diff options
Diffstat (limited to 'src/Helium/Data/Pseudocode/Core.agda')
| -rw-r--r-- | src/Helium/Data/Pseudocode/Core.agda | 117 |
1 files changed, 65 insertions, 52 deletions
diff --git a/src/Helium/Data/Pseudocode/Core.agda b/src/Helium/Data/Pseudocode/Core.agda index 0e85c0d..9f0c12d 100644 --- a/src/Helium/Data/Pseudocode/Core.agda +++ b/src/Helium/Data/Pseudocode/Core.agda @@ -9,7 +9,8 @@ module Helium.Data.Pseudocode.Core where open import Data.Bool using (Bool; true; false) -open import Data.Fin using (Fin; #_) +open import Data.Fin as Fin using (Fin) +open import Data.Fin.Patterns open import Data.Nat as ℕ using (ℕ; zero; suc) open import Data.Nat.Properties using (+-comm) open import Data.Product using (∃; _,_; proj₂; uncurry) @@ -130,53 +131,55 @@ module Code {o} (Σ : Vec Type o) where infix 4 _≟_ _<?_ data Expression {n} Γ where - lit : ∀ {t} → Literal t → Expression Γ t - state : ∀ i → Expression Γ (lookup Σ i) - var : ∀ i → Expression Γ (lookup Γ i) - abort : ∀ {t} → Expression Γ (fin 0) → Expression Γ t - _≟_ : ∀ {t} {hasEquality : True (hasEquality? t)} → Expression Γ t → Expression Γ t → Expression Γ bool - _<?_ : ∀ {t} {isNumeric : True (isNumeric? t)} → Expression Γ t → Expression Γ t → Expression Γ bool - inv : Expression Γ bool → Expression Γ bool - _&&_ : Expression Γ bool → Expression Γ bool → Expression Γ bool - _||_ : Expression Γ bool → Expression Γ bool → Expression Γ bool - not : ∀ {m} → Expression Γ (bits m) → Expression Γ (bits m) - _and_ : ∀ {m} → Expression Γ (bits m) → Expression Γ (bits m) → Expression Γ (bits m) - _or_ : ∀ {m} → Expression Γ (bits m) → Expression Γ (bits m) → Expression Γ (bits m) - [_] : ∀ {t} → Expression Γ (elemType t) → Expression Γ (asType t 1) - unbox : ∀ {t} → Expression Γ (asType t 1) → Expression Γ (elemType t) - _∶_ : ∀ {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}) + lit : ∀ {t} → Literal t → Expression Γ t + state : ∀ i → Expression Γ (lookup Σ i) + var : ∀ i → Expression Γ (lookup Γ i) + abort : ∀ {t} → Expression Γ (fin 0) → Expression Γ t + _≟_ : ∀ {t} {hasEquality : True (hasEquality? t)} → Expression Γ t → Expression Γ t → Expression Γ bool + _<?_ : ∀ {t} {isNumeric : True (isNumeric? t)} → Expression Γ t → Expression Γ t → Expression Γ bool + inv : Expression Γ bool → Expression Γ bool + _&&_ : Expression Γ bool → Expression Γ bool → Expression Γ bool + _||_ : Expression Γ bool → Expression Γ bool → Expression Γ bool + not : ∀ {m} → Expression Γ (bits m) → Expression Γ (bits m) + _and_ : ∀ {m} → Expression Γ (bits m) → Expression Γ (bits m) → Expression Γ (bits m) + _or_ : ∀ {m} → Expression Γ (bits m) → Expression Γ (bits m) → Expression Γ (bits m) + [_] : ∀ {t} → Expression Γ (elemType t) → Expression Γ (asType t 1) + unbox : ∀ {t} → Expression Γ (asType t 1) → Expression Γ (elemType t) + splice : ∀ {m n t} → Expression Γ (asType t m) → Expression Γ (asType t n) → Expression Γ (fin (suc n)) → Expression Γ (asType t (n ℕ.+ m)) + cut : ∀ {m n t} → Expression Γ (asType t (n ℕ.+ m)) → Expression Γ (fin (suc n)) → Expression Γ (tuple 2 (asType t m ∷ asType t n ∷ [])) + 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 → ℕ → Expression Γ t - _>>_ : Expression Γ int → ℕ → Expression Γ int - rnd : Expression Γ real → Expression Γ int - fin : ∀ {k ms n} → (All (Fin) ms → Fin n) → Expression Γ (tuple k (map fin ms)) → Expression Γ (fin n) - asInt : ∀ {m} → Expression Γ (fin m) → 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 → All (Expression Γ) {m} Δ → Expression Γ t + _^_ : ∀ {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 + fin : ∀ {k ms n} → (All (Fin) ms → Fin n) → Expression Γ (tuple k (map fin ms)) → Expression Γ (fin n) + asInt : ∀ {m} → Expression Γ (fin m) → 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 → All (Expression Γ) {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 → CanAssign (state i) var : ∀ i → CanAssign (var i) - 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 (elemType t)} → CanAssign e → CanAssign ([_] {t = t} e) - unbox : ∀ {t} {e : Expression Γ (asType t 1)} → CanAssign e → CanAssign (unbox 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) + abort : ∀ {t} e → CanAssign (abort {t = t} e) + [_] : ∀ {t e} → CanAssign e → CanAssign ([_] {t = t} e) + unbox : ∀ {t e} → CanAssign e → CanAssign (unbox {t = t} e) + splice : ∀ {m n t e₁ e₂} → CanAssign e₁ → CanAssign e₂ → ∀ e₃ → CanAssign (splice {m = m} {n} {t} e₁ e₂ e₃) + cut : ∀ {m n t e₁} → CanAssign e₁ → ∀ e₂ → CanAssign (cut {m = m} {n} {t} e₁ e₂) + cast : ∀ {i j t e} .(eq : i ≡ j) → CanAssign e → CanAssign (cast {t = t} eq e) + tup : ∀ {m ts es} → All (CanAssign ∘ proj₂) (reduce (λ {x} e → x , e) es) → CanAssign (tup {m = m} {ts} es) + head : ∀ {m t ts e} → CanAssign e → CanAssign (head {m = m} {t} {ts} e) + tail : ∀ {m t ts e} → CanAssign e → CanAssign (tail {m = m} {t} {ts} e) canAssign? (lit x) = no λ () canAssign? (state i) = yes (state i) canAssign? (var i) = yes (var i) - canAssign? (abort e) = yes abort + canAssign? (abort e) = yes (abort e) canAssign? (e ≟ e₁) = no λ () canAssign? (e <? e₁) = no λ () canAssign? (inv e) = no λ () @@ -187,8 +190,8 @@ module Code {o} (Σ : Vec Type o) where canAssign? (e or e₁) = no λ () 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′ (λ e → slice e e₁) (λ { (slice e e₁) → e }) (canAssign? e) + canAssign? (splice e e₁ e₂) = map′ (λ (e , e₁) → splice e e₁ e₂) (λ { (splice e e₁ _) → e , e₁ }) (canAssign? e ×-dec canAssign? e₁) + canAssign? (cut e e₁) = map′ (λ e → cut e e₁) (λ { (cut 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 () @@ -200,8 +203,8 @@ module Code {o} (Σ : Vec Type o) where 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) = no λ () - canAssign? (tail e) = no λ () + 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 () @@ -210,23 +213,27 @@ module Code {o} (Σ : Vec Type o) where data AssignsState where state : ∀ i → AssignsState (state i) - _∶ˡ_ : ∀ {m n t e₁ e₂ a₁} → AssignsState a₁ → ∀ a₂ → AssignsState (_∶_ {m = m} {n} {t} {e₁} {e₂} a₁ a₂) - _∶ʳ_ : ∀ {m n t e₁ e₂} a₁ {a₂} → AssignsState a₂ → AssignsState (_∶_ {m = m} {n} {t} {e₁} {e₂} a₁ a₂) [_] : ∀ {t e a} → AssignsState a → AssignsState ([_] {t = t} {e} a) unbox : ∀ {t e a} → AssignsState a → AssignsState (unbox {t = t} {e} a) - slice : ∀ {i j t e₁ a} → AssignsState a → ∀ e₂ → AssignsState (slice {i = i} {j} {t} {e₁} a e₂) + 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) tup : ∀ {m ts es as} → Any (AssignsState ∘ proj₂) (reduce (λ {x} a → x , a) as) → AssignsState (tup {m = m} {ts} {es} as) + 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 = no λ () - assignsState? (a ∶ a₁) = map′ [ (_∶ˡ a₁) , (a ∶ʳ_) ]′ (λ { (s ∶ˡ _) → inj₁ s ; (_ ∶ʳ s) → inj₂ s }) (assignsState? a ⊎-dec assignsState? a₁) + 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? (slice a e₂) = map′ (λ s → slice s e₂ ) (λ { (slice 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? (tup as) = map′ tup (λ { (tup ss) → ss }) (assignsStateAny? as) + 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) @@ -273,6 +280,12 @@ module Code {o} (Σ : Vec Type o) where infixl 6 _<<_ infixl 5 _-_ + _∶_ : ∀ {n Γ i j t} → Expression {n} Γ (asType t j) → Expression Γ (asType t i) → Expression Γ (asType t (i ℕ.+ j)) + e₁ ∶ e₂ = splice e₁ e₂ (lit (Fin.fromℕ _ ′f)) + + slice : ∀ {n Γ i j t} → Expression {n} Γ (asType t (i ℕ.+ j)) → Expression Γ (fin (suc i)) → Expression Γ (asType t j) + slice e₁ e₂ = head (cut e₁ e₂) + 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 @@ -288,8 +301,8 @@ module Code {o} (Σ : Vec Type o) where 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 ∷ []) ′xs) + lit (2 ′i) * uint {m = m} (slice x (lit (1F ′f))) + + ( if slice′ x (lit (0F ′f)) ≟ lit ((true ∷ []) ′xs) then lit (1 ′i) else lit (0 ′i)) @@ -297,7 +310,7 @@ module Code {o} (Σ : Vec Type o) where sint {m = zero} x = lit (0 ′i) sint {m = suc zero} x = if x ≟ lit ((true ∷ []) ′xs) 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 ∷ []) ′xs) + lit (2 ′i) * sint (slice {i = 1} x (lit (1F ′f))) + + ( if slice′ x (lit (0F ′f)) ≟ lit ((true ∷ []) ′xs) then lit (1 ′i) else lit (0 ′i)) |