fact stringlengths 5 670 | type stringclasses 3
values | library stringclasses 18
values | imports listlengths 0 48 | filename stringclasses 782
values | symbolic_name stringlengths 1 35 | docstring stringclasses 1
value |
|---|---|---|---|---|---|---|
RawMonadTd (F: Set f → Set g₁) (TF : Set f → Set g₂) : Set (suc f ⊔ g₁ ⊔ g₂)
where
field
lift : F A → TF A
rawMonad : RawMonad TF
open RawMonad rawMonad public
RawMonadT : (T : (Set f → Set g₁) → (Set f → Set g₂)) → Set (suc f ⊔ suc g₁ ⊔ g₂) | record | Effect | [
"Data.Bool.Base",
"Data.Unit.Polymorphic.Base",
"Effect.Choice",
"Effect.Empty",
"Effect.Applicative as App",
"Function.Base",
"Level"
] | Effect/Monad.agda | RawMonadTd | |
RawMonadT : (T : (Set f → Set g₁) → (Set f → Set g₂)) → Set (suc f ⊔ suc g₁ ⊔ g₂) | function | Effect | [
"Data.Bool.Base",
"Data.Unit.Polymorphic.Base",
"Effect.Choice",
"Effect.Empty",
"Effect.Applicative as App",
"Function.Base",
"Level"
] | Effect/Monad.agda | RawMonadT | |
id : A → A | function | Function | [
"Level"
] | Function/Base.agda | id | |
const : A → B → A | function | Function | [
"Level"
] | Function/Base.agda | const | |
constᵣ : A → B → B | function | Function | [
"Level"
] | Function/Base.agda | constᵣ | |
_∘_ : ∀ {A : Set a} {B : A → Set b} {C : {x : A} → B x → Set c} → | function | Function | [
"Level"
] | Function/Base.agda | _∘_ | |
_∘₂_ : ∀ {A₁ : Set a} {A₂ : A₁ → Set d} | function | Function | [
"Level"
] | Function/Base.agda | _∘₂_ | |
flip : ∀ {A : Set a} {B : Set b} {C : A → B → Set c} → | function | Function | [
"Level"
] | Function/Base.agda | flip | |
_$_ : ∀ {A : Set a} {B : A → Set b} → | function | Function | [
"Level"
] | Function/Base.agda | _$_ | |
_|>_ : ∀ {A : Set a} {B : A → Set b} → | function | Function | [
"Level"
] | Function/Base.agda | _|>_ | |
_ˢ_ : ∀ {A : Set a} {B : A → Set b} {C : (x : A) → B x → Set c} → | function | Function | [
"Level"
] | Function/Base.agda | _ˢ_ | |
_$- : ∀ {A : Set a} {B : A → Set b} → ((x : A) → B x) → ({x : A} → B x) | function | Function | [
"Level"
] | Function/Base.agda | _$- | |
λ- : ∀ {A : Set a} {B : A → Set b} → ({x : A} → B x) → ((x : A) → B x) | function | Function | [
"Level"
] | Function/Base.agda | λ- | |
case_returning_of_ : ∀ {A : Set a} (x : A) (B : A → Set b) → | function | Function | [
"Level"
] | Function/Base.agda | case_returning_of_ | |
_∘′_ : (B → C) → (A → B) → (A → C) | function | Function | [
"Level"
] | Function/Base.agda | _∘′_ | |
_∘₂′_ : (C → D) → (A → B → C) → (A → B → D) | function | Function | [
"Level"
] | Function/Base.agda | _∘₂′_ | |
flip′ : (A → B → C) → (B → A → C) | function | Function | [
"Level"
] | Function/Base.agda | flip′ | |
_$′_ : (A → B) → (A → B) | function | Function | [
"Level"
] | Function/Base.agda | _$′_ | |
_|>′_ : A → (A → B) → B | function | Function | [
"Level"
] | Function/Base.agda | _|>′_ | |
case_of_ : A → (A → B) → B | function | Function | [
"Level"
] | Function/Base.agda | case_of_ | |
_⟨_⟩_ : A → (A → B → C) → B → C | function | Function | [
"Level"
] | Function/Base.agda | _⟨_⟩_ | |
_∋_ : (A : Set a) → A → A | function | Function | [
"Level"
] | Function/Base.agda | _∋_ | |
typeOf : {A : Set a} → A → Set a | function | Function | [
"Level"
] | Function/Base.agda | typeOf | |
it : {A : Set a} → {{A}} → A | function | Function | [
"Level"
] | Function/Base.agda | it | |
_-⟪_⟫-_ : (A → B → C) → (C → D → E) → (A → B → D) → (A → B → E) | function | Function | [
"Level"
] | Function/Base.agda | _-⟪_⟫-_ | |
_-⟪_∣ : (A → B → C) → (C → B → D) → (A → B → D) | function | Function | [
"Level"
] | Function/Base.agda | _-⟪_∣ | |
_-⟨_∣ : (A → C) → (C → B → D) → (A → B → D) | function | Function | [
"Level"
] | Function/Base.agda | _-⟨_∣ | |
_-⟪_⟩-_ : (A → B → C) → (C → D → E) → (B → D) → (A → B → E) | function | Function | [
"Level"
] | Function/Base.agda | _-⟪_⟩-_ | |
_-⟨_⟫-_ : (A → C) → (C → D → E) → (A → B → D) → (A → B → E) | function | Function | [
"Level"
] | Function/Base.agda | _-⟨_⟫-_ | |
_-⟨_⟩-_ : (A → C) → (C → D → E) → (B → D) → (A → B → E) | function | Function | [
"Level"
] | Function/Base.agda | _-⟨_⟩-_ | |
_on₂_ : (C → C → D) → (A → B → C) → (A → B → D) | function | Function | [
"Level"
] | Function/Base.agda | _on₂_ | |
_on_ : (B → B → C) → (A → B) → (A → A → C) | function | Function | [
"Level"
] | Function/Base.agda | _on_ | |
_⤖_ : ∀ {f t} → Set f → Set t → Set _ | function | Function | [
"Level",
"Relation.Binary.Bundles",
"Relation.Binary.PropositionalEquality as ≡",
"Function.Equality as F",
"Function.Injection as Inj",
"Function.Surjection as Surj",
"Function.LeftInverse as Left"
] | Function/Bijection.agda | _⤖_ | |
bijection : ∀ {f t} {From : Set f} {To : Set t} → | function | Function | [
"Level",
"Relation.Binary.Bundles",
"Relation.Binary.PropositionalEquality as ≡",
"Function.Equality as F",
"Function.Injection as Inj",
"Function.Surjection as Surj",
"Function.LeftInverse as Left"
] | Function/Bijection.agda | bijection | |
id : ∀ {s₁ s₂} {S : Setoid s₁ s₂} → Bijection S S | function | Function | [
"Level",
"Relation.Binary.Bundles",
"Relation.Binary.PropositionalEquality as ≡",
"Function.Equality as F",
"Function.Injection as Inj",
"Function.Surjection as Surj",
"Function.LeftInverse as Left"
] | Function/Bijection.agda | id | |
_∘_ : ∀ {f₁ f₂ m₁ m₂ t₁ t₂} | function | Function | [
"Level",
"Relation.Binary.Bundles",
"Relation.Binary.PropositionalEquality as ≡",
"Function.Equality as F",
"Function.Injection as Inj",
"Function.Surjection as Surj",
"Function.LeftInverse as Left"
] | Function/Bijection.agda | _∘_ | |
_⟶ₛ_ : Setoid a ℓ₁ → Setoid b ℓ₂ → Set _ | function | Function | [
"Function.Base",
"Function.Definitions",
"Function.Structures",
"Level",
"Data.Product.Base",
"Relation.Binary.Bundles",
"Relation.Binary.Core",
"Relation.Binary.PropositionalEquality.Core as ≡",
"Relation.Binary.PropositionalEquality.Properties",
"Function.Consequences.Propositional"
] | Function/Bundles.agda | _⟶ₛ_ | |
_⟶_ : Set a → Set b → Set _ | function | Function | [
"Function.Base",
"Function.Definitions",
"Function.Structures",
"Level",
"Data.Product.Base",
"Relation.Binary.Bundles",
"Relation.Binary.Core",
"Relation.Binary.PropositionalEquality.Core as ≡",
"Relation.Binary.PropositionalEquality.Properties",
"Function.Consequences.Propositional"
] | Function/Bundles.agda | _⟶_ | |
_↣_ : Set a → Set b → Set _ | function | Function | [
"Function.Base",
"Function.Definitions",
"Function.Structures",
"Level",
"Data.Product.Base",
"Relation.Binary.Bundles",
"Relation.Binary.Core",
"Relation.Binary.PropositionalEquality.Core as ≡",
"Relation.Binary.PropositionalEquality.Properties",
"Function.Consequences.Propositional"
] | Function/Bundles.agda | _↣_ | |
_↠_ : Set a → Set b → Set _ | function | Function | [
"Function.Base",
"Function.Definitions",
"Function.Structures",
"Level",
"Data.Product.Base",
"Relation.Binary.Bundles",
"Relation.Binary.Core",
"Relation.Binary.PropositionalEquality.Core as ≡",
"Relation.Binary.PropositionalEquality.Properties",
"Function.Consequences.Propositional"
] | Function/Bundles.agda | _↠_ | |
_⤖_ : Set a → Set b → Set _ | function | Function | [
"Function.Base",
"Function.Definitions",
"Function.Structures",
"Level",
"Data.Product.Base",
"Relation.Binary.Bundles",
"Relation.Binary.Core",
"Relation.Binary.PropositionalEquality.Core as ≡",
"Relation.Binary.PropositionalEquality.Properties",
"Function.Consequences.Propositional"
] | Function/Bundles.agda | _⤖_ | |
_⇔_ : Set a → Set b → Set _ | function | Function | [
"Function.Base",
"Function.Definitions",
"Function.Structures",
"Level",
"Data.Product.Base",
"Relation.Binary.Bundles",
"Relation.Binary.Core",
"Relation.Binary.PropositionalEquality.Core as ≡",
"Relation.Binary.PropositionalEquality.Properties",
"Function.Consequences.Propositional"
] | Function/Bundles.agda | _⇔_ | |
_↩_ : Set a → Set b → Set _ | function | Function | [
"Function.Base",
"Function.Definitions",
"Function.Structures",
"Level",
"Data.Product.Base",
"Relation.Binary.Bundles",
"Relation.Binary.Core",
"Relation.Binary.PropositionalEquality.Core as ≡",
"Relation.Binary.PropositionalEquality.Properties",
"Function.Consequences.Propositional"
] | Function/Bundles.agda | _↩_ | |
_↪_ : Set a → Set b → Set _ | function | Function | [
"Function.Base",
"Function.Definitions",
"Function.Structures",
"Level",
"Data.Product.Base",
"Relation.Binary.Bundles",
"Relation.Binary.Core",
"Relation.Binary.PropositionalEquality.Core as ≡",
"Relation.Binary.PropositionalEquality.Properties",
"Function.Consequences.Propositional"
] | Function/Bundles.agda | _↪_ | |
_↩↪_ : Set a → Set b → Set _ | function | Function | [
"Function.Base",
"Function.Definitions",
"Function.Structures",
"Level",
"Data.Product.Base",
"Relation.Binary.Bundles",
"Relation.Binary.Core",
"Relation.Binary.PropositionalEquality.Core as ≡",
"Relation.Binary.PropositionalEquality.Properties",
"Function.Consequences.Propositional"
] | Function/Bundles.agda | _↩↪_ | |
_↔_ : Set a → Set b → Set _ | function | Function | [
"Function.Base",
"Function.Definitions",
"Function.Structures",
"Level",
"Data.Product.Base",
"Relation.Binary.Bundles",
"Relation.Binary.Core",
"Relation.Binary.PropositionalEquality.Core as ≡",
"Relation.Binary.PropositionalEquality.Properties",
"Function.Consequences.Propositional"
] | Function/Bundles.agda | _↔_ | |
contraInjective : ∀ (≈₂ : Rel B ℓ₂) → Injective ≈₁ ≈₂ f → | function | Function | [
"Data.Product.Base as Product",
"Function.Definitions",
"Level",
"Relation.Binary.Core",
"Relation.Binary.Bundles",
"Relation.Binary.Definitions",
"Relation.Nullary.Negation.Core"
] | Function/Consequences.agda | contraInjective | |
inverseˡ⇒surjective : ∀ (≈₂ : Rel B ℓ₂) → | function | Function | [
"Data.Product.Base as Product",
"Function.Definitions",
"Level",
"Relation.Binary.Core",
"Relation.Binary.Bundles",
"Relation.Binary.Definitions",
"Relation.Nullary.Negation.Core"
] | Function/Consequences.agda | inverseˡ⇒surjective | |
inverseʳ⇒injective : ∀ (≈₂ : Rel B ℓ₂) f → | function | Function | [
"Data.Product.Base as Product",
"Function.Definitions",
"Level",
"Relation.Binary.Core",
"Relation.Binary.Bundles",
"Relation.Binary.Definitions",
"Relation.Nullary.Negation.Core"
] | Function/Consequences.agda | inverseʳ⇒injective | |
inverseᵇ⇒bijective : ∀ (≈₂ : Rel B ℓ₂) → | function | Function | [
"Data.Product.Base as Product",
"Function.Definitions",
"Level",
"Relation.Binary.Core",
"Relation.Binary.Bundles",
"Relation.Binary.Definitions",
"Relation.Nullary.Negation.Core"
] | Function/Consequences.agda | inverseᵇ⇒bijective | |
surjective⇒strictlySurjective : ∀ (≈₂ : Rel B ℓ₂) → | function | Function | [
"Data.Product.Base as Product",
"Function.Definitions",
"Level",
"Relation.Binary.Core",
"Relation.Binary.Bundles",
"Relation.Binary.Definitions",
"Relation.Nullary.Negation.Core"
] | Function/Consequences.agda | surjective⇒strictlySurjective | |
strictlySurjective⇒surjective : Transitive ≈₂ → | function | Function | [
"Data.Product.Base as Product",
"Function.Definitions",
"Level",
"Relation.Binary.Core",
"Relation.Binary.Bundles",
"Relation.Binary.Definitions",
"Relation.Nullary.Negation.Core"
] | Function/Consequences.agda | strictlySurjective⇒surjective | |
inverseˡ⇒strictlyInverseˡ : ∀ (≈₁ : Rel A ℓ₁) (≈₂ : Rel B ℓ₂) → | function | Function | [
"Data.Product.Base as Product",
"Function.Definitions",
"Level",
"Relation.Binary.Core",
"Relation.Binary.Bundles",
"Relation.Binary.Definitions",
"Relation.Nullary.Negation.Core"
] | Function/Consequences.agda | inverseˡ⇒strictlyInverseˡ | |
strictlyInverseˡ⇒inverseˡ : Transitive ≈₂ → | function | Function | [
"Data.Product.Base as Product",
"Function.Definitions",
"Level",
"Relation.Binary.Core",
"Relation.Binary.Bundles",
"Relation.Binary.Definitions",
"Relation.Nullary.Negation.Core"
] | Function/Consequences.agda | strictlyInverseˡ⇒inverseˡ | |
inverseʳ⇒strictlyInverseʳ : ∀ (≈₁ : Rel A ℓ₁) (≈₂ : Rel B ℓ₂) → | function | Function | [
"Data.Product.Base as Product",
"Function.Definitions",
"Level",
"Relation.Binary.Core",
"Relation.Binary.Bundles",
"Relation.Binary.Definitions",
"Relation.Nullary.Negation.Core"
] | Function/Consequences.agda | inverseʳ⇒strictlyInverseʳ | |
strictlyInverseʳ⇒inverseʳ : Transitive ≈₁ → | function | Function | [
"Data.Product.Base as Product",
"Function.Definitions",
"Level",
"Relation.Binary.Core",
"Relation.Binary.Bundles",
"Relation.Binary.Definitions",
"Relation.Nullary.Negation.Core"
] | Function/Consequences.agda | strictlyInverseʳ⇒inverseʳ | |
Fun₁ : ∀ {a} → Set a → Set a | function | Function | [
"Level"
] | Function/Core.agda | Fun₁ | |
Fun₂ : ∀ {a} → Set a → Set a | function | Function | [
"Level"
] | Function/Core.agda | Fun₂ | |
Morphism : ∀ {a} → ∀ {b} → Set a → Set b → Set (a ⊔ b) | function | Function | [
"Level"
] | Function/Core.agda | Morphism | |
StrictlySurjective : Rel B ℓ₂ → (A → B) → Set _ | function | Function | [
"Data.Product.Base",
"Level",
"Relation.Binary.Core"
] | Function/Definitions.agda | StrictlySurjective | |
StrictlyInverseˡ : Rel B ℓ₂ → (A → B) → (B → A) → Set _ | function | Function | [
"Data.Product.Base",
"Level",
"Relation.Binary.Core"
] | Function/Definitions.agda | StrictlyInverseˡ | |
StrictlyInverseʳ : Rel A ℓ₁ → (A → B) → (B → A) → Set _ | function | Function | [
"Data.Product.Base",
"Level",
"Relation.Binary.Core"
] | Function/Definitions.agda | StrictlyInverseʳ | |
_⟶_ : ∀ {f₁ f₂ t₁ t₂} → Setoid f₁ f₂ → Setoid t₁ t₂ → Set _ | function | Function | [
"Function.Base",
"Level",
"Relation.Binary.Bundles",
"Relation.Binary.Indexed.Heterogeneous",
"Relation.Binary.Indexed.Heterogeneous.Construct.Trivial",
"Relation.Binary.PropositionalEquality.Core",
"Relation.Binary.PropositionalEquality.Properties"
] | Function/Equality.agda | _⟶_ | |
id : ∀ {a₁ a₂} {A : Setoid a₁ a₂} → A ⟶ A | function | Function | [
"Function.Base",
"Level",
"Relation.Binary.Bundles",
"Relation.Binary.Indexed.Heterogeneous",
"Relation.Binary.Indexed.Heterogeneous.Construct.Trivial",
"Relation.Binary.PropositionalEquality.Core",
"Relation.Binary.PropositionalEquality.Properties"
] | Function/Equality.agda | id | |
_∘_ : ∀ {a₁ a₂} {A : Setoid a₁ a₂} | function | Function | [
"Function.Base",
"Level",
"Relation.Binary.Bundles",
"Relation.Binary.Indexed.Heterogeneous",
"Relation.Binary.Indexed.Heterogeneous.Construct.Trivial",
"Relation.Binary.PropositionalEquality.Core",
"Relation.Binary.PropositionalEquality.Properties"
] | Function/Equality.agda | _∘_ | |
const : ∀ {a₁ a₂} {A : Setoid a₁ a₂} | function | Function | [
"Function.Base",
"Level",
"Relation.Binary.Bundles",
"Relation.Binary.Indexed.Heterogeneous",
"Relation.Binary.Indexed.Heterogeneous.Construct.Trivial",
"Relation.Binary.PropositionalEquality.Core",
"Relation.Binary.PropositionalEquality.Properties"
] | Function/Equality.agda | const | |
setoid : ∀ {f₁ f₂ t₁ t₂} | function | Function | [
"Function.Base",
"Level",
"Relation.Binary.Bundles",
"Relation.Binary.Indexed.Heterogeneous",
"Relation.Binary.Indexed.Heterogeneous.Construct.Trivial",
"Relation.Binary.PropositionalEquality.Core",
"Relation.Binary.PropositionalEquality.Properties"
] | Function/Equality.agda | setoid | |
_⇨_ : ∀ {f₁ f₂ t₁ t₂} → Setoid f₁ f₂ → Setoid t₁ t₂ → Setoid _ _ | function | Function | [
"Function.Base",
"Level",
"Relation.Binary.Bundles",
"Relation.Binary.Indexed.Heterogeneous",
"Relation.Binary.Indexed.Heterogeneous.Construct.Trivial",
"Relation.Binary.PropositionalEquality.Core",
"Relation.Binary.PropositionalEquality.Properties"
] | Function/Equality.agda | _⇨_ | |
≡-setoid : ∀ {f t₁ t₂} (From : Set f) → IndexedSetoid From t₁ t₂ → Setoid _ _ | function | Function | [
"Function.Base",
"Level",
"Relation.Binary.Bundles",
"Relation.Binary.Indexed.Heterogeneous",
"Relation.Binary.Indexed.Heterogeneous.Construct.Trivial",
"Relation.Binary.PropositionalEquality.Core",
"Relation.Binary.PropositionalEquality.Properties"
] | Function/Equality.agda | ≡-setoid | |
flip : ∀ {a₁ a₂} {A : Setoid a₁ a₂} | function | Function | [
"Function.Base",
"Level",
"Relation.Binary.Bundles",
"Relation.Binary.Indexed.Heterogeneous",
"Relation.Binary.Indexed.Heterogeneous.Construct.Trivial",
"Relation.Binary.PropositionalEquality.Core",
"Relation.Binary.PropositionalEquality.Properties"
] | Function/Equality.agda | flip | |
→-to-⟶ : ∀ {a b ℓ} {A : Set a} {B : Setoid b ℓ} → | function | Function | [
"Function.Base",
"Level",
"Relation.Binary.Bundles",
"Relation.Binary.Indexed.Heterogeneous",
"Relation.Binary.Indexed.Heterogeneous.Construct.Trivial",
"Relation.Binary.PropositionalEquality.Core",
"Relation.Binary.PropositionalEquality.Properties"
] | Function/Equality.agda | →-to-⟶ | |
_⇔_ : ∀ {f t} → Set f → Set t → Set _ | function | Function | [
"Function.Base",
"Function.Equality as F",
"Level",
"Relation.Binary.Bundles",
"Relation.Binary.Definitions",
"Relation.Binary.PropositionalEquality"
] | Function/Equivalence.agda | _⇔_ | |
equivalence : ∀ {f t} {From : Set f} {To : Set t} → | function | Function | [
"Function.Base",
"Function.Equality as F",
"Level",
"Relation.Binary.Bundles",
"Relation.Binary.Definitions",
"Relation.Binary.PropositionalEquality"
] | Function/Equivalence.agda | equivalence | |
id : ∀ {s₁ s₂} → Reflexive (Equivalence {s₁} {s₂}) | function | Function | [
"Function.Base",
"Function.Equality as F",
"Level",
"Relation.Binary.Bundles",
"Relation.Binary.Definitions",
"Relation.Binary.PropositionalEquality"
] | Function/Equivalence.agda | id | |
_∘_ : ∀ {f₁ f₂ m₁ m₂ t₁ t₂} → | function | Function | [
"Function.Base",
"Function.Equality as F",
"Level",
"Relation.Binary.Bundles",
"Relation.Binary.Definitions",
"Relation.Binary.PropositionalEquality"
] | Function/Equivalence.agda | _∘_ | |
sym : ∀ {f₁ f₂ t₁ t₂} → | function | Function | [
"Function.Base",
"Function.Equality as F",
"Level",
"Relation.Binary.Bundles",
"Relation.Binary.Definitions",
"Relation.Binary.PropositionalEquality"
] | Function/Equivalence.agda | sym | |
setoid : (s₁ s₂ : Level) → Setoid (suc (s₁ ⊔ s₂)) (s₁ ⊔ s₂) | function | Function | [
"Function.Base",
"Function.Equality as F",
"Level",
"Relation.Binary.Bundles",
"Relation.Binary.Definitions",
"Relation.Binary.PropositionalEquality"
] | Function/Equivalence.agda | setoid | |
map : ∀ {f₁ f₂ t₁ t₂} {From : Setoid f₁ f₂} {To : Setoid t₁ t₂} | function | Function | [
"Function.Base",
"Function.Equality as F",
"Level",
"Relation.Binary.Bundles",
"Relation.Binary.Definitions",
"Relation.Binary.PropositionalEquality"
] | Function/Equivalence.agda | map | |
zip : ∀ {f₁₁ f₂₁ t₁₁ t₂₁} | function | Function | [
"Function.Base",
"Function.Equality as F",
"Level",
"Relation.Binary.Bundles",
"Relation.Binary.Definitions",
"Relation.Binary.PropositionalEquality"
] | Function/Equivalence.agda | zip | |
_≃_ {a b} (A: Set a) (B : Set b) : Set (a ⊔ b)
where
field
to : A → B
from : B → A
left-inverse-of : ∀ x → from (to x) ≡ x
right-inverse-of : ∀ x → to (from x) ≡ x
left-right :
∀ x → cong to (left-inverse-of x) ≡ right-inverse-of (to x)
-- Half adjoint equ... | record | Function | [
"Function.Base",
"Function.Equality",
"Function.Inverse as Inv",
"Level",
"Relation.Binary.PropositionalEquality"
] | Function/HalfAdjointEquivalence.agda | _≃_ | |
↔→≃ : ∀ {a b} {A : Set a} {B : Set b} → A ↔ B → A ≃ B | function | Function | [
"Function.Base",
"Function.Equality",
"Function.Inverse as Inv",
"Level",
"Relation.Binary.PropositionalEquality"
] | Function/HalfAdjointEquivalence.agda | ↔→≃ | |
Injective : ∀ {a₁ a₂ b₁ b₂} {A : Setoid a₁ a₂} {B : Setoid b₁ b₂} → | function | Function | [
"Function.Base as Fun",
"Level",
"Relation.Binary.Bundles",
"Function.Equality as F",
"Relation.Binary.PropositionalEquality as ≡"
] | Function/Injection.agda | Injective | |
_↣_ : ∀ {f t} → Set f → Set t → Set _ | function | Function | [
"Function.Base as Fun",
"Level",
"Relation.Binary.Bundles",
"Function.Equality as F",
"Relation.Binary.PropositionalEquality as ≡"
] | Function/Injection.agda | _↣_ | |
injection : ∀ {f t} {From : Set f} {To : Set t} → (to : From → To) → | function | Function | [
"Function.Base as Fun",
"Level",
"Relation.Binary.Bundles",
"Function.Equality as F",
"Relation.Binary.PropositionalEquality as ≡"
] | Function/Injection.agda | injection | |
id : ∀ {s₁ s₂} {S : Setoid s₁ s₂} → Injection S S | function | Function | [
"Function.Base as Fun",
"Level",
"Relation.Binary.Bundles",
"Function.Equality as F",
"Relation.Binary.PropositionalEquality as ≡"
] | Function/Injection.agda | id | |
_∘_ : ∀ {f₁ f₂ m₁ m₂ t₁ t₂} | function | Function | [
"Function.Base as Fun",
"Level",
"Relation.Binary.Bundles",
"Function.Equality as F",
"Relation.Binary.PropositionalEquality as ≡"
] | Function/Injection.agda | _∘_ | |
_↔_ : ∀ {f t} → Set f → Set t → Set _ | function | Function | [
"Level",
"Function.Base",
"Function.Bijection",
"Function.Equality as F",
"Function.LeftInverse as Left",
"Relation.Binary.Bundles",
"Relation.Binary.Definitions",
"Relation.Binary.PropositionalEquality as ≡",
"Relation.Unary"
] | Function/Inverse.agda | _↔_ | |
_↔̇_ : ∀ {i f t} {I : Set i} → Pred I f → Pred I t → Set _ | function | Function | [
"Level",
"Function.Base",
"Function.Bijection",
"Function.Equality as F",
"Function.LeftInverse as Left",
"Relation.Binary.Bundles",
"Relation.Binary.Definitions",
"Relation.Binary.PropositionalEquality as ≡",
"Relation.Unary"
] | Function/Inverse.agda | _↔̇_ | |
inverse : ∀ {f t} {From : Set f} {To : Set t} → | function | Function | [
"Level",
"Function.Base",
"Function.Bijection",
"Function.Equality as F",
"Function.LeftInverse as Left",
"Relation.Binary.Bundles",
"Relation.Binary.Definitions",
"Relation.Binary.PropositionalEquality as ≡",
"Relation.Unary"
] | Function/Inverse.agda | inverse | |
fromBijection : ∀ {f₁ f₂ t₁ t₂} {From : Setoid f₁ f₂} {To : Setoid t₁ t₂} → | function | Function | [
"Level",
"Function.Base",
"Function.Bijection",
"Function.Equality as F",
"Function.LeftInverse as Left",
"Relation.Binary.Bundles",
"Relation.Binary.Definitions",
"Relation.Binary.PropositionalEquality as ≡",
"Relation.Unary"
] | Function/Inverse.agda | fromBijection | |
id : ∀ {s₁ s₂} → Reflexive (Inverse {s₁} {s₂}) | function | Function | [
"Level",
"Function.Base",
"Function.Bijection",
"Function.Equality as F",
"Function.LeftInverse as Left",
"Relation.Binary.Bundles",
"Relation.Binary.Definitions",
"Relation.Binary.PropositionalEquality as ≡",
"Relation.Unary"
] | Function/Inverse.agda | id | |
_∘_ : ∀ {f₁ f₂ m₁ m₂ t₁ t₂} → | function | Function | [
"Level",
"Function.Base",
"Function.Bijection",
"Function.Equality as F",
"Function.LeftInverse as Left",
"Relation.Binary.Bundles",
"Relation.Binary.Definitions",
"Relation.Binary.PropositionalEquality as ≡",
"Relation.Unary"
] | Function/Inverse.agda | _∘_ | |
sym : ∀ {f₁ f₂ t₁ t₂} → | function | Function | [
"Level",
"Function.Base",
"Function.Bijection",
"Function.Equality as F",
"Function.LeftInverse as Left",
"Relation.Binary.Bundles",
"Relation.Binary.Definitions",
"Relation.Binary.PropositionalEquality as ≡",
"Relation.Unary"
] | Function/Inverse.agda | sym | |
map : ∀ {f₁ f₂ t₁ t₂} {From : Setoid f₁ f₂} {To : Setoid t₁ t₂} | function | Function | [
"Level",
"Function.Base",
"Function.Bijection",
"Function.Equality as F",
"Function.LeftInverse as Left",
"Relation.Binary.Bundles",
"Relation.Binary.Definitions",
"Relation.Binary.PropositionalEquality as ≡",
"Relation.Unary"
] | Function/Inverse.agda | map | |
zip : ∀ {f₁₁ f₂₁ t₁₁ t₂₁} | function | Function | [
"Level",
"Function.Base",
"Function.Bijection",
"Function.Equality as F",
"Function.LeftInverse as Left",
"Relation.Binary.Bundles",
"Relation.Binary.Definitions",
"Relation.Binary.PropositionalEquality as ≡",
"Relation.Unary"
] | Function/Inverse.agda | zip | |
_LeftInverseOf_ : ∀ {f₁ f₂ t₁ t₂} {From : Setoid f₁ f₂} {To : Setoid t₁ t₂} → | function | Function | [
"Level",
"Relation.Binary.Reasoning.Setoid",
"Relation.Binary.Bundles",
"Function.Equality as Eq",
"Function.Equivalence",
"Function.Injection",
"Relation.Binary.PropositionalEquality as ≡"
] | Function/LeftInverse.agda | _LeftInverseOf_ | |
_RightInverseOf_ : ∀ {f₁ f₂ t₁ t₂} {From : Setoid f₁ f₂} {To : Setoid t₁ t₂} → | function | Function | [
"Level",
"Relation.Binary.Reasoning.Setoid",
"Relation.Binary.Bundles",
"Function.Equality as Eq",
"Function.Equivalence",
"Function.Injection",
"Relation.Binary.PropositionalEquality as ≡"
] | Function/LeftInverse.agda | _RightInverseOf_ | |
RightInverse : ∀ {f₁ f₂ t₁ t₂} | function | Function | [
"Level",
"Relation.Binary.Reasoning.Setoid",
"Relation.Binary.Bundles",
"Function.Equality as Eq",
"Function.Equivalence",
"Function.Injection",
"Relation.Binary.PropositionalEquality as ≡"
] | Function/LeftInverse.agda | RightInverse | |
_↞_ : ∀ {f t} → Set f → Set t → Set _ | function | Function | [
"Level",
"Relation.Binary.Reasoning.Setoid",
"Relation.Binary.Bundles",
"Function.Equality as Eq",
"Function.Equivalence",
"Function.Injection",
"Relation.Binary.PropositionalEquality as ≡"
] | Function/LeftInverse.agda | _↞_ | |
leftInverse : ∀ {f t} {From : Set f} {To : Set t} → | function | Function | [
"Level",
"Relation.Binary.Reasoning.Setoid",
"Relation.Binary.Bundles",
"Function.Equality as Eq",
"Function.Equivalence",
"Function.Injection",
"Relation.Binary.PropositionalEquality as ≡"
] | Function/LeftInverse.agda | leftInverse |
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