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Diffstat (limited to 'Data/Circuit/Gate.agda')
| -rw-r--r-- | Data/Circuit/Gate.agda | 137 |
1 files changed, 137 insertions, 0 deletions
diff --git a/Data/Circuit/Gate.agda b/Data/Circuit/Gate.agda new file mode 100644 index 0000000..8ce7e0a --- /dev/null +++ b/Data/Circuit/Gate.agda @@ -0,0 +1,137 @@ +{-# OPTIONS --without-K --safe #-} + +module Data.Circuit.Gate where + +open import Level using (0ℓ) +open import Data.Castable using (Castable) +open import Data.Hypergraph.Label using (HypergraphLabel) +open import Data.String using (String) +open import Data.Nat.Base using (ℕ; _≤_) +open import Data.Nat.Properties using (≤-refl; ≤-trans; ≤-antisym; ≤-total) +open import Relation.Binary.PropositionalEquality using (_≡_; refl; sym; trans; subst; isEquivalence; cong) +import Relation.Binary.PropositionalEquality as ≡ + +import Data.Nat as Nat +import Data.Fin as Fin + +data Gate : ℕ → Set where + ZERO : Gate 1 + ONE : Gate 1 + ID : Gate 2 + NOT : Gate 2 + AND : Gate 3 + OR : Gate 3 + XOR : Gate 3 + NAND : Gate 3 + NOR : Gate 3 + XNOR : Gate 3 + +cast-gate : {e e′ : ℕ} → .(e ≡ e′) → Gate e → Gate e′ +cast-gate {1} {1} eq g = g +cast-gate {2} {2} eq g = g +cast-gate {3} {3} eq g = g + +cast-gate-trans + : {m n o : ℕ} + → .(eq₁ : m ≡ n) + .(eq₂ : n ≡ o) + (g : Gate m) + → cast-gate eq₂ (cast-gate eq₁ g) ≡ cast-gate (trans eq₁ eq₂) g +cast-gate-trans {1} {1} {1} eq₁ eq₂ g = refl +cast-gate-trans {2} {2} {2} eq₁ eq₂ g = refl +cast-gate-trans {3} {3} {3} eq₁ eq₂ g = refl + +cast-gate-is-id : {m : ℕ} .(eq : m ≡ m) (g : Gate m) → cast-gate eq g ≡ g +cast-gate-is-id {1} eq g = refl +cast-gate-is-id {2} eq g = refl +cast-gate-is-id {3} eq g = refl + +subst-is-cast-gate : {m n : ℕ} (eq : m ≡ n) (g : Gate m) → subst Gate eq g ≡ cast-gate eq g +subst-is-cast-gate refl g = sym (cast-gate-is-id refl g) + +GateCastable : Castable +GateCastable = record + { B = Gate + ; isCastable = record + { cast = cast-gate + ; cast-trans = cast-gate-trans + ; cast-is-id = cast-gate-is-id + ; subst-is-cast = subst-is-cast-gate + } + } + +showGate : (n : ℕ) → Gate n → String +showGate _ ZERO = "ZERO" +showGate _ ONE = "ONE" +showGate _ ID = "ID" +showGate _ NOT = "NOT" +showGate _ AND = "AND" +showGate _ OR = "OR" +showGate _ XOR = "XOR" +showGate _ NAND = "NAND" +showGate _ NOR = "NOR" +showGate _ XNOR = "XNOR" + +toℕ : (n : ℕ) → Gate n → ℕ +toℕ 1 ZERO = 0 +toℕ 1 ONE = 1 +toℕ 2 ID = 0 +toℕ 2 NOT = 1 +toℕ 3 AND = 0 +toℕ 3 OR = 1 +toℕ 3 XOR = 2 +toℕ 3 NAND = 3 +toℕ 3 NOR = 4 +toℕ 3 XNOR = 5 + +toℕ-injective : {n : ℕ} {x y : Gate n} → toℕ n x ≡ toℕ n y → x ≡ y +toℕ-injective {1} {ZERO} {ZERO} refl = refl +toℕ-injective {1} {ONE} {ONE} refl = refl +toℕ-injective {2} {ID} {ID} refl = refl +toℕ-injective {2} {NOT} {NOT} refl = refl +toℕ-injective {3} {AND} {AND} refl = refl +toℕ-injective {3} {OR} {OR} refl = refl +toℕ-injective {3} {XOR} {XOR} refl = refl +toℕ-injective {3} {NAND} {NAND} refl = refl +toℕ-injective {3} {NOR} {NOR} refl = refl +toℕ-injective {3} {XNOR} {XNOR} refl = refl + +open import Relation.Binary using (Rel; Decidable; DecidableEquality) +import Relation.Nullary.Decidable as Dec + +_[_≤_] : (n : ℕ) → Rel (Gate n) 0ℓ +_[_≤_] n x y = toℕ n x ≤ toℕ n y + +_≟_ : {n : ℕ} → DecidableEquality (Gate n) +_≟_ {n} x y = Dec.map′ toℕ-injective (cong (toℕ n)) (toℕ n x Nat.≟ toℕ n y) + +_≤?_ : {n : ℕ} → Decidable (n [_≤_]) +_≤?_ {n} x y = toℕ n x Nat.≤? toℕ n y + +GateLabel : HypergraphLabel +GateLabel = record + { Label = Gate + ; showLabel = showGate + ; isCastable = record + { cast = cast-gate + ; cast-trans = cast-gate-trans + ; cast-is-id = cast-gate-is-id + ; subst-is-cast = subst-is-cast-gate + } + ; _[_≤_] = λ n x y → toℕ n x ≤ toℕ n y + ; isDecTotalOrder = λ n → record + { isTotalOrder = record + { isPartialOrder = record + { isPreorder = record + { isEquivalence = isEquivalence + ; reflexive = λ { refl → ≤-refl } + ; trans = ≤-trans + } + ; antisym = λ i≤j j≤i → toℕ-injective (≤-antisym i≤j j≤i) + } + ; total = λ { x y → ≤-total (toℕ n x) (toℕ n y) } + } + ; _≟_ = _≟_ + ; _≤?_ = _≤?_ + } + } |