diff options
Diffstat (limited to 'src/Helium/Data/Pseudocode/Core.agda')
| -rw-r--r-- | src/Helium/Data/Pseudocode/Core.agda | 84 |
1 files changed, 47 insertions, 37 deletions
diff --git a/src/Helium/Data/Pseudocode/Core.agda b/src/Helium/Data/Pseudocode/Core.agda index 7b21824..a63cc39 100644 --- a/src/Helium/Data/Pseudocode/Core.agda +++ b/src/Helium/Data/Pseudocode/Core.agda @@ -8,9 +8,10 @@ module Helium.Data.Pseudocode.Core where -open import Data.Bool using (Bool) +open import Data.Bool using (Bool; true; false) open import Data.Fin using (Fin; #_) -open import Data.Nat as ℕ using (ℕ; suc) +open import Data.Nat as ℕ using (ℕ; zero; suc) +open import Data.Nat.Properties using (+-comm) open import Data.Product using (∃; _,_; proj₂; uncurry) open import Data.Vec using (Vec; []; _∷_; lookup; map) open import Data.Vec.Relation.Unary.All using (All; []; _∷_; reduce; all?) @@ -29,7 +30,6 @@ data Type : Set where fin : (n : ℕ) → Type real : Type bits : (n : ℕ) → Type - enum : (n : ℕ) → Type tuple : ∀ n → Vec Type n → Type array : Type → (n : ℕ) → Type @@ -42,7 +42,6 @@ data HasEquality : Type → Set where fin : ∀ {n} → HasEquality (fin n) real : HasEquality real bits : ∀ {n} → HasEquality (bits n) - enum : ∀ {n} → HasEquality (enum n) hasEquality? : Decidable HasEquality hasEquality? unit = no (λ ()) @@ -51,7 +50,6 @@ hasEquality? int = yes int hasEquality? (fin n) = yes fin hasEquality? real = yes real hasEquality? (bits n) = yes bits -hasEquality? (enum n) = yes enum hasEquality? (tuple n x) = no (λ ()) hasEquality? (array t n) = no (λ ()) @@ -66,7 +64,6 @@ isNumeric? int = yes int isNumeric? real = yes real isNumeric? (fin n) = no (λ ()) isNumeric? (bits n) = no (λ ()) -isNumeric? (enum n) = no (λ ()) isNumeric? (tuple n x) = no (λ ()) isNumeric? (array t n) = no (λ ()) @@ -95,8 +92,7 @@ data Literal : Type → Set where _′f : ∀ {n} → Fin n → Literal (fin n) _′r : ℕ → Literal real _′x : ∀ {n} → Vec Bool n → Literal (bits n) - _′e : ∀ {n} → Fin n → Literal (enum n) - _′a : ∀ {n t} → Vec (Literal t) n → Literal (array t n) + _′a : ∀ {n t} → Literal t → Literal (array t n) --- Expressions, references, statements, functions and procedures @@ -111,7 +107,8 @@ module Code {o} (Σ : Vec Type o) where infix 8 -_ infixr 7 _^_ - infixl 6 _*_ _/_ _and_ + infixl 6 _*_ _and_ _>>_ + -- infixl 6 _/_ infixl 5 _+_ _or_ _&&_ _||_ _∶_ infix 4 _≟_ _<?_ @@ -130,42 +127,37 @@ module Code {o} (Σ : Vec Type o) where _or_ : ∀ {n} → Expression Γ (bits n) → Expression Γ (bits n) → Expression Γ (bits n) [_] : ∀ {t} → Expression Γ t → Expression Γ (array t 1) unbox : ∀ {t} → Expression Γ (array t 1) → Expression Γ t - _∶_ : ∀ {m n t} → Expression Γ (asType t m) → Expression Γ (asType t n) → Expression Γ (asType t (m ℕ.+ n)) + _∶_ : ∀ {m n t} → Expression Γ (asType t m) → Expression Γ (asType t n) → Expression Γ (asType t (n ℕ.+ m)) slice : ∀ {i j t} → Expression Γ (asType t (i ℕ.+ j)) → Expression Γ (fin (suc i)) → Expression Γ (asType t j) cast : ∀ {i j t} → .(eq : i ≡ j) → Expression Γ (asType t i) → Expression Γ (asType t j) -_ : ∀ {t} {isNumeric : True (isNumeric? t)} → Expression Γ t → Expression Γ t _+_ : ∀ {t₁ t₂} {isNumeric₁ : True (isNumeric? t₁)} {isNumeric₂ : True (isNumeric? t₂)} → Expression Γ t₁ → Expression Γ t₂ → Expression Γ (combineNumeric t₁ t₂ {isNumeric₁} {isNumeric₂}) _*_ : ∀ {t₁ t₂} {isNumeric₁ : True (isNumeric? t₁)} {isNumeric₂ : True (isNumeric? t₂)} → Expression Γ t₁ → Expression Γ t₂ → Expression Γ (combineNumeric t₁ t₂ {isNumeric₁} {isNumeric₂}) - _/_ : Expression Γ real → Expression Γ real → Expression Γ real - _^_ : ∀ {t} {isNumeric : True (isNumeric? t)} → Expression Γ t → Expression Γ int → Expression Γ t - sint : ∀ {n} → Expression Γ (bits n) → Expression Γ int - uint : ∀ {n} → Expression Γ (bits n) → Expression Γ int + -- _/_ : Expression Γ real → Expression Γ real → Expression Γ real + _^_ : ∀ {t} {isNumeric : True (isNumeric? t)} → Expression Γ t → ℕ → Expression Γ t + _>>_ : Expression Γ int → ℕ → Expression Γ int rnd : Expression Γ real → Expression Γ int - get : ℕ → Expression Γ int → Expression Γ bit + -- get : ℕ → Expression Γ int → Expression Γ bit fin : ∀ {k ms n} → (All (Fin) ms → Fin n) → Expression Γ (tuple k (map fin ms)) → Expression Γ (fin n) asInt : ∀ {n} → Expression Γ (fin n) → Expression Γ int tup : ∀ {m ts} → All (Expression Γ) ts → Expression Γ (tuple m ts) - head : ∀ {m t ts} → Expression Γ (tuple (suc m) (t ∷ ts)) → Expression Γ t - tail : ∀ {m t ts} → Expression Γ (tuple (suc m) (t ∷ ts)) → Expression Γ (tuple m ts) call : ∀ {t m Δ} → Function Δ t → Expression Γ (tuple m Δ) → Expression Γ t if_then_else_ : ∀ {t} → Expression Γ bool → Expression Γ t → Expression Γ t → Expression Γ t data CanAssign {n} {Γ} where - state : ∀ {i} {i<o : True (i ℕ.<? o)} → CanAssign (state i {i<o}) - var : ∀ {i} {i<n : True (i ℕ.<? n)} → CanAssign (var i {i<n}) + state : ∀ i {i<o : True (i ℕ.<? o)} → CanAssign (state i {i<o}) + var : ∀ i {i<n : True (i ℕ.<? n)} → CanAssign (var i {i<n}) abort : ∀ {t} {e : Expression Γ (fin 0)} → CanAssign (abort {t = t} e) _∶_ : ∀ {m n t} {e₁ : Expression Γ (asType t m)} {e₂ : Expression Γ (asType t n)} → CanAssign e₁ → CanAssign e₂ → CanAssign (e₁ ∶ e₂) [_] : ∀ {t} {e : Expression Γ t} → CanAssign e → CanAssign [ e ] unbox : ∀ {t} {e : Expression Γ (array t 1)} → CanAssign e → CanAssign (unbox e) - slice : ∀ {i j t} {e₁ : Expression Γ (asType t (i ℕ.+ j))} {e₂ : Expression Γ (fin (suc i))} → CanAssign e₁ → CanAssign (slice e₁ e₂) - cast : ∀ {i j t} {e : Expression Γ (asType t i)} .{eq : i ≡ j} → CanAssign e → CanAssign (cast eq e) + slice : ∀ {i j t} {e₁ : Expression Γ (asType t (i ℕ.+ j))} → CanAssign e₁ → (e₂ : Expression Γ (fin (suc i))) → CanAssign (slice e₁ e₂) + cast : ∀ {i j t} {e : Expression Γ (asType t i)} .(eq : i ≡ j) → CanAssign e → CanAssign (cast eq e) tup : ∀ {m ts} {es : All (Expression Γ) {m} ts} → All (CanAssign ∘ proj₂) (reduce (λ {x} e → x , e) es) → CanAssign (tup es) - head : ∀ {m t ts} {e : Expression Γ (tuple (suc m) (t ∷ ts))} → CanAssign e → CanAssign (head e) - tail : ∀ {m t ts} {e : Expression Γ (tuple (suc m) (t ∷ ts))} → CanAssign e → CanAssign (tail e) canAssign? (lit x) = no λ () - canAssign? (state i) = yes state - canAssign? (var i) = yes var + canAssign? (state i) = yes (state i) + canAssign? (var i) = yes (var i) canAssign? (abort e) = yes abort canAssign? (e ≟ e₁) = no λ () canAssign? (e <? e₁) = no λ () @@ -178,22 +170,19 @@ module Code {o} (Σ : Vec Type o) where canAssign? [ e ] = map′ [_] (λ { [ e ] → e }) (canAssign? e) canAssign? (unbox e) = map′ unbox (λ { (unbox e) → e }) (canAssign? e) canAssign? (e ∶ e₁) = map′ (uncurry _∶_) (λ { (e ∶ e₁) → e , e₁ }) (canAssign? e ×-dec canAssign? e₁) - canAssign? (slice e e₁) = map′ slice (λ { (slice e) → e }) (canAssign? e) - canAssign? (cast eq e) = map′ cast (λ { (cast e) → e }) (canAssign? e) + canAssign? (slice e e₁) = map′ (λ e → slice e e₁) (λ { (slice e e₁) → e }) (canAssign? e) + canAssign? (cast eq e) = map′ (cast eq) (λ { (cast eq e) → e }) (canAssign? e) canAssign? (- e) = no λ () canAssign? (e + e₁) = no λ () canAssign? (e * e₁) = no λ () - canAssign? (e / e₁) = no λ () + -- canAssign? (e / e₁) = no λ () canAssign? (e ^ e₁) = no λ () - canAssign? (sint e) = no λ () - canAssign? (uint e) = no λ () + canAssign? (e >> e₁) = no λ () canAssign? (rnd e) = no λ () - canAssign? (get x e) = no λ () + -- canAssign? (get x e) = no λ () canAssign? (fin x e) = no λ () canAssign? (asInt e) = no λ () canAssign? (tup es) = map′ tup (λ { (tup es) → es }) (canAssignAll? es) - canAssign? (head e) = map′ head (λ { (head e) → e }) (canAssign? e) - canAssign? (tail e) = map′ tail (λ { (tail e) → e }) (canAssign? e) canAssign? (call x e) = no λ () canAssign? (if e then e₁ else e₂) = no λ () @@ -222,13 +211,34 @@ module Code {o} (Σ : Vec Type o) where _∙end : Statement Γ unit → Procedure Γ declare : ∀ {t} → Expression Γ t → Procedure (t ∷ Γ) → Procedure Γ - infixl 6 _<<_ _>>_ + infixl 6 _<<_ infixl 5 _-_ + + slice′ : ∀ {n Γ i j t} → Expression {n} Γ (asType t (i ℕ.+ j)) → Expression Γ (fin (suc j)) → Expression Γ (asType t i) + slice′ {i = i} e₁ e₂ = slice (cast (+-comm i _) e₁) e₂ + _-_ : ∀ {n Γ t₁ t₂} {isNumeric₁ : True (isNumeric? t₁)} {isNumeric₂ : True (isNumeric? t₂)} → Expression {n} Γ t₁ → Expression Γ t₂ → Expression Γ (combineNumeric t₁ t₂ {isNumeric₁} {isNumeric₂}) _-_ {isNumeric₂ = isNumeric₂} x y = x + (-_ {isNumeric = isNumeric₂} y) - _<<_ : ∀ {n Γ} → Expression {n} Γ int → Expression Γ int → Expression Γ int + _<<_ : ∀ {n Γ} → Expression {n} Γ int → ℕ → Expression Γ int x << n = rnd (x * lit (2 ′r) ^ n) - _>>_ : ∀ {n Γ} → Expression {n} Γ int → Expression Γ int → Expression Γ int - x >> n = rnd (x * lit (2 ′r) ^ - n) + get : ∀ {n Γ} → ℕ → Expression {n} Γ int → Expression Γ bit + get i x = if x - x >> suc i << suc i <? lit (2 ′i) ^ i then lit ((false ∷ []) ′x) else lit ((true ∷ []) ′x) + + uint : ∀ {n Γ m} → Expression {n} Γ (bits m) → Expression Γ int + uint {m = zero} x = lit (0 ′i) + uint {m = suc m} x = + lit (2 ′i) * uint {m = m} (slice x (lit ((# 1) ′f))) + + ( if slice′ x (lit ((# 0) ′f)) ≟ lit ((true ∷ []) ′x) + then lit (1 ′i) + else lit (0 ′i)) + + sint : ∀ {n Γ m} → Expression {n} Γ (bits m) → Expression Γ int + sint {m = zero} x = lit (0 ′i) + sint {m = suc zero} x = if x ≟ lit ((true ∷ []) ′x) then - lit (1 ′i) else lit (0 ′i) + sint {m = suc (suc m)} x = + lit (2 ′i) * sint (slice {i = 1} x (lit ((# 1) ′f))) + + ( if slice′ x (lit ((# 0) ′f)) ≟ lit ((true ∷ []) ′x) + then lit (1 ′i) + else lit (0 ′i)) |