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Tidy up: s/Set/Type + flags + levels
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‎Class/Applicative.agda

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{-# OPTIONS --without-K #-}
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{-# OPTIONS --cubical-compatible #-}
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module Class.Applicative where
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open import Class.Applicative.Core public

‎Class/Applicative/Core.agda

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{-# OPTIONS --without-K #-}
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{-# OPTIONS --cubical-compatible #-}
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module Class.Applicative.Core where
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open import Class.Prelude

‎Class/Applicative/Instances.agda

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{-# OPTIONS --without-K #-}
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{-# OPTIONS --cubical-compatible #-}
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module Class.Applicative.Instances where
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open import Class.Prelude

‎Class/Bifunctor.agda

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{-# OPTIONS --without-K #-}
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{-# OPTIONS --cubical-compatible #-}
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module Class.Bifunctor where
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open import Class.Prelude hiding (A; B; C)

‎Class/CommutativeMonoid.agda

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{-# OPTIONS --safe --without-K #-}
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{-# OPTIONS --cubical-compatible #-}
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module Class.CommutativeMonoid where
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open import Class.CommutativeMonoid.Core public

‎Class/CommutativeMonoid/Core.agda

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{-# OPTIONS --safe --without-K #-}
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{-# OPTIONS --cubical-compatible #-}
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module Class.CommutativeMonoid.Core where
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5-
import Algebra as Alg
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open import Class.Prelude
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open import Class.Semigroup
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open import Class.Monoid
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import Algebra as Alg
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record CommutativeMonoid c ℓ Carrier : Type (lsuc (c ⊔ ℓ)) where
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infix 4 _≈_
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field
@@ -19,7 +19,8 @@ module Conversion {c ℓ} where
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toBundle : ∀ {Carrier} → CommutativeMonoid c ℓ Carrier → Alg.CommutativeMonoid c ℓ
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toBundle c = record { CommutativeMonoid c }
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22-
fromBundle : (m : Alg.CommutativeMonoid c ℓ) → CommutativeMonoid c ℓ (Alg.CommutativeMonoid.Carrier m)
22+
fromBundle : (m : Alg.CommutativeMonoid c ℓ)
23+
→ CommutativeMonoid c ℓ (Alg.CommutativeMonoid.Carrier m)
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fromBundle c = record
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{ Alg.CommutativeMonoid c using (_≈_; isCommutativeMonoid)
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; semigroup = λ where ._◇_ → Alg.CommutativeMonoid._∙_ c

‎Class/CommutativeMonoid/Instances.agda

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{-# OPTIONS --safe --without-K #-}
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{-# OPTIONS --cubical-compatible #-}
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module Class.CommutativeMonoid.Instances where
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‎Class/Core.agda

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{-# OPTIONS --without-K #-}
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{-# OPTIONS --cubical-compatible #-}
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module Class.Core where
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open import Class.Prelude

‎Class/Default.agda

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-- Types with a default value.
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------------------------------------------------------------------------
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{-# OPTIONS --without-K #-}
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{-# OPTIONS --cubical-compatible #-}
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module Class.Default where
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open import Class.Prelude

‎Class/Foldable.agda

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{-# OPTIONS --without-K #-}
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{-# OPTIONS --cubical-compatible #-}
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module Class.Foldable where
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open import Class.Foldable.Core public

‎Class/Foldable/Core.agda

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{-# OPTIONS --without-K #-}
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{-# OPTIONS --cubical-compatible #-}
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module Class.Foldable.Core where
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open import Class.Prelude

‎Class/Foldable/Instances.agda

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{-# OPTIONS --without-K #-}
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{-# OPTIONS --cubical-compatible #-}
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module Class.Foldable.Instances where
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open import Class.Prelude

‎Class/Functor.agda

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{-# OPTIONS --without-K #-}
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{-# OPTIONS --cubical-compatible #-}
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module Class.Functor where
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open import Class.Functor.Core public

‎Class/Functor/Core.agda

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{-# OPTIONS --without-K #-}
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{-# OPTIONS --cubical-compatible #-}
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module Class.Functor.Core where
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open import Class.Prelude

‎Class/Functor/Instances.agda

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{-# OPTIONS --without-K #-}
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{-# OPTIONS --cubical-compatible #-}
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module Class.Functor.Instances where
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open import Class.Prelude

‎Class/HasAdd.agda

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{-# OPTIONS --safe --cubical-compatible #-}
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{-# OPTIONS --cubical-compatible #-}
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module Class.HasAdd where
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open import Class.HasAdd.Core public

‎Class/HasAdd/Core.agda

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{-# OPTIONS --safe --cubical-compatible #-}
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{-# OPTIONS --cubical-compatible #-}
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module Class.HasAdd.Core where
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record HasAdd (A : Set) : Set where
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open import Class.Prelude
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6+
record HasAdd (A : Type ℓ) : Type ℓ where
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infixl 6 _+_
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field _+_ : A → A → A
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open HasAdd ⦃ ... ⦄ public
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open HasAdd ⦃...⦄ public

‎Class/HasAdd/Instance.agda

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{-# OPTIONS --safe --cubical-compatible #-}
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{-# OPTIONS --cubical-compatible #-}
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module Class.HasAdd.Instance where
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open import Class.HasAdd.Core

‎Class/HasOrder.agda

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{-# OPTIONS --safe #-}
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module Class.HasOrder where
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open import Class.HasOrder.Core public

‎Class/HasOrder/Core.agda

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{-# OPTIONS --safe #-}
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{-# OPTIONS --without-K #-}
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module Class.HasOrder.Core where
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open import Class.Prelude
55
open import Class.Decidable
6-
open import Data.Empty
7-
open import Data.Product
8-
open import Data.Sum
9-
open import Function
10-
open import Level
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open import Relation.Binary
12-
open import Relation.Binary using () renaming (Decidable to Decidable²)
13-
open import Relation.Binary.PropositionalEquality
14-
open import Relation.Nullary
6+
open import Function.Bundles using (module Equivalence; mk⇔; _⇔_)
7+
open import Relation.Binary using
8+
( IsPreorder; IsPartialOrder; IsEquivalence; Total; IsTotalOrder
9+
; IsStrictTotalOrder; IsStrictPartialOrder
10+
; Irreflexive; Antisymmetric; Asymmetric; Transitive
11+
)
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1613
open Equivalence
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18-
module _ {a} {A : Set a} where
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module _ {_≈_ : Rel A a} where
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module _ {A : Type ℓ} where
16+
module _ {_≈_ : Rel A ℓ′} {ℓ″ ℓ‴} (let 𝐿 = lsuc ℓ ⊔ ℓ′ ⊔ lsuc ℓ″ ⊔ lsuc ℓ‴) where
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21-
record HasPreorder : Set (suc a) where
18+
record HasPreorder : Type 𝐿 where
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infix 4 _≤_ _<_ _≥_ _>_
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field
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_≤_ _<_ : Rel A a
21+
_≤_ : Rel A ℓ″
22+
_<_ : Rel A ℓ‴
2523
≤-isPreorder : IsPreorder _≈_ _≤_
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<-irrefl : Irreflexive _≈_ _<_
27-
≤⇔<∨≈ : ∀ {x y} → x ≤ y ⇔ (x < y ⊎ x ≈ y)
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≤⇔<∨≈ : ∀ {x y : A} → x ≤ y ⇔ (x < y ⊎ x ≈ y)
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_≥_ = flip _≤_
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_>_ = flip _<_
@@ -33,10 +31,10 @@ module _ {a} {A : Set a} where
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using ()
3432
renaming (isEquivalence to ≈-isEquivalence; refl to ≤-refl; trans to ≤-trans)
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36-
_≤?_ : ⦃ _≤_ ⁇² ⦄ → Decidable _≤_
34+
_≤?_ : ⦃ _≤_ ⁇² ⦄ → Decidable² _≤_
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_≤?_ = dec²
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39-
_<?_ : ⦃ _<_ ⁇² ⦄ → Decidable _<_
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_<?_ : ⦃ _<_ ⁇² ⦄ → Decidable² _<_
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_<?_ = dec²
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infix 4 _<?_ _≤?_
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5654
open HasPreorder ⦃...⦄
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58-
record HasDecPreorder : Set (suc a) where
56+
record HasDecPreorder : Type 𝐿 where
5957
field ⦃ hasPreorder ⦄ : HasPreorder
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⦃ dec-≤ ⦄ : _≤_ ⁇²
6159
⦃ dec-< ⦄ : _<_ ⁇²
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63-
record HasPartialOrder : Set (suc a) where
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record HasPartialOrder : Type 𝐿 where
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field
6563
⦃ hasPreorder ⦄ : HasPreorder
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≤-antisym : Antisymmetric _≈_ _≤_
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9189
open HasPartialOrder ⦃...⦄
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93-
record HasDecPartialOrder : Set (suc a) where
91+
record HasDecPartialOrder : Type 𝐿 where
9492
field
9593
⦃ hasPartialOrder ⦄ : HasPartialOrder
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⦃ dec-≤ ⦄ : _≤_ ⁇²
9795
⦃ dec-< ⦄ : _<_ ⁇²
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99-
record HasTotalOrder : Set (suc a) where
97+
record HasTotalOrder : Type 𝐿 where
10098
field
10199
⦃ hasPartialOrder ⦄ : HasPartialOrder
102100
≤-total : Total _≤_
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107105
open IsEquivalence ≈-isEquivalence renaming (sym to ≈-sym)
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109-
≮⇒≥ : Decidable _≈_ → ∀ {x y} → ¬ (x < y) → y ≤ x
107+
≮⇒≥ : Decidable² _≈_ → ∀ {x y} → ¬ (x < y) → y ≤ x
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≮⇒≥ _≈?_ {x} {y} x≮y with x ≈? y | ≤-total y x
111109
... | yes x≈y | _ = IsPreorder.reflexive ≤-isPreorder (≈-sym x≈y)
112110
... | _ | inj₁ y≤x = y≤x
113111
... | no x≉y | inj₂ x≤y = contradiction (≤∧≉⇒< (x≤y , x≉y)) x≮y
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115113
open HasTotalOrder ⦃...⦄
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117-
record HasDecTotalOrder : Set (suc a) where
115+
record HasDecTotalOrder : Type 𝐿 where
118116
field
119117
⦃ hasTotalOrder ⦄ : HasTotalOrder
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⦃ dec-≤ ⦄ : _≤_ ⁇²
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133131
open HasTotalOrder ⦃...⦄ public hiding (hasPartialOrder)
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open HasDecTotalOrder ⦃...⦄ public hiding (hasTotalOrder)
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136-
module _ {a} {A : Set a} {_≈_ : Rel A a} where
134+
module _ {A : Type ℓ} {_≈_ : Rel A ℓ′} where
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138-
module _ {_≤_ : Rel A a} where
136+
module _ {_≤_ : Rel A ℓ″} where
139137
import Relation.Binary.Construct.NonStrictToStrict _≈_ _≤_ as SNS
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141139
module _ (≤-isPreorder : IsPreorder _≈_ _≤_)
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158156
; ≤-antisym = antsym
159157
}
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161-
module _ {_<_ : Rel A a} where
159+
module _ {_<_ : Rel A ℓ″} where
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163161
import Relation.Binary.Construct.StrictToNonStrict _≈_ _<_ as SNS
164162

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181179
; ≤-antisym = SNS.isPartialOrder <-isStrictPartialOrder .IsPartialOrder.antisym
182180
}
183181

184-
185182
module _ (<-isStrictTotalOrder : IsStrictTotalOrder _≈_ _<_) where
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187184
private spo = IsStrictTotalOrder.isStrictPartialOrder <-isStrictTotalOrder

‎Class/HasOrder/Instance.agda

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{-# OPTIONS --safe #-}
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{-# OPTIONS --without-K #-}
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module Class.HasOrder.Instance where
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open import Class.DecEq

‎Class/Monad.agda

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{-# OPTIONS --without-K #-}
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{-# OPTIONS --cubical-compatible #-}
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module Class.Monad where
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open import Class.Monad.Core public

‎Class/Monad/Core.agda

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{-# OPTIONS --without-K #-}
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module Class.Monad.Core where
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open import Class.Prelude

‎Class/Monad/Instances.agda

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{-# OPTIONS --without-K #-}
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module Class.Monad.Instances where
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open import Class.Prelude

‎Class/Monoid.agda

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{-# OPTIONS --without-K #-}
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module Class.Monoid where
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open import Class.Monoid.Core public

‎Class/Monoid/Core.agda

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{-# OPTIONS --without-K #-}
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module Class.Monoid.Core where
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open import Class.Prelude

‎Class/Monoid/Instances.agda

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{-# OPTIONS --without-K #-}
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module Class.Monoid.Instances where
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open import Class.Prelude

‎Class/Prelude.agda

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{-# OPTIONS --without-K #-}
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module Class.Prelude where
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open import Agda.Primitive public
55
using () renaming (Set to Type; Setω to Typeω)
66
open import Level public
77
using (Level; _⊔_) renaming (suc to lsuc)
8-
open import Function public
9-
using (id; _∘_; _∋_; _$_; const; constᵣ; flip; it)
8+
open import Function.Base public
9+
using (id; _∘_; _∋_; _$_; const; constᵣ; flip; it; case_of_)
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1111
open import Data.Empty public
1212
using (⊥; ⊥-elim)
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4444
using (These; this; that; these)
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4646
open import Relation.Nullary public
47-
using (¬_; Dec; yes; no)
47+
using (¬_; Dec; yes; no; contradiction)
4848
open import Relation.Nullary.Decidable public
4949
using (⌊_⌋; dec-yes; isYes)
5050
open import Relation.Unary public
@@ -54,7 +54,7 @@ open import Relation.Binary public
5454
using (REL; Rel; DecidableEquality)
5555
renaming (Decidable to Decidable²)
5656
module _ {a b c} where
57-
3REL : (A : Set a) (B : Set b) (C : Set c) (ℓ : Level) → Type _
57+
3REL : (A : Type a) (B : Type b) (C : Type c) (ℓ : Level) → Type _
5858
3REL A B C ℓ = A → B → C → Type ℓ
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6060
Decidable³ : ∀ {A B C ℓ} → 3REL A B C ℓ → Type _
@@ -66,7 +66,7 @@ open import Reflection public
6666
using (TC; Arg; Abs)
6767

6868
variable
69-
ℓ ℓ′ ℓ″ : Level
69+
ℓ ℓ′ ℓ″ ℓ‴ : Level
7070
A B C : Type ℓ
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7272
module Alg (_~_ : Rel A ℓ) where

‎Class/Semigroup.agda

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{-# OPTIONS --without-K #-}
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module Class.Semigroup where
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open import Class.Semigroup.Core public

‎Class/Semigroup/Core.agda

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{-# OPTIONS --without-K #-}
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module Class.Semigroup.Core where
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open import Class.Prelude

‎Class/Semigroup/Derive.agda

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‎Class/Semigroup/Instances.agda

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module Class.Semigroup.Instances where
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open import Class.Prelude

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