fact stringlengths 5 24.4k | type stringclasses 3
values | library stringclasses 2
values | imports listlengths 0 70 | filename stringlengths 18 57 | symbolic_name stringlengths 1 32 | docstring stringclasses 1
value |
|---|---|---|---|---|---|---|
nat-unassoc-to : f ⇒ (g ⊗ h) ⊗ i → f ⇒ g ⊗ h ⊗ i | function | src | [
"open import 1Lab.Reflection.Copattern",
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection",
"open import Cat.Prelude",
"open import Data.List.Base",
"import Cat.Functor.Compose"
] | src/Cat/Functor/Coherence.agda | nat-unassoc-to | |
nat-unassoc-from : (f ⊗ g) ⊗ h ⇒ i → f ⊗ g ⊗ h ⇒ i | function | src | [
"open import 1Lab.Reflection.Copattern",
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection",
"open import Cat.Prelude",
"open import Data.List.Base",
"import Cat.Functor.Compose"
] | src/Cat/Functor/Coherence.agda | nat-unassoc-from | |
nat-idl-to : f ⇒ Id ⊗ g → f ⇒ g | function | src | [
"open import 1Lab.Reflection.Copattern",
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection",
"open import Cat.Prelude",
"open import Data.List.Base",
"import Cat.Functor.Compose"
] | src/Cat/Functor/Coherence.agda | nat-idl-to | |
nat-idl-from : Id ⊗ f ⇒ g → f ⇒ g | function | src | [
"open import 1Lab.Reflection.Copattern",
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection",
"open import Cat.Prelude",
"open import Data.List.Base",
"import Cat.Functor.Compose"
] | src/Cat/Functor/Coherence.agda | nat-idl-from | |
nat-unidl-to : f ⇒ g → f ⇒ Id ⊗ g | function | src | [
"open import 1Lab.Reflection.Copattern",
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection",
"open import Cat.Prelude",
"open import Data.List.Base",
"import Cat.Functor.Compose"
] | src/Cat/Functor/Coherence.agda | nat-unidl-to | |
nat-unidl-from : f ⇒ g → Id ⊗ f ⇒ g | function | src | [
"open import 1Lab.Reflection.Copattern",
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection",
"open import Cat.Prelude",
"open import Data.List.Base",
"import Cat.Functor.Compose"
] | src/Cat/Functor/Coherence.agda | nat-unidl-from | |
nat-unidr-to : f ⇒ g → f ⇒ g ⊗ Id | function | src | [
"open import 1Lab.Reflection.Copattern",
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection",
"open import Cat.Prelude",
"open import Data.List.Base",
"import Cat.Functor.Compose"
] | src/Cat/Functor/Coherence.agda | nat-unidr-to | |
nat-unidr-from : f ⇒ g → f ⊗ Id ⇒ g | function | src | [
"open import 1Lab.Reflection.Copattern",
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection",
"open import Cat.Prelude",
"open import Data.List.Base",
"import Cat.Functor.Compose"
] | src/Cat/Functor/Coherence.agda | nat-unidr-from | |
op-compose-into : f ⇒ Functor.op (g ⊗ h) → f ⇒ Functor.op g ⊗ Functor.op h | function | src | [
"open import 1Lab.Reflection.Copattern",
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection",
"open import Cat.Prelude",
"open import Data.List.Base",
"import Cat.Functor.Compose"
] | src/Cat/Functor/Coherence.agda | op-compose-into | |
F-id : ∀ {U : ⌞ C ⌟} {x} → F₁ {U} id x ≡ x | function | src | [
"open import Cat.Prelude hiding (ap ; ap₂)",
"import Cat.Functor.Reasoning as Func",
"import Cat.Reasoning as Cat"
] | src/Cat/Functor/Reasoning/Presheaf.agda | F-id | |
elim : f ≡ id → F₁ f x ≡ x | function | src | [
"open import Cat.Prelude hiding (ap ; ap₂)",
"import Cat.Functor.Reasoning as Func",
"import Cat.Reasoning as Cat"
] | src/Cat/Functor/Reasoning/Presheaf.agda | elim | |
intro : id ≡ f → x ≡ F₁ f x | function | src | [
"open import Cat.Prelude hiding (ap ; ap₂)",
"import Cat.Functor.Reasoning as Func",
"import Cat.Reasoning as Cat"
] | src/Cat/Functor/Reasoning/Presheaf.agda | intro | |
collapse : f ∘ g ≡ h → F₁ f (F₁ g x) ≡ F₁ h x | function | src | [
"open import Cat.Prelude hiding (ap ; ap₂)",
"import Cat.Functor.Reasoning as Func",
"import Cat.Reasoning as Cat"
] | src/Cat/Functor/Reasoning/Presheaf.agda | collapse | |
expand : h ≡ f ∘ g → F₁ h x ≡ F₁ f (F₁ g x) | function | src | [
"open import Cat.Prelude hiding (ap ; ap₂)",
"import Cat.Functor.Reasoning as Func",
"import Cat.Reasoning as Cat"
] | src/Cat/Functor/Reasoning/Presheaf.agda | expand | |
weave : f ∘ g ≡ h ∘ i → F₁ f (F₁ g x) ≡ F₁ h (F₁ i x) | function | src | [
"open import Cat.Prelude hiding (ap ; ap₂)",
"import Cat.Functor.Reasoning as Func",
"import Cat.Reasoning as Cat"
] | src/Cat/Functor/Reasoning/Presheaf.agda | weave | |
annihilate : f ∘ g ≡ id → F₁ f (F₁ g x) ≡ x | function | src | [
"open import Cat.Prelude hiding (ap ; ap₂)",
"import Cat.Functor.Reasoning as Func",
"import Cat.Reasoning as Cat"
] | src/Cat/Functor/Reasoning/Presheaf.agda | annihilate | |
conjure : id ≡ f ∘ g → x ≡ F₁ f (F₁ g x) | function | src | [
"open import Cat.Prelude hiding (ap ; ap₂)",
"import Cat.Functor.Reasoning as Func",
"import Cat.Reasoning as Cat"
] | src/Cat/Functor/Reasoning/Presheaf.agda | conjure | |
ap : x ≡ y → F₁ f x ≡ F₁ f y | function | src | [
"open import Cat.Prelude hiding (ap ; ap₂)",
"import Cat.Functor.Reasoning as Func",
"import Cat.Reasoning as Cat"
] | src/Cat/Functor/Reasoning/Presheaf.agda | ap | |
ap₂ : f ≡ g → x ≡ y → F₁ f x ≡ F₁ g y | function | src | [
"open import Cat.Prelude hiding (ap ; ap₂)",
"import Cat.Functor.Reasoning as Func",
"import Cat.Reasoning as Cat"
] | src/Cat/Functor/Reasoning/Presheaf.agda | ap₂ | |
uncons : (x : A) (xs : Finset A) → x ∈ᶠˢ xs → xs ≡ x ∷ xs | function | src | [
"open import 1Lab.Prelude",
"open import Data.List.Membership",
"open import Data.Finset.Base",
"open import Data.Fin.Finite",
"open import Data.Nat.Base",
"open import Data.Sum.Base",
"open import Data.Dec",
"import 1Lab.Reflection"
] | src/Data/Finset/Properties.agda | uncons | |
delete : ⦃ _ : Discrete A ⦄ → A → Finset A → Finset A | function | src | [
"open import 1Lab.Prelude",
"open import Data.List.Membership",
"open import Data.Finset.Base",
"open import Data.Fin.Finite",
"open import Data.Nat.Base",
"open import Data.Sum.Base",
"open import Data.Dec",
"import 1Lab.Reflection"
] | src/Data/Finset/Properties.agda | delete | |
powerset : Finset A → Finset (Finset A) | function | src | [
"open import 1Lab.Prelude",
"open import Data.List.Membership",
"open import Data.Finset.Base",
"open import Data.Fin.Finite",
"open import Data.Nat.Base",
"open import Data.Sum.Base",
"open import Data.Dec",
"import 1Lab.Reflection"
] | src/Data/Finset/Properties.agda | powerset | |
powerlist : List A → List (Finset A) | function | src | [
"open import 1Lab.Prelude",
"open import Data.List.Membership",
"open import Data.Finset.Base",
"open import Data.Fin.Finite",
"open import Data.Nat.Base",
"open import Data.Sum.Base",
"open import Data.Dec",
"import 1Lab.Reflection"
] | src/Data/Finset/Properties.agda | powerlist | |
powerlist-is-nubbed : ⦃ _ : Discrete A ⦄ (xs : List A) → is-nubbed xs → is-nubbed (powerlist xs) | function | src | [
"open import 1Lab.Prelude",
"open import Data.List.Membership",
"open import Data.Finset.Base",
"open import Data.Fin.Finite",
"open import Data.Nat.Base",
"open import Data.Sum.Base",
"open import Data.Dec",
"import 1Lab.Reflection"
] | src/Data/Finset/Properties.agda | powerlist-is-nubbed | |
symᵢ-symᵢ : ∀ {ℓ} {A : Type ℓ} {x y : A} (p : x ≡ᵢ y) → symᵢ (symᵢ p) ≡ p | function | src | [
"open import 1Lab.Path.Groupoid",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Id.Base"
] | src/Data/Id/Properties.agda | symᵢ-symᵢ | |
symᵢ-from : ∀ {ℓ} {A : Type ℓ} {x y : A} (p : x ≡ y) → symᵢ (Id≃path.from p) ≡ Id≃path.from (sym p) | function | src | [
"open import 1Lab.Path.Groupoid",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Id.Base"
] | src/Data/Id/Properties.agda | symᵢ-from | |
apᵢ-from : (f : A → B) {x y : A} (p : x ≡ y) → apᵢ f (Id≃path.from p) ≡ Id≃path.from (ap f p) | function | src | [
"open import 1Lab.Path.Groupoid",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Id.Base"
] | src/Data/Id/Properties.agda | apᵢ-from | |
apᵢ-symᵢ : (f : A → B) (p : x ≡ᵢ y) → apᵢ f (symᵢ p) ≡ᵢ symᵢ (apᵢ f p) | function | src | [
"open import 1Lab.Path.Groupoid",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Id.Base"
] | src/Data/Id/Properties.agda | apᵢ-symᵢ | |
symPᵢ : {a b : A} {x : P a} {y : P b} (p : a ≡ᵢ b) → Id-over P p x y → Id-over P (symᵢ p) y x | function | src | [
"open import 1Lab.Path.Groupoid",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Id.Base"
] | src/Data/Id/Properties.agda | symPᵢ | |
symᵢ-to : (p : x ≡ᵢ y) → Id≃path.to (symᵢ p) ≡ sym (Id≃path.to p) | function | src | [
"open import 1Lab.Path.Groupoid",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Id.Base"
] | src/Data/Id/Properties.agda | symᵢ-to | |
Pi : (xs : List A) → (A → Type ℓ') → Type _ | function | src | [
"open import 1Lab.Prelude",
"open import Data.List.Membership",
"open import Data.Fin.Product",
"open import Data.List.Sigma",
"open import Data.List.Base",
"open import Data.Fin.Base"
] | src/Data/List/Pi.agda | Pi | |
pi : (xs : List A) (ys : ∀ a → List (P a)) → List (Pi xs P) | function | src | [
"open import 1Lab.Prelude",
"open import Data.List.Membership",
"open import Data.Fin.Product",
"open import Data.List.Sigma",
"open import Data.List.Base",
"open import Data.Fin.Base"
] | src/Data/List/Pi.agda | pi | |
Pi' : (xs : List A) → (A → Type ℓ') → Type _ | function | src | [
"open import 1Lab.Prelude",
"open import Data.List.Membership",
"open import Data.Fin.Product",
"open import Data.List.Sigma",
"open import Data.List.Base",
"open import Data.Fin.Base"
] | src/Data/List/Pi.agda | Pi' | |
by-elim-ℚ : ∀ {ℓ} (n : Name) {ty : Type ℓ} → ty → TC ⊤ | function | src | [
"open import 1Lab.Reflection hiding ([_])",
"open import 1Lab.Prelude",
"open import Data.Rational.Base hiding (_/_)"
] | src/Data/Rational/Reflection.agda | by-elim-ℚ | |
build : Variables Ratio → Term → TC (Term × Variables Ratio) | function | src | [
"open import 1Lab.Reflection.Variables",
"open import 1Lab.Reflection hiding (absurd)",
"open import 1Lab.Prelude",
"open import Algebra.Ring.Cat.Initial",
"open import Algebra.Ring.Commutative",
"open import Algebra.Ring.Solver renaming (module Impl to RImpl)",
"open import Algebra.Ring",
"open impor... | src/Data/Rational/Solver.agda | build | |
Abs {a} (A : Type a) : Type a where constructor abs field abs-name : String abs-binder : A {-# BUILTIN ABS Abs #-} {-# BUILTIN ABSABS abs #-} instance Discrete-Abs : ∀ {ℓ} {A : Type ℓ} ⦃ _ : Discrete A ⦄ → Discrete (Abs A) Discrete-Abs = Discrete-inj (λ (abs n b) → n , b) (λ p → ap₂ abs (ap fst p) (ap snd p)) auto | record | src | [
"open import 1Lab.Path.IdentitySystem",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.String.Base",
"open import Data.Dec.Base",
"open import Data.Id.Base"
] | src/Data/Reflection/Abs.agda | Abs | |
Visibility : Type where visible hidden instance' : Visibility | data | src | [
"open import 1Lab.Path.IdentitySystem",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Bool.Base",
"open import Data.List.Base",
"open import Data.Dec.Base",
"open import Data.Id.Base",
"open import Meta.Traversable",
"open import Meta.Idiom"
] | src/Data/Reflection/Argument.agda | Visibility | |
Relevance : Type where relevant irrelevant : Relevance | data | src | [
"open import 1Lab.Path.IdentitySystem",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Bool.Base",
"open import Data.List.Base",
"open import Data.Dec.Base",
"open import Data.Id.Base",
"open import Meta.Traversable",
"open import Meta.Idiom"
] | src/Data/Reflection/Argument.agda | Relevance | |
Quantity : Type where quantity-0 quantity-ω : Quantity | data | src | [
"open import 1Lab.Path.IdentitySystem",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Bool.Base",
"open import Data.List.Base",
"open import Data.Dec.Base",
"open import Data.Id.Base",
"open import Meta.Traversable",
"open import Meta.Idiom"
] | src/Data/Reflection/Argument.agda | Quantity | |
Modality : Type where constructor modality field r : Relevance q : Quantity pattern default-modality = modality relevant quantity-ω | record | src | [
"open import 1Lab.Path.IdentitySystem",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Bool.Base",
"open import Data.List.Base",
"open import Data.Dec.Base",
"open import Data.Id.Base",
"open import Meta.Traversable",
"open import Meta.Idiom"
] | src/Data/Reflection/Argument.agda | Modality | |
ArgInfo : Type where constructor arginfo field arg-vis : Visibility arg-modality : Modality pattern default-ai = arginfo visible default-modality | record | src | [
"open import 1Lab.Path.IdentitySystem",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Bool.Base",
"open import Data.List.Base",
"open import Data.Dec.Base",
"open import Data.Id.Base",
"open import Meta.Traversable",
"open import Meta.Idiom"
] | src/Data/Reflection/Argument.agda | ArgInfo | |
Arg {a} (A : Type a) : Type a where constructor arg field arg-info : ArgInfo unarg : A {-# BUILTIN HIDING Visibility #-} {-# BUILTIN VISIBLE visible #-} {-# BUILTIN HIDDEN hidden #-} {-# BUILTIN INSTANCE instance' #-} {-# BUILTIN RELEVANCE Relevance #-} {-# BUILTIN RELEVANT relevant #-} {-# BUILTIN IRRELEVANT irrelevan... | record | src | [
"open import 1Lab.Path.IdentitySystem",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Bool.Base",
"open import Data.List.Base",
"open import Data.Dec.Base",
"open import Data.Id.Base",
"open import Meta.Traversable",
"open import Meta.Idiom"
] | src/Data/Reflection/Argument.agda | Arg | |
Has-visibility {ℓ} (A : Type ℓ) : Type ℓ where field set-visibility : Visibility → A → A | record | src | [
"open import 1Lab.Path.IdentitySystem",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Bool.Base",
"open import Data.List.Base",
"open import Data.Dec.Base",
"open import Data.Id.Base",
"open import Meta.Traversable",
"open import Meta.Idiom"
] | src/Data/Reflection/Argument.agda | Has-visibility | |
hide : ∀ {ℓ} {A : Type ℓ} → ⦃ Has-visibility A ⦄ → A → A | function | src | [
"open import 1Lab.Path.IdentitySystem",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Bool.Base",
"open import Data.List.Base",
"open import Data.Dec.Base",
"open import Data.Id.Base",
"open import Meta.Traversable",
"open import Meta.Idiom"
] | src/Data/Reflection/Argument.agda | hide | |
hide-if : ∀ {ℓ} {A : Type ℓ} → ⦃ Has-visibility A ⦄ → Bool → A → A | function | src | [
"open import 1Lab.Path.IdentitySystem",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Bool.Base",
"open import Data.List.Base",
"open import Data.Dec.Base",
"open import Data.Id.Base",
"open import Meta.Traversable",
"open import Meta.Idiom"
] | src/Data/Reflection/Argument.agda | hide-if | |
ErrorPart : Type where strErr : String → ErrorPart termErr : Term → ErrorPart pattErr : Pattern → ErrorPart nameErr : Name → ErrorPart {-# BUILTIN AGDAERRORPART ErrorPart #-} {-# BUILTIN AGDAERRORPARTSTRING strErr #-} {-# BUILTIN AGDAERRORPARTTERM termErr #-} {-# BUILTIN AGDAERRORPARTPATT pattErr #-} {-# BUILTIN AGDAER... | data | src | [
"open import 1Lab.Type",
"open import Data.Reflection.Name",
"open import Data.Reflection.Term",
"open import Data.String.Base",
"open import Data.List.Base",
"open import Meta.Append"
] | src/Data/Reflection/Error.agda | ErrorPart | |
Associativity : Type where left-assoc : Associativity right-assoc : Associativity non-assoc : Associativity | data | src | [
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Float.Base",
"open import Data.Dec.Base",
"open import Data.Id.Base"
] | src/Data/Reflection/Fixity.agda | Associativity | |
Precedence : Type where related : Float → Precedence unrelated : Precedence | data | src | [
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Float.Base",
"open import Data.Dec.Base",
"open import Data.Id.Base"
] | src/Data/Reflection/Fixity.agda | Precedence | |
Fixity : Type where fixity : Associativity → Precedence → Fixity {-# BUILTIN ASSOC Associativity #-} {-# BUILTIN ASSOCLEFT left-assoc #-} {-# BUILTIN ASSOCRIGHT right-assoc #-} {-# BUILTIN ASSOCNON non-assoc #-} {-# BUILTIN PRECEDENCE Precedence #-} {-# BUILTIN PRECRELATED related #-} {-# BUILTIN PRECUNRELATED unrelate... | data | src | [
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Float.Base",
"open import Data.Dec.Base",
"open import Data.Id.Base"
] | src/Data/Reflection/Fixity.agda | Fixity | |
suc-precedence : Precedence → Precedence | function | src | [
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Float.Base",
"open import Data.Dec.Base",
"open import Data.Id.Base"
] | src/Data/Reflection/Fixity.agda | suc-precedence | |
prec-parens : Precedence → Precedence → Bool | function | src | [
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Float.Base",
"open import Data.Dec.Base",
"open import Data.Id.Base"
] | src/Data/Reflection/Fixity.agda | prec-parens | |
Literal : Type where nat : (n : Nat) → Literal word64 : (n : Word64) → Literal float : (x : Float) → Literal char : (c : Char) → Literal string : (s : String) → Literal name : (x : Name) → Literal meta : (x : Meta) → Literal {-# BUILTIN AGDALITERAL Literal #-} {-# BUILTIN AGDALITNAT nat #-} {-# BUILTIN AGDALITWORD64 wo... | data | src | [
"open import 1Lab.Path.IdentitySystem",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Reflection.Meta",
"open import Data.Reflection.Name",
"open import Data.String.Base",
"open import Data.Float.Base",
"open import Data.Char.Base",
"open import Data.Word.Base",
"open import ... | src/Data/Reflection/Literal.agda | Literal | |
Blocker : Type where blocker-any : List Blocker → Blocker blocker-all : List Blocker → Blocker blocker-meta : Meta → Blocker {-# BUILTIN AGDABLOCKER Blocker #-} {-# BUILTIN AGDABLOCKERANY blocker-any #-} {-# BUILTIN AGDABLOCKERALL blocker-all #-} {-# BUILTIN AGDABLOCKERMETA blocker-meta #-} | data | src | [
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.String.Base",
"open import Data.String.Show",
"open import Data.Bool.Base",
"open import Data.List.Base",
"open import Data.Dec.Base",
"open import Data.Nat.Base",
"open import Data.Id.Base"
] | src/Data/Reflection/Meta.agda | Blocker | |
Term : Type | data | src | [
"open import 1Lab.Path.IdentitySystem",
"open import 1Lab.Path",
"open import 1Lab.Type hiding (absurd)",
"open import Data.Reflection.Argument",
"open import Data.Reflection.Literal",
"open import Data.Reflection.Meta",
"open import Data.Reflection.Name",
"open import Data.Reflection.Abs",
"open im... | src/Data/Reflection/Term.agda | Term | |
Sort : Type | data | src | [
"open import 1Lab.Path.IdentitySystem",
"open import 1Lab.Path",
"open import 1Lab.Type hiding (absurd)",
"open import Data.Reflection.Argument",
"open import Data.Reflection.Literal",
"open import Data.Reflection.Meta",
"open import Data.Reflection.Name",
"open import Data.Reflection.Abs",
"open im... | src/Data/Reflection/Term.agda | Sort | |
Pattern : Type | data | src | [
"open import 1Lab.Path.IdentitySystem",
"open import 1Lab.Path",
"open import 1Lab.Type hiding (absurd)",
"open import Data.Reflection.Argument",
"open import Data.Reflection.Literal",
"open import Data.Reflection.Meta",
"open import Data.Reflection.Name",
"open import Data.Reflection.Abs",
"open im... | src/Data/Reflection/Term.agda | Pattern | |
Clause : Type Telescope = List (String × Arg Term) | data | src | [
"open import 1Lab.Path.IdentitySystem",
"open import 1Lab.Path",
"open import 1Lab.Type hiding (absurd)",
"open import Data.Reflection.Argument",
"open import Data.Reflection.Literal",
"open import Data.Reflection.Meta",
"open import Data.Reflection.Name",
"open import Data.Reflection.Abs",
"open im... | src/Data/Reflection/Term.agda | Clause | |
Term where var : (x : Nat) (args : List (Arg Term)) → Term con : (c : Name) (args : List (Arg Term)) → Term def : (f : Name) (args : List (Arg Term)) → Term lam : (v : Visibility) (t : Abs Term) → Term pat-lam : (cs : List Clause) (args : List (Arg Term)) → Term pi : (a : Arg Term) (b : Abs Term) → Term agda-sort : (s ... | data | src | [
"open import 1Lab.Path.IdentitySystem",
"open import 1Lab.Path",
"open import 1Lab.Type hiding (absurd)",
"open import Data.Reflection.Argument",
"open import Data.Reflection.Literal",
"open import Data.Reflection.Meta",
"open import Data.Reflection.Name",
"open import Data.Reflection.Abs",
"open im... | src/Data/Reflection/Term.agda | Term | |
Sort where set : (t : Term) → Sort lit : (n : Nat) → Sort prop : (t : Term) → Sort propLit : (n : Nat) → Sort inf : (n : Nat) → Sort unknown : Sort | data | src | [
"open import 1Lab.Path.IdentitySystem",
"open import 1Lab.Path",
"open import 1Lab.Type hiding (absurd)",
"open import Data.Reflection.Argument",
"open import Data.Reflection.Literal",
"open import Data.Reflection.Meta",
"open import Data.Reflection.Name",
"open import Data.Reflection.Abs",
"open im... | src/Data/Reflection/Term.agda | Sort | |
Pattern where con : (c : Name) (ps : List (Arg Pattern)) → Pattern dot : (t : Term) → Pattern var : (x : Nat) → Pattern lit : (l : Literal) → Pattern proj : (f : Name) → Pattern absurd : (x : Nat) → Pattern -- absurd patterns count as variables | data | src | [
"open import 1Lab.Path.IdentitySystem",
"open import 1Lab.Path",
"open import 1Lab.Type hiding (absurd)",
"open import Data.Reflection.Argument",
"open import Data.Reflection.Literal",
"open import Data.Reflection.Meta",
"open import Data.Reflection.Name",
"open import Data.Reflection.Abs",
"open im... | src/Data/Reflection/Term.agda | Pattern | |
Clause where clause : (tel : Telescope) (ps : List (Arg Pattern)) (t : Term) → Clause absurd-clause : (tel : Telescope) (ps : List (Arg Pattern)) → Clause {-# BUILTIN AGDATERM Term #-} {-# BUILTIN AGDASORT Sort #-} {-# BUILTIN AGDAPATTERN Pattern #-} {-# BUILTIN AGDACLAUSE Clause #-} {-# BUILTIN AGDATERMVAR var #-} {-#... | data | src | [
"open import 1Lab.Path.IdentitySystem",
"open import 1Lab.Path",
"open import 1Lab.Type hiding (absurd)",
"open import Data.Reflection.Argument",
"open import Data.Reflection.Literal",
"open import Data.Reflection.Meta",
"open import Data.Reflection.Name",
"open import Data.Reflection.Abs",
"open im... | src/Data/Reflection/Term.agda | Clause | |
Definition : Type where function : (cs : List Clause) → Definition data-type : (pars : Nat) (cs : List Name) → Definition record-type : (c : Name) (fs : List (Arg Name)) → Definition data-cons : (d : Name) (q : Quantity) → Definition axiom : Definition prim-fun : Definition {-# BUILTIN AGDADEFINITION Definition #-} {-#... | data | src | [
"open import 1Lab.Path.IdentitySystem",
"open import 1Lab.Path",
"open import 1Lab.Type hiding (absurd)",
"open import Data.Reflection.Argument",
"open import Data.Reflection.Literal",
"open import Data.Reflection.Meta",
"open import Data.Reflection.Name",
"open import Data.Reflection.Abs",
"open im... | src/Data/Reflection/Term.agda | Definition | |
Has-neutrals {ℓ} (A : Type ℓ) : Type (lsuc ℓ) where field neutral : A → Type ℓ applyⁿᵉ : (d : A) ⦃ _ : neutral d ⦄ (arg : List (Arg A)) → A | record | src | [
"open import 1Lab.Path.IdentitySystem",
"open import 1Lab.Path",
"open import 1Lab.Type hiding (absurd)",
"open import Data.Reflection.Argument",
"open import Data.Reflection.Literal",
"open import Data.Reflection.Meta",
"open import Data.Reflection.Name",
"open import Data.Reflection.Abs",
"open im... | src/Data/Reflection/Term.agda | Has-neutrals | |
pi-view : Term → Telescope × Term | function | src | [
"open import 1Lab.Path.IdentitySystem",
"open import 1Lab.Path",
"open import 1Lab.Type hiding (absurd)",
"open import Data.Reflection.Argument",
"open import Data.Reflection.Literal",
"open import Data.Reflection.Meta",
"open import Data.Reflection.Name",
"open import Data.Reflection.Abs",
"open im... | src/Data/Reflection/Term.agda | pi-view | |
pi-impl-view : Term → Telescope × Term | function | src | [
"open import 1Lab.Path.IdentitySystem",
"open import 1Lab.Path",
"open import 1Lab.Type hiding (absurd)",
"open import Data.Reflection.Argument",
"open import Data.Reflection.Literal",
"open import Data.Reflection.Meta",
"open import Data.Reflection.Name",
"open import Data.Reflection.Abs",
"open im... | src/Data/Reflection/Term.agda | pi-impl-view | |
unpi-view : Telescope → Term → Term | function | src | [
"open import 1Lab.Path.IdentitySystem",
"open import 1Lab.Path",
"open import 1Lab.Type hiding (absurd)",
"open import Data.Reflection.Argument",
"open import Data.Reflection.Literal",
"open import Data.Reflection.Meta",
"open import Data.Reflection.Name",
"open import Data.Reflection.Abs",
"open im... | src/Data/Reflection/Term.agda | unpi-view | |
Example : tel→args (a : {b : {c : C} → B} → A) = (λ {b} → a {λ {c} → b {c}}) | function | src | [
"open import 1Lab.Path.IdentitySystem",
"open import 1Lab.Path",
"open import 1Lab.Type hiding (absurd)",
"open import Data.Reflection.Argument",
"open import Data.Reflection.Literal",
"open import Data.Reflection.Meta",
"open import Data.Reflection.Name",
"open import Data.Reflection.Abs",
"open im... | src/Data/Reflection/Term.agda | Example | |
list-term : List Term → Term | function | src | [
"open import 1Lab.Path.IdentitySystem",
"open import 1Lab.Path",
"open import 1Lab.Type hiding (absurd)",
"open import Data.Reflection.Argument",
"open import Data.Reflection.Literal",
"open import Data.Reflection.Meta",
"open import Data.Reflection.Name",
"open import Data.Reflection.Abs",
"open im... | src/Data/Reflection/Term.agda | list-term | |
list-pattern : List (Arg Pattern) → Pattern | function | src | [
"open import 1Lab.Path.IdentitySystem",
"open import 1Lab.Path",
"open import 1Lab.Type hiding (absurd)",
"open import Data.Reflection.Argument",
"open import Data.Reflection.Literal",
"open import Data.Reflection.Meta",
"open import Data.Reflection.Name",
"open import Data.Reflection.Abs",
"open im... | src/Data/Reflection/Term.agda | list-pattern | |
https : //github.com/agda/agda/graphs/contributors or from the git | function | support | [] | support/shake/LICENSE.agda | https | |
_ : ∀ {ℓ} {A B : Type ℓ} → is-equiv (path→equiv {A = A} {B}) | function | src | [
"open import 1Lab.Univalence",
"open import 1Lab.Equiv",
"open import 1Lab.HLevel",
"open import 1Lab.Type",
"open import 1Lab.Path",
"open import Cat.Base",
"open import 1Lab.Type -- Basics of type universes",
"open import 1Lab.Path -- The key idea in cubical type theory",
"open impor... | src/index.lagda.md | _ | |
structure : a [[**bicategory**]]. | function | src | [
"open import 1Lab.Univalence",
"open import 1Lab.Equiv",
"open import 1Lab.HLevel",
"open import 1Lab.Type",
"open import 1Lab.Path",
"open import Cat.Base",
"open import 1Lab.Type -- Basics of type universes",
"open import 1Lab.Path -- The key idea in cubical type theory",
"open impor... | src/index.lagda.md | structure | |
geometry : [[frames]] and [[lattices]]. | function | src | [
"open import 1Lab.Univalence",
"open import 1Lab.Equiv",
"open import 1Lab.HLevel",
"open import 1Lab.Type",
"open import 1Lab.Path",
"open import Cat.Base",
"open import 1Lab.Type -- Basics of type universes",
"open import 1Lab.Path -- The key idea in cubical type theory",
"open impor... | src/index.lagda.md | geometry | |
LEM : Type | function | src | [
"open import 1Lab.Prelude",
"open import Data.Bool",
"open import Data.Dec",
"open import Data.Sum",
"open import Homotopy.Space.Suspension.Properties",
"open import Homotopy.Space.Suspension",
"open import Meta.Invariant"
] | src/1Lab/Classical.lagda.md | LEM | |
DNE : Type | function | src | [
"open import 1Lab.Prelude",
"open import Data.Bool",
"open import Data.Dec",
"open import Data.Sum",
"open import Homotopy.Space.Suspension.Properties",
"open import Homotopy.Space.Suspension",
"open import Meta.Invariant"
] | src/1Lab/Classical.lagda.md | DNE | |
LEM-is-prop : is-prop LEM | function | src | [
"open import 1Lab.Prelude",
"open import Data.Bool",
"open import Data.Dec",
"open import Data.Sum",
"open import Homotopy.Space.Suspension.Properties",
"open import Homotopy.Space.Suspension",
"open import Meta.Invariant"
] | src/1Lab/Classical.lagda.md | LEM-is-prop | |
DNE-is-prop : is-prop DNE | function | src | [
"open import 1Lab.Prelude",
"open import Data.Bool",
"open import Data.Dec",
"open import Data.Sum",
"open import Homotopy.Space.Suspension.Properties",
"open import Homotopy.Space.Suspension",
"open import Meta.Invariant"
] | src/1Lab/Classical.lagda.md | DNE-is-prop | |
WLEM : Type | function | src | [
"open import 1Lab.Prelude",
"open import Data.Bool",
"open import Data.Dec",
"open import Data.Sum",
"open import Homotopy.Space.Suspension.Properties",
"open import Homotopy.Space.Suspension",
"open import Meta.Invariant"
] | src/1Lab/Classical.lagda.md | WLEM | |
WLEM-is-prop : is-prop WLEM | function | src | [
"open import 1Lab.Prelude",
"open import Data.Bool",
"open import Data.Dec",
"open import Data.Sum",
"open import Homotopy.Space.Suspension.Properties",
"open import Homotopy.Space.Suspension",
"open import Meta.Invariant"
] | src/1Lab/Classical.lagda.md | WLEM-is-prop | |
Axiom-of-choice : Typeω | function | src | [
"open import 1Lab.Prelude",
"open import Data.Bool",
"open import Data.Dec",
"open import Data.Sum",
"open import Homotopy.Space.Suspension.Properties",
"open import Homotopy.Space.Suspension",
"open import Meta.Invariant"
] | src/1Lab/Classical.lagda.md | Axiom-of-choice | |
Surjections-split : Typeω | function | src | [
"open import 1Lab.Prelude",
"open import Data.Bool",
"open import Data.Dec",
"open import Data.Sum",
"open import Homotopy.Space.Suspension.Properties",
"open import Homotopy.Space.Suspension",
"open import Meta.Invariant"
] | src/1Lab/Classical.lagda.md | Surjections-split | |
is-iso (f : A → B) : Type (level-of A ⊔ level-of B) where no-eta-equality constructor iso field from : B → A rinv : is-right-inverse from f linv : is-left-inverse from f ``` It's immediate from the symmetry of the definition that if $g$ is a two-sided inverse to $f$, then $f$ also inverts $g$: an isomorphism's inverse ... | record | src | [
"open import 1Lab.Path.Reasoning",
"open import 1Lab.Path.Groupoid",
"open import 1Lab.HLevel",
"open import 1Lab.Path",
"open import 1Lab.Type"
] | src/1Lab/Equiv.lagda.md | is-iso | |
is-equiv (f : A → B) : Type (level-of A ⊔ level-of B) where no-eta-equality field is-eqv : (y : B) → is-contr (fibre f y) ``` <!-- ```agda {-# INLINE is-equiv.constructor #-} | record | src | [
"open import 1Lab.Path.Reasoning",
"open import 1Lab.Path.Groupoid",
"open import 1Lab.HLevel",
"open import 1Lab.Path",
"open import 1Lab.Type"
] | src/1Lab/Equiv.lagda.md | is-equiv | |
type , the proof that this is an equivalence looks very similar to the proof that the identity function is an equivalence: ```agda Lift-≃ : ∀ {a ℓ} {A : Type a} → Lift ℓ A ≃ A Lift-≃ .fst (lift a) = a Lift-≃ .snd .is-eqv a .centre = lift a , refl Lift-≃ .snd .is-eqv a .paths (x , p) i .fst = lift (p (~ i)) Lift-≃ .snd ... | record | src | [
"open import 1Lab.Path.Reasoning",
"open import 1Lab.Path.Groupoid",
"open import 1Lab.HLevel",
"open import 1Lab.Path",
"open import 1Lab.Type"
] | src/1Lab/Equiv.lagda.md | type | |
is-left-inverse : (B → A) → (A → B) → Type _ | function | src | [
"open import 1Lab.Path.Reasoning",
"open import 1Lab.Path.Groupoid",
"open import 1Lab.HLevel",
"open import 1Lab.Path",
"open import 1Lab.Type"
] | src/1Lab/Equiv.lagda.md | is-left-inverse | |
is-right-inverse : (B → A) → (A → B) → Type _ | function | src | [
"open import 1Lab.Path.Reasoning",
"open import 1Lab.Path.Groupoid",
"open import 1Lab.HLevel",
"open import 1Lab.Path",
"open import 1Lab.Type"
] | src/1Lab/Equiv.lagda.md | is-right-inverse | |
Iso : ∀ {ℓ₁ ℓ₂} → Type ℓ₁ → Type ℓ₂ → Type _ | function | src | [
"open import 1Lab.Path.Reasoning",
"open import 1Lab.Path.Groupoid",
"open import 1Lab.HLevel",
"open import 1Lab.Path",
"open import 1Lab.Type"
] | src/1Lab/Equiv.lagda.md | Iso | |
fibre : (A → B) → B → Type _ | function | src | [
"open import 1Lab.Path.Reasoning",
"open import 1Lab.Path.Groupoid",
"open import 1Lab.HLevel",
"open import 1Lab.Path",
"open import 1Lab.Type"
] | src/1Lab/Equiv.lagda.md | fibre | |
theory : [[contractibility|contractible]]. This is exactly the | function | src | [
"open import 1Lab.Path.Reasoning",
"open import 1Lab.Path.Groupoid",
"open import 1Lab.HLevel",
"open import 1Lab.Path",
"open import 1Lab.Type"
] | src/1Lab/Equiv.lagda.md | theory | |
id-equiv : is-equiv {A = A} id | function | src | [
"open import 1Lab.Path.Reasoning",
"open import 1Lab.Path.Groupoid",
"open import 1Lab.HLevel",
"open import 1Lab.Path",
"open import 1Lab.Type"
] | src/1Lab/Equiv.lagda.md | id-equiv | |
equiv-centre : (e : A ≃ B) (y : B) → fibre (e .fst) y | function | src | [
"open import 1Lab.Path.Reasoning",
"open import 1Lab.Path.Groupoid",
"open import 1Lab.HLevel",
"open import 1Lab.Path",
"open import 1Lab.Type"
] | src/1Lab/Equiv.lagda.md | equiv-centre | |
is-equiv-is-prop : (f : A → B) → is-prop (is-equiv f) | function | src | [
"open import 1Lab.Path.Reasoning",
"open import 1Lab.Path.Groupoid",
"open import 1Lab.HLevel",
"open import 1Lab.Path",
"open import 1Lab.Type"
] | src/1Lab/Equiv.lagda.md | is-equiv-is-prop | |
inverse-is-equiv : {f : A → B} (eqv : is-equiv f) → is-equiv (equiv→inverse eqv) | function | src | [
"open import 1Lab.Path.Reasoning",
"open import 1Lab.Path.Groupoid",
"open import 1Lab.HLevel",
"open import 1Lab.Path",
"open import 1Lab.Type"
] | src/1Lab/Equiv.lagda.md | inverse-is-equiv | |
sym-equiv : ∀ {ℓ} {A : Type ℓ} {x y : A} → (x ≡ y) ≃ (y ≡ x) | function | src | [
"open import 1Lab.Path.Reasoning",
"open import 1Lab.Path.Groupoid",
"open import 1Lab.HLevel",
"open import 1Lab.Path",
"open import 1Lab.Type"
] | src/1Lab/Equiv.lagda.md | sym-equiv | |
_ : ∘-closed is-equiv | function | src | [
"open import 1Lab.Path.Reasoning",
"open import 1Lab.Path.Groupoid",
"open import 1Lab.HLevel",
"open import 1Lab.Path",
"open import 1Lab.Type"
] | src/1Lab/Equiv.lagda.md | _ | |
is-contr {ℓ} (A : Type ℓ) : Type ℓ where constructor contr field centre : A paths : (x : A) → centre ≡ x | record | src | [
"open import 1Lab.Path",
"open import 1Lab.Type"
] | src/1Lab/HLevel.lagda.md | is-contr | |
is-prop : ∀ {ℓ} → Type ℓ → Type ℓ | function | src | [
"open import 1Lab.Path",
"open import 1Lab.Type"
] | src/1Lab/HLevel.lagda.md | is-prop | |
subst-prop : ∀ {ℓ ℓ'} {A : Type ℓ} {P : A → Type ℓ'} → is-prop A → ∀ a → P a → ∀ b → P b | function | src | [
"open import 1Lab.Path",
"open import 1Lab.Type"
] | src/1Lab/HLevel.lagda.md | subst-prop | |
is-set : ∀ {ℓ} → Type ℓ → Type ℓ | function | src | [
"open import 1Lab.Path",
"open import 1Lab.Type"
] | src/1Lab/HLevel.lagda.md | is-set | |
is-hlevel : ∀ {ℓ} → Type ℓ → Nat → Type _ | function | src | [
"open import 1Lab.Path",
"open import 1Lab.Type"
] | src/1Lab/HLevel.lagda.md | is-hlevel |
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