From 5f4d1cf740591476d3c7bc270fd11a2c578ab7e6 Mon Sep 17 00:00:00 2001 From: Jacques Comeaux Date: Wed, 5 Nov 2025 08:11:48 -0600 Subject: Adjust universe levels --- DecorationFunctor/Hypergraph/Labeled.agda | 48 +++++++++++++++---------------- 1 file changed, 24 insertions(+), 24 deletions(-) (limited to 'DecorationFunctor/Hypergraph/Labeled.agda') diff --git a/DecorationFunctor/Hypergraph/Labeled.agda b/DecorationFunctor/Hypergraph/Labeled.agda index 083ff80..33a7a89 100644 --- a/DecorationFunctor/Hypergraph/Labeled.agda +++ b/DecorationFunctor/Hypergraph/Labeled.agda @@ -1,6 +1,8 @@ {-# OPTIONS --without-K --safe #-} -module DecorationFunctor.Hypergraph.Labeled where +open import Level using (Level; 0ℓ; lift) + +module DecorationFunctor.Hypergraph.Labeled {c ℓ : Level} where import Categories.Morphism as Morphism @@ -37,32 +39,30 @@ open import Data.Fin.Properties ) open import Data.Nat using (ℕ; _+_) open import Data.Product.Base using (_,_; Σ) -open import Data.Product.Relation.Binary.Pointwise.NonDependent using (×-setoid) +open import Data.Product.Relation.Binary.Pointwise.NonDependent using (_×ₛ_) open import Data.Sum.Base using (_⊎_; map; inj₁; inj₂; swap; map₂) renaming ([_,_]′ to [_,_]) open import Data.Sum.Properties using (map-map; [,]-map; [,]-∘; [-,]-cong; [,-]-cong; [,]-cong; map-cong; swap-involutive) -open import Data.Unit using (tt) open import Data.Unit.Properties using () renaming (≡-setoid to ⊤-setoid) open import Function.Base using (_∘_; id; const; case_of_; case_returning_of_) -open import Function.Bundles using (Func; Inverse; _↔_; mk↔) +open import Function.Bundles using (Func; Inverse; _↔_; mk↔; _⟶ₛ_) open import Function.Construct.Composition using (_↔-∘_) open import Function.Construct.Identity using (↔-id) open import Function.Construct.Symmetry using (↔-sym) -open import Level using (0ℓ; lift) - open import Relation.Binary.Bundles using (Setoid) open import Relation.Binary.PropositionalEquality using (_≗_) open import Relation.Binary.PropositionalEquality.Core using (_≡_; erefl; refl; sym; trans; cong; cong₂; subst; cong-app) open import Relation.Binary.PropositionalEquality.Properties using (isEquivalence; module ≡-Reasoning; dcong; dcong₂; subst-∘; subst-subst; sym-cong; subst-subst-sym; trans-cong; cong-∘; trans-reflʳ) open import Relation.Nullary.Negation.Core using (¬_) -open Cartesian (Setoids-Cartesian {0ℓ} {0ℓ}) using (products) +open Cartesian (Setoids-Cartesian {c} {ℓ}) using (products) open Cocartesian Nat-Cocartesian using (coproducts) open FinitelyCocompleteCategory Nat-FinitelyCocomplete using () renaming (symmetricMonoidalCategory to Nat-smc) -open Morphism (Setoids 0ℓ 0ℓ) using (_≅_) +open import Category.Monoidal.Instance.Nat using (Nat,+,0) +open Morphism (Setoids c ℓ) using (_≅_) open Lax using (SymmetricMonoidalFunctor) open BinaryProducts products using (-×-) @@ -70,7 +70,7 @@ open BinaryCoproducts coproducts using (-+-) renaming (+-assoc to Nat-+-assoc) open import Data.Circuit.Gate using (Gate; cast-gate; cast-gate-trans; cast-gate-is-id; subst-is-cast-gate) -record Hypergraph (v : ℕ) : Set where +record Hypergraph (v : ℕ) : Set c where field h : ℕ @@ -78,7 +78,7 @@ record Hypergraph (v : ℕ) : Set where j : (e : Fin h) → Fin (a e) → Fin v l : (e : Fin h) → Gate (a e) -record Hypergraph-same {n : ℕ} (H H′ : Hypergraph n) : Set where +record Hypergraph-same {n : ℕ} (H H′ : Hypergraph n) : Set ℓ where open Hypergraph H public open Hypergraph H′ renaming (h to h′; a to a′; j to j′; l to l′) public @@ -183,7 +183,7 @@ Hypergraph-same-trans ≡H₁ ≡H₂ = record ≗l₂ : (e : Fin (h ≡H₁)) → cast-gate _ (l′ ≡H₁ (to ≡H₁ e)) ≡ cast-gate _ (l′ ≡H₂ (to ≡H₂ (to ≡H₁ e))) ≗l₂ e = trans (cong (cast-gate _) (≗l ≡H₂ (to ≡H₁ e))) (cast-gate-trans _ (sym (≗a ≡H₁ e)) (l′ ≡H₂ (to ≡H₂ (to ≡H₁ e)))) -Hypergraph-setoid : ℕ → Setoid 0ℓ 0ℓ +Hypergraph-setoid : ℕ → Setoid c ℓ Hypergraph-setoid p = record { Carrier = Hypergraph p ; _≈_ = Hypergraph-same @@ -217,7 +217,7 @@ Hypergraph-same-cong f ≡H = record where open Hypergraph-same ≡H -Hypergraph-Func : (Fin n → Fin m) → Func (Hypergraph-setoid n) (Hypergraph-setoid m) +Hypergraph-Func : (Fin n → Fin m) → Hypergraph-setoid n ⟶ₛ Hypergraph-setoid m Hypergraph-Func f = record { to = map-nodes f ; cong = Hypergraph-same-cong f @@ -249,9 +249,9 @@ homomorphism {n} {m} {o} {H} f g = record where open Hypergraph-same Hypergraph-same-refl -F : Functor Nat (Setoids 0ℓ 0ℓ) +F : Functor Nat (Setoids c ℓ) F = record - { F₀ = Hypergraph-setoid + { F₀ = λ n → Hypergraph-setoid n ; F₁ = Hypergraph-Func ; identity = λ { {n} {H} → Hypergraph-same-refl {H = H} } ; homomorphism = λ { {f = f} {g = g} → homomorphism f g } @@ -268,7 +268,7 @@ empty-hypergraph = record ; l = λ () } -ε : Func (SingletonSetoid {0ℓ} {0ℓ}) (Hypergraph-setoid 0) +ε : SingletonSetoid {c} {ℓ} ⟶ₛ Hypergraph-setoid 0 ε = record { to = const empty-hypergraph ; cong = const Hypergraph-same-refl @@ -430,7 +430,7 @@ commute {n} {n′} {m} {m′} {H₁} {H₂} f g = record ; sym-commute = λ { (f , g) {H₁ , H₂} → Hypergraph-same-sym (commute {H₁ = H₁} {H₂ = H₂} f g) } } where - η : Func (×-setoid (Hypergraph-setoid n) (Hypergraph-setoid m)) (Hypergraph-setoid (n + m)) + η : Hypergraph-setoid n ×ₛ Hypergraph-setoid m ⟶ₛ Hypergraph-setoid (n + m) η = record { to = λ { (H₁ , H₂) → together H₁ H₂ } ; cong = λ { (≡H₁ , ≡H₂) → together-resp-same ≡H₁ ≡H₂ } @@ -551,7 +551,7 @@ n+0↔n n = record to∘from : (x : Fin n) → to (from x) ≡ x to∘from x rewrite splitAt-↑ˡ n x 0 = refl -unitaryʳ : Hypergraph-same (map-nodes ([ (λ x → x) , (λ ()) ] ∘ splitAt n) (together H empty-hypergraph)) H +unitaryʳ : Hypergraph-same (map-nodes ([ id , (λ ()) ] ∘ splitAt n) (together H empty-hypergraph)) H unitaryʳ {n} {H} = record { ↔h = h+0↔h ; ≗a = ≗a @@ -658,8 +658,8 @@ braiding {n} {m} {H₁} {H₂} = record ≗l e | inj₁ e₁ rewrite splitAt-↑ʳ H₂.h H₁.h e₁ = sym (cast-gate-is-id refl (H₁.l e₁)) ≗l e | inj₂ e₂ rewrite splitAt-↑ˡ H₂.h e₂ H₁.h = sym (cast-gate-is-id refl (H₂.l e₂)) -hypergraph : SymmetricMonoidalFunctor Nat-smc (Setoids-× {0ℓ}) -hypergraph = record +Circ : SymmetricMonoidalFunctor Nat,+,0 Setoids-× +Circ = record { F = F ; isBraidedMonoidal = record { isMonoidal = record @@ -676,20 +676,20 @@ hypergraph = record } } where - η : Func (×-setoid (Hypergraph-setoid n) (Hypergraph-setoid m)) (Hypergraph-setoid (n + m)) + η : Hypergraph-setoid n ×ₛ Hypergraph-setoid m ⟶ₛ Hypergraph-setoid (n + m) η = record { to = λ { (H₁ , H₂) → together H₁ H₂ } ; cong = λ { (≡H₁ , ≡H₂) → together-resp-same ≡H₁ ≡H₂ } } -module F = SymmetricMonoidalFunctor hypergraph +module F = SymmetricMonoidalFunctor Circ open Gate -and-gate : Func (SingletonSetoid {0ℓ} {0ℓ}) (F.₀ 3) +and-gate : SingletonSetoid {c} {ℓ} ⟶ₛ F.₀ 3 and-gate = record - { to = λ { (lift tt) → and-graph } - ; cong = λ { (lift tt) → Hypergraph-same-refl } + { to = λ _ → and-graph + ; cong = λ _ → Hypergraph-same-refl } where and-graph : Hypergraph 3 -- cgit v1.2.3