut e e₁) = map′ (λ e → cut e e₁) (λ { (cut e e₁) → e }) (referencesState? e) + referencesState? (cast eq e) = map′ (cast eq) (λ { (cast eq e) → e }) (referencesState? e) + referencesState? (- e) = no λ () + referencesState? (e + e₁) = no λ () + referencesState? (e * e₁) = no λ () + referencesState? (e ^ x) = no λ () + referencesState? (e >> x) = no λ () + referencesState? (rnd e) = no λ () + referencesState? (fin x e) = no λ () + referencesState? (asInt e) = no λ () + referencesState? nil = no λ () + referencesState? (cons e e₁) = map′ [ (λ e → consˡ e e₁) , (λ e₁ → consʳ e e₁) ]′ (λ { (consˡ e e₁) → inj₁ e ; (consʳ e e₁) → inj₂ e₁ }) (referencesState? e ⊎-dec referencesState? e₁) + referencesState? (head e) = map′ head (λ { (head e) → e }) (referencesState? e) + referencesState? (tail e) = map′ tail (λ { (tail e) → e }) (referencesState? e) + referencesState? (call f es) = no λ () + referencesState? (if e then e₁ else e₂) = no λ () infix 4 _≔_ infixl 2 if_then_else_ @@ -254,22 +269,22 @@ module Code {o} (Σ : Vec Type o) where for : ∀ m → Statement (fin m ∷ Γ) → Statement Γ data ChangesState where - _∙ˡ_ : ∀ {s₁} → ChangesState s₁ → ∀ s₂ → ChangesState (s₁ ∙ s₂) - _∙ʳ_ : ∀ s₁ {s₂} → ChangesState s₂ → ChangesState (s₁ ∙ s₂) - _≔_ : ∀ {t ref} canAssign {assignsState : True (assignsState? (toWitness canAssign))} e₂ → ChangesState (_≔_ {t = t} ref {canAssign} e₂) + _∙ˡ_ : ∀ {s} → ChangesState s → ∀ s₁ → ChangesState (s ∙ s₁) + _∙ʳ_ : ∀ s {s₁} → ChangesState s₁ → ChangesState (s ∙ s₁) + _≔_ : ∀ {t} ref {canAssign : True (canAssign? ref)} {refsState : True (referencesState? ref)} e₂ → ChangesState (_≔_ {t = t} ref {canAssign} e₂) declare : ∀ {t} e {s} → ChangesState s → ChangesState (declare {t = t} e s) - invoke : ∀ {m Δ} p e → ChangesState (invoke {m = m} {Δ} p e) - if_then′_else_ : ∀ e {s₁} → ChangesState s₁ → ∀ s₂ → ChangesState (if e then s₁ else s₂) - if_then_else′_ : ∀ e s₁ {s₂} → ChangesState s₂ → ChangesState (if e then s₁ else s₂) + invoke : ∀ {m Δ} p es → ChangesState (invoke {m = m} {Δ} p es) + if_then′_else_ : ∀ e {s} → ChangesState s → ∀ s₁ → ChangesState (if e then s else s₁) + if_then_else′_ : ∀ e s {s₁} → ChangesState s₁ → ChangesState (if e then s else s₁) for : ∀ m {s} → ChangesState s → ChangesState (for m s) - changesState? (s₁ ∙ s₂) = map′ [ _∙ˡ s₂ , s₁ ∙ʳ_ ]′ (λ { (s ∙ˡ _) → inj₁ s ; (_ ∙ʳ s) → inj₂ s }) (changesState? s₁ ⊎-dec changesState? s₂) - changesState? skip = no λ () - changesState? (_≔_ ref {a} e) = map′ (λ s → _≔_ a {fromWitness s} e) (λ { (_≔_ _ {s} _) → toWitness s }) (assignsState? (toWitness a)) - changesState? (declare e s) = map′ (declare e) (λ { (declare e s) → s }) (changesState? s) - changesState? (invoke p e) = yes (invoke p e) - changesState? (if e then s₁ else s₂) = map′ [ if e then′_else s₂ , if e then s₁ else′_ ]′ (λ { (if _ then′ s else _) → inj₁ s ; (if _ then _ else′ s) → inj₂ s }) (changesState? s₁ ⊎-dec changesState? s₂) - changesState? (for m s) = map′ (for m) (λ { (for m s) → s }) (changesState? s) + changesState? (s ∙ s₁) = map′ [ _∙ˡ s₁ , s ∙ʳ_ ]′ (λ { (s ∙ˡ s₁) → inj₁ s ; (s ∙ʳ s₁) → inj₂ s₁ }) (changesState? s ⊎-dec changesState? s₁) + changesState? skip = no λ () + changesState? (_≔_ ref e) = map′ (λ refsState → _≔_ ref {refsState = fromWitness refsState} e) (λ { (_≔_ ref {refsState = refsState} e) → toWitness refsState }) (referencesState? ref) + changesState? (declare e s) = map′ (declare e) (λ { (declare e s) → s }) (changesState? s) + changesState? (invoke p e) = yes (invoke p e) + changesState? (if e then s else s₁) = map′ [ if e then′_else s₁ , if e then s else′_ ]′ (λ { (if e then′ s else s₁) → inj₁ s ; (if e then s else′ s₁) → inj₂ s₁ }) (changesState? s ⊎-dec changesState? s₁) + changesState? (for m s) = map′ (for m) (λ { (for m s) → s }) (changesState? s) data Function Γ ret where _∙return_ : (s : Statement Γ) → {False (changesState? s)} → Expression Γ ret → Function Γ ret @@ -279,7 +294,7 @@ module Code {o} (Σ : Vec Type o) where _∙end : Statement Γ → Procedure Γ infixl 6 _<<_ - infixl 5 _-_ + infixl 5 _-_ _∶_ tup : ∀ {n Γ m ts} → All (Expression {n} Γ) ts → Expression Γ (tuple m ts) tup [] = nil |