Proof Assistant Projects
Collection
Digesting proof assistant libraries for AI ingestion. • 84 items • Updated • 3
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 |
|---|---|---|---|---|---|---|
Extensional (A : Type ℓ) ℓ-rel : Type (ℓ ⊔ lsuc ℓ-rel) where no-eta-equality field Pathᵉ : A → A → Type ℓ-rel reflᵉ : ∀ x → Pathᵉ x x idsᵉ : is-identity-system Pathᵉ reflᵉ {-# INLINE Extensional.constructor #-} | record | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Path.IdentitySystem",
"open import 1Lab.Function.Embedding",
"open import 1Lab.Reflection.HLevel",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.HLevel.Closure",
"open import 1Lab.Reflection",
"open import 1Lab.Truncation",
"open im... | src/1Lab/Extensionality.agda | Extensional | |
proposition : any pair of identity systems is connected by an equivalence | function | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Path.IdentitySystem",
"open import 1Lab.Function.Embedding",
"open import 1Lab.Reflection.HLevel",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.HLevel.Closure",
"open import 1Lab.Reflection",
"open import 1Lab.Truncation",
"open im... | src/1Lab/Extensionality.agda | proposition | |
points : - ext: turn extensional equality into equality | function | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Path.IdentitySystem",
"open import 1Lab.Function.Embedding",
"open import 1Lab.Reflection.HLevel",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.HLevel.Closure",
"open import 1Lab.Reflection",
"open import 1Lab.Truncation",
"open im... | src/1Lab/Extensionality.agda | points | |
Inductive {ℓ} (A : Type ℓ) ℓm : Type (ℓ ⊔ lsuc ℓm) where field methods : Type ℓm from : methods → A | record | src | [
"open import 1Lab.Reflection",
"open import 1Lab.Univalence",
"open import 1Lab.Equiv",
"open import 1Lab.Type hiding (case_of_ ; case_return_of_)",
"open import 1Lab.Path"
] | src/1Lab/Inductive.agda | Inductive | |
case_of_ : ∀ {ℓ ℓ'} {A : Type ℓ} {B : Type ℓ'} ⦃ r : Inductive (A → B) ℓm ⦄ → A → r .methods → B | function | src | [
"open import 1Lab.Reflection",
"open import 1Lab.Univalence",
"open import 1Lab.Equiv",
"open import 1Lab.Type hiding (case_of_ ; case_return_of_)",
"open import 1Lab.Path"
] | src/1Lab/Inductive.agda | case_of_ | |
case_return_of_ : ∀ {ℓ ℓ'} {A : Type ℓ} (x : A) (B : A → Type ℓ') ⦃ r : Inductive (∀ x → B x) ℓm ⦄ (f : r .methods) → B x | function | src | [
"open import 1Lab.Reflection",
"open import 1Lab.Univalence",
"open import 1Lab.Equiv",
"open import 1Lab.Type hiding (case_of_ ; case_return_of_)",
"open import 1Lab.Path"
] | src/1Lab/Inductive.agda | case_return_of_ | |
Membership {ℓ ℓe} (A : Type ℓe) (ℙA : Type ℓ) ℓm : Type (ℓ ⊔ ℓe ⊔ lsuc ℓm) where field _∈_ : A → ℙA → Type ℓm infix 30 _∈_ | record | src | [
"open import 1Lab.Underlying",
"open import 1Lab.Type hiding (Σ-syntax)"
] | src/1Lab/Membership.agda | Membership | |
Inclusion {ℓ} (ℙA : Type ℓ) ℓi : Type (ℓ ⊔ lsuc (ℓi)) where field _⊆_ : ℙA → ℙA → Type ℓi infix 30 _⊆_ | record | src | [
"open import 1Lab.Underlying",
"open import 1Lab.Type hiding (Σ-syntax)"
] | src/1Lab/Membership.agda | Inclusion | |
Underlying {ℓ} (T : Type ℓ) : Typeω where field ℓ-underlying : Level ⌞_⌟ : T → Type ℓ-underlying | record | src | [
"open import 1Lab.HLevel.Universe",
"open import 1Lab.HLevel.Closure",
"open import 1Lab.Truncation hiding (∃-syntax)",
"open import 1Lab.Resizing",
"open import 1Lab.HLevel",
"open import 1Lab.Path",
"open import 1Lab.Type hiding (Σ-syntax)",
"open import Data.Bool.Base"
] | src/1Lab/Underlying.agda | Underlying | |
Funlike {ℓ ℓ' ℓ''} (A : Type ℓ) (arg : Type ℓ') (out : arg → Type ℓ'') : Type (ℓ ⊔ ℓ' ⊔ ℓ'') where field _·_ : A → (x : arg) → out x infixl 999 _·_ | record | src | [
"open import 1Lab.HLevel.Universe",
"open import 1Lab.HLevel.Closure",
"open import 1Lab.Truncation hiding (∃-syntax)",
"open import 1Lab.Resizing",
"open import 1Lab.HLevel",
"open import 1Lab.Path",
"open import 1Lab.Type hiding (Σ-syntax)",
"open import Data.Bool.Base"
] | src/1Lab/Underlying.agda | Funlike | |
make-copattern : Bool → Name → Term → Term → TC ⊤ | function | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Reflection",
"open import 1Lab.Path",
"open import 1Lab.Type"
] | src/1Lab/Reflection/Copattern.agda | make-copattern | |
repack-record : Term → Term → TC Term | function | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Reflection",
"open import 1Lab.Path",
"open import 1Lab.Type"
] | src/1Lab/Reflection/Copattern.agda | repack-record | |
type-for : String → Bool → Name → Term → TC ⊤ | function | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Reflection",
"open import 1Lab.Path",
"open import 1Lab.Type"
] | src/1Lab/Reflection/Copattern.agda | type-for | |
declare-copattern : ∀ {ℓ} {A : Type ℓ} → Name → A → TC ⊤ | function | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Reflection",
"open import 1Lab.Path",
"open import 1Lab.Type"
] | src/1Lab/Reflection/Copattern.agda | declare-copattern | |
declare-copatternω : ∀ {U : Typeω} → Name → U → TC ⊤ | function | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Reflection",
"open import 1Lab.Path",
"open import 1Lab.Type"
] | src/1Lab/Reflection/Copattern.agda | declare-copatternω | |
define-eta-expansion : Name → TC ⊤ | function | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Reflection",
"open import 1Lab.Path",
"open import 1Lab.Type"
] | src/1Lab/Reflection/Copattern.agda | define-eta-expansion | |
hlevel-projection (proj : Name) : Type where field has-level : Name -- ^ The name of the h-level lemma. It must be sufficient to apply -- this to the "relevant" argument, see 'get-argument' below. In -- practice, this means that has-level lemmas take a single, visible -- argument. get-argument : List (Arg Term) → TC Te... | record | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Function.Embedding",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Equiv.Fibrewise",
"open import 1Lab.HLevel.Universe",
"open import 1Lab.HLevel.Closure",
"open import 1Lab.Reflection",
"open import 1Lab.Type.Sigma",
"open import 1... | src/1Lab/Reflection/HLevel.agda | hlevel-projection | |
is-hlevel-le : ∀ {ℓ} {A : Type ℓ} n k → n ≤ k → is-hlevel A n → is-hlevel A k | function | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Function.Embedding",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Equiv.Fibrewise",
"open import 1Lab.HLevel.Universe",
"open import 1Lab.HLevel.Closure",
"open import 1Lab.Reflection",
"open import 1Lab.Type.Sigma",
"open import 1... | src/1Lab/Reflection/HLevel.agda | is-hlevel-le | |
hlevel-proj : ∀ {ℓ} → Type ℓ → Nat → Term → TC ⊤ | function | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Function.Embedding",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Equiv.Fibrewise",
"open import 1Lab.HLevel.Universe",
"open import 1Lab.HLevel.Closure",
"open import 1Lab.Reflection",
"open import 1Lab.Type.Sigma",
"open import 1... | src/1Lab/Reflection/HLevel.agda | hlevel-proj | |
Elim-options : Type where field -- Whether to generate an induction principle or a recursion principle. -- (P : D → Type ℓ) vs (P : Type ℓ) induction : Bool -- If `just n`, assume the motive has hlevel n and omit methods accordingly. into-hlevel : Maybe Nat -- Hide the motive argument in the eliminator's type? -- (P : ... | record | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Reflection",
"open import 1Lab.Type.Sigma",
"open import 1Lab.Type.Pi",
"open import 1Lab.HLevel",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Nat.Base",
"open import Meta.Append... | src/1Lab/Reflection/Induction.agda | Elim-options | |
pi-view-path : Term → Telescope | function | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Reflection",
"open import 1Lab.Type.Sigma",
"open import 1Lab.Type.Pi",
"open import 1Lab.HLevel",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Nat.Base",
"open import Meta.Append... | src/1Lab/Reflection/Induction.agda | pi-view-path | |
subst-replacements : Subst → Replacements → Replacements | function | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Reflection",
"open import 1Lab.Type.Sigma",
"open import 1Lab.Type.Pi",
"open import 1Lab.HLevel",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Nat.Base",
"open import Meta.Append... | src/1Lab/Reflection/Induction.agda | subst-replacements | |
make-elim-with : Elim-options → Name → Name → TC ⊤ | function | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Reflection",
"open import 1Lab.Type.Sigma",
"open import 1Lab.Type.Pi",
"open import 1Lab.HLevel",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Nat.Base",
"open import Meta.Append... | src/1Lab/Reflection/Induction.agda | make-elim-with | |
_into_ : Elim-options → Nat → Elim-options | function | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Reflection",
"open import 1Lab.Type.Sigma",
"open import 1Lab.Type.Pi",
"open import 1Lab.HLevel",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Nat.Base",
"open import Meta.Append... | src/1Lab/Reflection/Induction.agda | _into_ | |
abstract-marker : Term → Maybe Term | function | src | [
"open import 1Lab.Reflection",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Maybe.Base",
"open import Prim.Data.Nat"
] | src/1Lab/Reflection/Marker.agda | abstract-marker | |
type whose components can all immediately be seen to have h-level n. That is, this works for things like Cat.Morphism._↪_, since the H-Level automation already works for showing that its representation as a Σ-type has hlevel 2, but it does not work for Algebra.Group.is-group, since that requires specific knowledge abou... | record | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection.HLevel",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.HLevel.Closure",
"open import 1Lab.Reflection",
"open import 1Lab.Equiv",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Nat.Base",
"open impor... | src/1Lab/Reflection/Record.agda | type | |
Fields : Type | function | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection.HLevel",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.HLevel.Closure",
"open import 1Lab.Reflection",
"open import 1Lab.Equiv",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Nat.Base",
"open impor... | src/1Lab/Reflection/Record.agda | Fields | |
undo-clause : Name × List Name → Clause | function | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection.HLevel",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.HLevel.Closure",
"open import 1Lab.Reflection",
"open import 1Lab.Equiv",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Nat.Base",
"open impor... | src/1Lab/Reflection/Record.agda | undo-clause | |
redo-clause : Name × List Name → Clause | function | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection.HLevel",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.HLevel.Closure",
"open import 1Lab.Reflection",
"open import 1Lab.Equiv",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Nat.Base",
"open impor... | src/1Lab/Reflection/Record.agda | redo-clause | |
undo-redo-clause : Name × List Name → Clause | function | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection.HLevel",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.HLevel.Closure",
"open import 1Lab.Reflection",
"open import 1Lab.Equiv",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Nat.Base",
"open impor... | src/1Lab/Reflection/Record.agda | undo-redo-clause | |
redo-undo-clause : Name × List Name → Clause | function | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection.HLevel",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.HLevel.Closure",
"open import 1Lab.Reflection",
"open import 1Lab.Equiv",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Nat.Base",
"open impor... | src/1Lab/Reflection/Record.agda | redo-undo-clause | |
instantiate' : Term → Term → Term | function | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection.HLevel",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.HLevel.Closure",
"open import 1Lab.Reflection",
"open import 1Lab.Equiv",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Nat.Base",
"open impor... | src/1Lab/Reflection/Record.agda | instantiate' | |
Σ-pathpⁿ : List Term → Term | function | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection.HLevel",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.HLevel.Closure",
"open import 1Lab.Reflection",
"open import 1Lab.Equiv",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Nat.Base",
"open impor... | src/1Lab/Reflection/Record.agda | Σ-pathpⁿ | |
make-record-iso-sigma : Bool → Name → Name → TC ⊤ | function | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection.HLevel",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.HLevel.Closure",
"open import 1Lab.Reflection",
"open import 1Lab.Equiv",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Nat.Base",
"open impor... | src/1Lab/Reflection/Record.agda | make-record-iso-sigma | |
Usage : slap | function | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection.HLevel",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.HLevel.Closure",
"open import 1Lab.Reflection",
"open import 1Lab.Equiv",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Nat.Base",
"open impor... | src/1Lab/Reflection/Record.agda | Usage | |
declare-record-iso : Name → Name → TC ⊤ | function | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection.HLevel",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.HLevel.Closure",
"open import 1Lab.Reflection",
"open import 1Lab.Equiv",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Nat.Base",
"open impor... | src/1Lab/Reflection/Record.agda | declare-record-iso | |
define-record-iso : Name → Name → TC ⊤ | function | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection.HLevel",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.HLevel.Closure",
"open import 1Lab.Reflection",
"open import 1Lab.Equiv",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Nat.Base",
"open impor... | src/1Lab/Reflection/Record.agda | define-record-iso | |
make-record-path : Bool → Name → Name → TC ⊤ | function | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection.HLevel",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.HLevel.Closure",
"open import 1Lab.Reflection",
"open import 1Lab.Equiv",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Nat.Base",
"open impor... | src/1Lab/Reflection/Record.agda | make-record-path | |
declare-record-path : Name → Name → TC ⊤ | function | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection.HLevel",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.HLevel.Closure",
"open import 1Lab.Reflection",
"open import 1Lab.Equiv",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Nat.Base",
"open impor... | src/1Lab/Reflection/Record.agda | declare-record-path | |
define-record-path : Name → Name → TC ⊤ | function | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection.HLevel",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.HLevel.Closure",
"open import 1Lab.Reflection",
"open import 1Lab.Equiv",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Nat.Base",
"open impor... | src/1Lab/Reflection/Record.agda | define-record-path | |
declare-record-hlevel : (n : Nat) → Name → Name → TC ⊤ | function | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection.HLevel",
"open import 1Lab.Reflection.Subst",
"open import 1Lab.HLevel.Closure",
"open import 1Lab.Reflection",
"open import 1Lab.Equiv",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.Nat.Base",
"open impor... | src/1Lab/Reflection/Record.agda | declare-record-hlevel | |
Constructor : Type where constructor conhead field -- Name of the constructor itself: con-name : Name -- Name of the data type: con-data : Name -- Quantity of the constructor. con-quantity : Quantity -- Argument telescope for the constructor, with the datatype's -- parameters removed. con-arguments : Telescope -- Retur... | record | src | [
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Reflection",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.String.Show",
"open import Meta.Foldable",
"open import Meta.Append"
] | src/1Lab/Reflection/Signature.agda | Constructor | |
Has-constr {ℓ} (A : Type ℓ) : Type ℓ where field from-constr : Name → A | record | src | [
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Reflection",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.String.Show",
"open import Meta.Foldable",
"open import Meta.Append"
] | src/1Lab/Reflection/Signature.agda | Has-constr | |
Has-def {ℓ} (A : Type ℓ) : Type ℓ where field from-def : Name → A instance Has-constr-Pattern : Has-constr Pattern Has-constr-Pattern = record { from-constr = con₀ } Has-constr-Term : Has-constr Term Has-constr-Term = record { from-constr = con₀ } Has-def-Term : Has-def Term Has-def-Term = record { from-def = def₀ } Ha... | record | src | [
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Reflection",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.String.Show",
"open import Meta.Foldable",
"open import Meta.Append"
] | src/1Lab/Reflection/Signature.agda | Has-def | |
get-data-type : Name → TC (Nat × List Name) | function | src | [
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Reflection",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.String.Show",
"open import Meta.Foldable",
"open import Meta.Append"
] | src/1Lab/Reflection/Signature.agda | get-data-type | |
get-record-type : Name → TC (Name × List (Arg Name)) | function | src | [
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Reflection",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.String.Show",
"open import Meta.Foldable",
"open import Meta.Append"
] | src/1Lab/Reflection/Signature.agda | get-record-type | |
get-con-quantity : Name → TC Quantity | function | src | [
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Reflection",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.String.Show",
"open import Meta.Foldable",
"open import Meta.Append"
] | src/1Lab/Reflection/Signature.agda | get-con-quantity | |
get-type-constructors : Name → TC (List Constructor) | function | src | [
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Reflection",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.String.Show",
"open import Meta.Foldable",
"open import Meta.Append"
] | src/1Lab/Reflection/Signature.agda | get-type-constructors | |
get-constructor : Name → TC Constructor | function | src | [
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Reflection",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.String.Show",
"open import Meta.Foldable",
"open import Meta.Append"
] | src/1Lab/Reflection/Signature.agda | get-constructor | |
get-record : Term → TC (Name × List (Arg Name)) | function | src | [
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Reflection",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.String.Show",
"open import Meta.Foldable",
"open import Meta.Append"
] | src/1Lab/Reflection/Signature.agda | get-record | |
get-argument-tele : Name → TC Telescope | function | src | [
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Reflection",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.String.Show",
"open import Meta.Foldable",
"open import Meta.Append"
] | src/1Lab/Reflection/Signature.agda | get-argument-tele | |
_ : Path Term (it Σ) (def (quote Σ) []) | function | src | [
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Reflection",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.String.Show",
"open import Meta.Foldable",
"open import Meta.Append"
] | src/1Lab/Reflection/Signature.agda | _ | |
_ : Path Term (`constructor Σ) (con₀ (quote _,_)) | function | src | [
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Reflection",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.String.Show",
"open import Meta.Foldable",
"open import Meta.Append"
] | src/1Lab/Reflection/Signature.agda | _ | |
_ : Path (Term → Term → Term) (itₙ Σ) (λ x y → def (quote Σ) (argN x ∷ argN y ∷ [])) | function | src | [
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Reflection",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.String.Show",
"open import Meta.Foldable",
"open import Meta.Append"
] | src/1Lab/Reflection/Signature.agda | _ | |
is-defined : Name → TC Bool | function | src | [
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Reflection",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.String.Show",
"open import Meta.Foldable",
"open import Meta.Append"
] | src/1Lab/Reflection/Signature.agda | is-defined | |
render-name : Name → TC String | function | src | [
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Reflection",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.String.Show",
"open import Meta.Foldable",
"open import Meta.Append"
] | src/1Lab/Reflection/Signature.agda | render-name | |
helper-function-name : Name → String → TC Name | function | src | [
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Reflection",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.String.Show",
"open import Meta.Foldable",
"open import Meta.Append"
] | src/1Lab/Reflection/Signature.agda | helper-function-name | |
helper-function : Name → String → Term → List Clause → TC Name | function | src | [
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Reflection",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.String.Show",
"open import Meta.Foldable",
"open import Meta.Append"
] | src/1Lab/Reflection/Signature.agda | helper-function | |
define-abbrev : Name → String → Term → Term → TC Term | function | src | [
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Reflection",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.String.Show",
"open import Meta.Foldable",
"open import Meta.Append"
] | src/1Lab/Reflection/Signature.agda | define-abbrev | |
instance-telescope : (Arg Term → Term) → Name → TC (Telescope × List (Arg Term)) | function | src | [
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Reflection",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.String.Show",
"open import Meta.Foldable",
"open import Meta.Append"
] | src/1Lab/Reflection/Signature.agda | instance-telescope | |
instance-type : (Arg Term → Term) → Name → TC Term | function | src | [
"open import 1Lab.Reflection.Subst",
"open import 1Lab.Reflection",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.String.Show",
"open import Meta.Foldable",
"open import Meta.Append"
] | src/1Lab/Reflection/Signature.agda | instance-type | |
SimpleSolver : Type where constructor simple-solver field dont-reduce : List Name build-expr : Term → TC Term invoke-solver : Term → Term → Term invoke-normaliser : Term → Term | record | src | [
"open import 1Lab.Prelude",
"open import 1Lab.Reflection",
"open import 1Lab.Reflection.Variables",
"open import Data.List.Base"
] | src/1Lab/Reflection/Solver.agda | SimpleSolver | |
VariableSolver {ℓ} (A : Type ℓ) : Type ℓ where constructor var-solver field dont-reduce : List Name build-expr : Variables A → Term → TC (Term × Variables A) invoke-solver : Term → Term → Term → Term invoke-normaliser : Term → Term → Term | record | src | [
"open import 1Lab.Prelude",
"open import 1Lab.Reflection",
"open import 1Lab.Reflection.Variables",
"open import Data.List.Base"
] | src/1Lab/Reflection/Solver.agda | VariableSolver | |
solver-failed : Term → Term → TC A | function | src | [
"open import 1Lab.Prelude",
"open import 1Lab.Reflection",
"open import 1Lab.Reflection.Variables",
"open import Data.List.Base"
] | src/1Lab/Reflection/Solver.agda | solver-failed | |
print-repr : Term → Term → TC A | function | src | [
"open import 1Lab.Prelude",
"open import 1Lab.Reflection",
"open import 1Lab.Reflection.Variables",
"open import Data.List.Base"
] | src/1Lab/Reflection/Solver.agda | print-repr | |
print-var-repr : Term → Term → Term → TC A | function | src | [
"open import 1Lab.Prelude",
"open import 1Lab.Reflection",
"open import 1Lab.Reflection.Variables",
"open import Data.List.Base"
] | src/1Lab/Reflection/Solver.agda | print-var-repr | |
Subst : Type where ids : Subst _∷_ : Term → Subst → Subst wk : Nat → Subst → Subst lift : Nat → Subst → Subst strengthen : Nat → Subst → Subst infixr 20 _∷_ wkS : Nat → Subst → Subst wkS zero ρ = ρ wkS n (wk x ρ) = wk (n + x) ρ wkS n ρ = wk n ρ liftS : Nat → Subst → Subst liftS zero ρ = ρ liftS n ids = ids liftS n (lif... | data | src | [
"open import 1Lab.Reflection",
"open import 1Lab.Type",
"open import Data.Maybe.Base",
"open import Meta.Foldable",
"open import Prim.Data.Nat"
] | src/1Lab/Reflection/Subst.agda | Subst | |
Has-subst {ℓ} (A : Type ℓ) : Type (lsuc ℓ) where field applyS : Subst → A → A | record | src | [
"open import 1Lab.Reflection",
"open import 1Lab.Type",
"open import Data.Maybe.Base",
"open import Meta.Foldable",
"open import Prim.Data.Nat"
] | src/1Lab/Reflection/Subst.agda | Has-subst | |
wkS : Nat → Subst → Subst | function | src | [
"open import 1Lab.Reflection",
"open import 1Lab.Type",
"open import Data.Maybe.Base",
"open import Meta.Foldable",
"open import Prim.Data.Nat"
] | src/1Lab/Reflection/Subst.agda | wkS | |
liftS : Nat → Subst → Subst | function | src | [
"open import 1Lab.Reflection",
"open import 1Lab.Type",
"open import Data.Maybe.Base",
"open import Meta.Foldable",
"open import Prim.Data.Nat"
] | src/1Lab/Reflection/Subst.agda | liftS | |
raiseS : Nat → Subst | function | src | [
"open import 1Lab.Reflection",
"open import 1Lab.Type",
"open import Data.Maybe.Base",
"open import Meta.Foldable",
"open import Prim.Data.Nat"
] | src/1Lab/Reflection/Subst.agda | raiseS | |
raise-fromS : Nat → Nat → Subst | function | src | [
"open import 1Lab.Reflection",
"open import 1Lab.Type",
"open import Data.Maybe.Base",
"open import Meta.Foldable",
"open import Prim.Data.Nat"
] | src/1Lab/Reflection/Subst.agda | raise-fromS | |
singletonS : Nat → Term → Subst | function | src | [
"open import 1Lab.Reflection",
"open import 1Lab.Type",
"open import Data.Maybe.Base",
"open import Meta.Foldable",
"open import Prim.Data.Nat"
] | src/1Lab/Reflection/Subst.agda | singletonS | |
inplaceS : Nat → Term → Subst | function | src | [
"open import 1Lab.Reflection",
"open import 1Lab.Type",
"open import Data.Maybe.Base",
"open import Meta.Foldable",
"open import Prim.Data.Nat"
] | src/1Lab/Reflection/Subst.agda | inplaceS | |
raise : ∀ {ℓ} {A : Type ℓ} ⦃ _ : Has-subst A ⦄ → Nat → A → A | function | src | [
"open import 1Lab.Reflection",
"open import 1Lab.Type",
"open import Data.Maybe.Base",
"open import Meta.Foldable",
"open import Prim.Data.Nat"
] | src/1Lab/Reflection/Subst.agda | raise | |
subst-clause : Subst → Clause → Clause | function | src | [
"open import 1Lab.Reflection",
"open import 1Lab.Type",
"open import Data.Maybe.Base",
"open import Meta.Foldable",
"open import Prim.Data.Nat"
] | src/1Lab/Reflection/Subst.agda | subst-clause | |
subst-tm : Subst → Term → Term | function | src | [
"open import 1Lab.Reflection",
"open import 1Lab.Type",
"open import Data.Maybe.Base",
"open import Meta.Foldable",
"open import Prim.Data.Nat"
] | src/1Lab/Reflection/Subst.agda | subst-tm | |
apply-tm : Term → Arg Term → Term | function | src | [
"open import 1Lab.Reflection",
"open import 1Lab.Type",
"open import Data.Maybe.Base",
"open import Meta.Foldable",
"open import Prim.Data.Nat"
] | src/1Lab/Reflection/Subst.agda | apply-tm | |
subst-tel : Subst → Telescope → Telescope | function | src | [
"open import 1Lab.Reflection",
"open import 1Lab.Type",
"open import Data.Maybe.Base",
"open import Meta.Foldable",
"open import Prim.Data.Nat"
] | src/1Lab/Reflection/Subst.agda | subst-tel | |
lookup-tm : (σ : Subst) (i : Nat) → Term | function | src | [
"open import 1Lab.Reflection",
"open import 1Lab.Type",
"open import Data.Maybe.Base",
"open import Meta.Foldable",
"open import Prim.Data.Nat"
] | src/1Lab/Reflection/Subst.agda | lookup-tm | |
apply-abs : ∀ {ℓ} {A : Type ℓ} ⦃ _ : Has-subst A ⦄ → Abs A → Term → A | function | src | [
"open import 1Lab.Reflection",
"open import 1Lab.Type",
"open import Data.Maybe.Base",
"open import Meta.Foldable",
"open import Prim.Data.Nat"
] | src/1Lab/Reflection/Subst.agda | apply-abs | |
pi-apply : Term → List (Arg Term) → Maybe Term | function | src | [
"open import 1Lab.Reflection",
"open import 1Lab.Type",
"open import Data.Maybe.Base",
"open import Meta.Foldable",
"open import Prim.Data.Nat"
] | src/1Lab/Reflection/Subst.agda | pi-apply | |
pi-applyTC : Term → List (Arg Term) → TC Term | function | src | [
"open import 1Lab.Reflection",
"open import 1Lab.Type",
"open import Data.Maybe.Base",
"open import Meta.Foldable",
"open import Prim.Data.Nat"
] | src/1Lab/Reflection/Subst.agda | pi-applyTC | |
name-of-glue : Name | function | src | [
"open import 1Lab.Reflection",
"open import 1Lab.Univalence",
"open import 1Lab.Type",
"open import Prim.Extension",
"open import Prim.HCompU",
"open import Prim.Kan",
"import 1Lab.Univalence as U"
] | src/1Lab/Reflection/Univalence.agda | name-of-glue | |
Env {ℓ} (A : Type ℓ) : Nat → Type ℓ where [] : Env A zero _▷_ : ∀ {n} → Env A n → A → Env A (suc n) | data | src | [
"open import 1Lab.Reflection hiding (reverse)",
"open import 1Lab.Type",
"open import Data.Dec.Base",
"open import Data.Fin.Base"
] | src/1Lab/Reflection/Variables.agda | Env | |
Variables {a} (A : Type a) : Type a where constructor mk-variables field {nvars} : Nat -- We store the bindings in reverse order so that it's -- cheap to add a new one. bound : Env A nvars variables : Term → Maybe Term | record | src | [
"open import 1Lab.Reflection hiding (reverse)",
"open import 1Lab.Type",
"open import Data.Dec.Base",
"open import Data.Fin.Base"
] | src/1Lab/Reflection/Variables.agda | Variables | |
empty-vars : Variables A | function | src | [
"open import 1Lab.Reflection hiding (reverse)",
"open import 1Lab.Type",
"open import Data.Dec.Base",
"open import Data.Fin.Base"
] | src/1Lab/Reflection/Variables.agda | empty-vars | |
bind-var : Variables A → Term → TC (Term × Variables A) | function | src | [
"open import 1Lab.Reflection hiding (reverse)",
"open import 1Lab.Type",
"open import Data.Dec.Base",
"open import Data.Fin.Base"
] | src/1Lab/Reflection/Variables.agda | bind-var | |
environment : Variables A → TC (Term × Term) | function | src | [
"open import 1Lab.Reflection hiding (reverse)",
"open import 1Lab.Type",
"open import Data.Dec.Base",
"open import Data.Fin.Base"
] | src/1Lab/Reflection/Variables.agda | environment | |
derive-show : Name → Name → TC ⊤ | function | src | [
"open import 1Lab.Reflection.Signature",
"open import 1Lab.Reflection",
"open import 1Lab.Type",
"open import Data.Reflection.Term",
"open import Data.String.Show",
"open import Data.String.Base",
"open import Data.Char.Base",
"open import Data.Fin.Base",
"open import Data.Vec.Base hiding (map)",
... | src/1Lab/Reflection/Deriving/Show.agda | derive-show | |
makeAutoStr-term : Nat → Term → TC ⊤ | function | src | [
"open import 1Lab.Univalence.SIP",
"open import 1Lab.Reflection",
"open import 1Lab.Type.Sigma",
"open import 1Lab.Univalence",
"open import 1Lab.Equiv",
"open import 1Lab.Path",
"open import 1Lab.Type",
"open import Data.List.Base"
] | src/1Lab/Univalence/SIP/Auto.agda | makeAutoStr-term | |
Module-notation {ℓ ℓm} (R : Ring ℓ) (T : Type ℓm) : Type (ℓ ⊔ ℓm) where private module R = Ring-on (R .snd) field instance additive-group : Abelian-group-on T private _+_ : T → T → T _+_ = Abelian-group-on._*_ additive-group field +-comm : (a b : T) → a + b ≡ b + a _⋆_ : ⌞ R ⌟ → T → T ⋆-distribl : ∀ r x y → r ⋆ (x + y)... | record | src | [
"open import Algebra.Group.Notation",
"open import Algebra.Ring.Module",
"open import Algebra.Group.Ab",
"open import Algebra.Group",
"open import Algebra.Ring",
"open import Cat.Prelude hiding (_+_ ; _*_)"
] | src/Algebra/Ring/Module/Notation.agda | Module-notation | |
module-notation : ∀ {ℓ ℓm} {R : Ring ℓ} (M : Module R ℓm) → Module-notation R ⌞ M ⌟ | function | src | [
"open import Algebra.Group.Notation",
"open import Algebra.Ring.Module",
"open import Algebra.Group.Ab",
"open import Algebra.Group",
"open import Algebra.Ring",
"open import Cat.Prelude hiding (_+_ ; _*_)"
] | src/Algebra/Ring/Module/Notation.agda | module-notation | |
Dualises {ℓ} (T : Type ℓ) : Type where field dualiser : Name | record | 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 | Dualises | |
make-cohere : ∀ {ℓ} {S : Type ℓ} → S → Term → TC ⊤ | 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 | make-cohere | |
make-dualise : ∀ {ℓ} {S : Type ℓ} → S → Term → TC ⊤ | 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 | make-dualise | |
cohere-into : ∀ {ℓ ℓ'} {S : Type ℓ'} → Name → (T : Type ℓ) → S → TC ⊤ | 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 | cohere-into | |
define-coherence : Name → TC ⊤ | 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 | define-coherence | |
nat-assoc-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-assoc-to | |
nat-assoc-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-assoc-from |
End of preview. Expand in Data Studio
Agda-1Lab
Structured dataset from 1Lab — Cross-linked reference resource for HoTT.
2,114 declarations extracted from Agda source files.
Applications
- Training language models on formal proofs
- Fine-tuning theorem provers
- Retrieval-augmented generation for proof assistants
- Learning proof embeddings and representations
Source
- Repository: https://github.com/plt-amy/1lab
Schema
| Column | Type | Description |
|---|---|---|
| fact | string | Declaration body |
| type | string | data, record, function |
| library | string | Source module |
| imports | list | Required imports |
| filename | string | Source file path |
| symbolic_name | string | Identifier |
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