Proof Assistant Projects
Collection
Digesting proof assistant libraries for AI ingestion. • 103 items • Updated • 3
Datasets:
statement stringlengths 5 5.51k | proof stringlengths 0 9.78k | type stringclasses 3
values | symbolic_name stringlengths 1 37 | library stringclasses 373
values | filename stringclasses 929
values | imports listlengths 0 48 | deps listlengths 0 58 | docstring stringclasses 1
value | source_url stringclasses 1
value | commit stringclasses 1
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RecStruct : Set a → (ℓ₁ ℓ₂ : Level) → Set _ | RecStruct A = PT A A
-- A recursor builder constructs an instance of a recursion structure
-- for a given input. | function | RecStruct | Root | src/Induction.agda | [
"Level",
"Relation.Unary",
"Relation.Unary.PredicateTransformer"
] | [
"PT"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | |
RecursorBuilder : RecStruct A ℓ₁ ℓ₂ → Set _ | RecursorBuilder Rec = ∀ P → Rec P ⊆′ P → Universal (Rec P)
-- A recursor can be used to actually compute/prove something useful. | function | RecursorBuilder | Root | src/Induction.agda | [
"Level",
"Relation.Unary",
"Relation.Unary.PredicateTransformer"
] | [
"Rec",
"RecStruct",
"Universal"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | |
Recursor : RecStruct A ℓ₁ ℓ₂ → Set _ | Recursor Rec = ∀ P → Rec P ⊆′ P → Universal P
-- And recursors can be constructed from recursor builders. | function | Recursor | Root | src/Induction.agda | [
"Level",
"Relation.Unary",
"Relation.Unary.PredicateTransformer"
] | [
"Rec",
"RecStruct",
"Universal"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | |
build : RecursorBuilder Rec → Recursor Rec | build builder P f x = f x (builder P f x)
-- We can repeat the exercise above for subsets of the type we are
-- recursing over. | function | build | Root | src/Induction.agda | [
"Level",
"Relation.Unary",
"Relation.Unary.PredicateTransformer"
] | [
"Rec",
"Recursor",
"RecursorBuilder"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | |
SubsetRecursorBuilder : Pred A ℓ → RecStruct A ℓ₁ ℓ₂ → Set _ | SubsetRecursorBuilder Q Rec = ∀ P → Rec P ⊆′ P → Q ⊆′ Rec P | function | SubsetRecursorBuilder | Root | src/Induction.agda | [
"Level",
"Relation.Unary",
"Relation.Unary.PredicateTransformer"
] | [
"Pred",
"Rec",
"RecStruct"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | |
SubsetRecursor : Pred A ℓ → RecStruct A ℓ₁ ℓ₂ → Set _ | SubsetRecursor Q Rec = ∀ P → Rec P ⊆′ P → Q ⊆′ P | function | SubsetRecursor | Root | src/Induction.agda | [
"Level",
"Relation.Unary",
"Relation.Unary.PredicateTransformer"
] | [
"Pred",
"Rec",
"RecStruct"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | |
subsetBuild : SubsetRecursorBuilder Q Rec → SubsetRecursor Q Rec | subsetBuild builder P f x q = f x (builder P f x q) | function | subsetBuild | Root | src/Induction.agda | [
"Level",
"Relation.Unary",
"Relation.Unary.PredicateTransformer"
] | [
"Rec",
"SubsetRecursor",
"SubsetRecursorBuilder"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | |
Lift {a} ℓ (A : Set a) : Set (a ⊔ ℓ) where
constructor lift
field lower : A | record | Lift | Root | src/Level.agda | [
"Agda.Primitive"
] | [
"lift",
"lower"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
0ℓ : Level | 0ℓ = zero | function | 0ℓ | Root | src/Level.agda | [
"Agda.Primitive"
] | [
"zero"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | |
levelOfType : ∀ {a} → Set a → Level | levelOfType {a} _ = a | function | levelOfType | Root | src/Level.agda | [
"Agda.Primitive"
] | [] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | |
levelOfTerm : ∀ {a} {A : Set a} → A → Level | levelOfTerm {a} _ = a | function | levelOfTerm | Root | src/Level.agda | [
"Agda.Primitive"
] | [] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | |
Arg-info = Information.ArgInfo
{-# WARNING_ON_USAGE Arg-info
"Warning: Arg-info was deprecated in v1.3.
Please use Reflection.AST.Argument.Information's ArgInfo instead."
#-} | function | Arg-info | Root | src/Reflection.agda | [
"Reflection.AST",
"Reflection.TCM",
"Reflection.TCM.Syntax",
"Reflection.AST.Abstraction",
"Reflection.AST.Argument",
"Reflection.AST.Definition",
"Reflection.AST.Meta",
"Reflection.AST.Name",
"Reflection.AST.Literal",
"Reflection.AST.Pattern",
"Reflection.AST.Term",
"Reflection.AST.Argument.M... | [] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
_≟-Lit_ = Literal._≟_
{-# WARNING_ON_USAGE _≟-Lit_
"Warning: _≟-Lit_ was deprecated in v1.3.
Please use Reflection.AST.Literal's _≟_ instead."
#-} | function | _≟-Lit_ | Root | src/Reflection.agda | [
"Reflection.AST",
"Reflection.TCM",
"Reflection.TCM.Syntax",
"Reflection.AST.Abstraction",
"Reflection.AST.Argument",
"Reflection.AST.Definition",
"Reflection.AST.Meta",
"Reflection.AST.Name",
"Reflection.AST.Literal",
"Reflection.AST.Pattern",
"Reflection.AST.Term",
"Reflection.AST.Argument.M... | [] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
_≟-Name_ = Name._≟_
{-# WARNING_ON_USAGE _≟-Name_
"Warning: _≟-Name_ was deprecated in v1.3.
Please use Reflection.AST.Name's _≟_ instead."
#-} | function | _≟-Name_ | Root | src/Reflection.agda | [
"Reflection.AST",
"Reflection.TCM",
"Reflection.TCM.Syntax",
"Reflection.AST.Abstraction",
"Reflection.AST.Argument",
"Reflection.AST.Definition",
"Reflection.AST.Meta",
"Reflection.AST.Name",
"Reflection.AST.Literal",
"Reflection.AST.Pattern",
"Reflection.AST.Term",
"Reflection.AST.Argument.M... | [] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
_≟-Meta_ = Meta._≟_
{-# WARNING_ON_USAGE _≟-Meta_
"Warning: _≟-Meta_ was deprecated in v1.3.
Please use Reflection.AST.Meta's _≟_ instead."
#-} | function | _≟-Meta_ | Root | src/Reflection.agda | [
"Reflection.AST",
"Reflection.TCM",
"Reflection.TCM.Syntax",
"Reflection.AST.Abstraction",
"Reflection.AST.Argument",
"Reflection.AST.Definition",
"Reflection.AST.Meta",
"Reflection.AST.Name",
"Reflection.AST.Literal",
"Reflection.AST.Pattern",
"Reflection.AST.Term",
"Reflection.AST.Argument.M... | [] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
_≟-Visibility_ = Visibility._≟_
{-# WARNING_ON_USAGE _≟-Visibility_
"Warning: _≟-Visibility_ was deprecated in v1.3.
Please use Reflection.AST.Argument.Visibility's _≟_ instead."
#-} | function | _≟-Visibility_ | Root | src/Reflection.agda | [
"Reflection.AST",
"Reflection.TCM",
"Reflection.TCM.Syntax",
"Reflection.AST.Abstraction",
"Reflection.AST.Argument",
"Reflection.AST.Definition",
"Reflection.AST.Meta",
"Reflection.AST.Name",
"Reflection.AST.Literal",
"Reflection.AST.Pattern",
"Reflection.AST.Term",
"Reflection.AST.Argument.M... | [] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
_≟-Relevance_ = Relevance._≟_
{-# WARNING_ON_USAGE _≟-Relevance_
"Warning: _≟-Relevance_ was deprecated in v1.3.
Please use Reflection.AST.Argument.Relevance's _≟_ instead."
#-} | function | _≟-Relevance_ | Root | src/Reflection.agda | [
"Reflection.AST",
"Reflection.TCM",
"Reflection.TCM.Syntax",
"Reflection.AST.Abstraction",
"Reflection.AST.Argument",
"Reflection.AST.Definition",
"Reflection.AST.Meta",
"Reflection.AST.Name",
"Reflection.AST.Literal",
"Reflection.AST.Pattern",
"Reflection.AST.Term",
"Reflection.AST.Argument.M... | [] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
_≟-Arg-info_ = Information._≟_
{-# WARNING_ON_USAGE _≟-Arg-info_
"Warning: _≟-Arg-info_ was deprecated in v1.3.
Please use Reflection.AST.Argument.Information's _≟_ instead."
#-} | function | _≟-Arg-info_ | Root | src/Reflection.agda | [
"Reflection.AST",
"Reflection.TCM",
"Reflection.TCM.Syntax",
"Reflection.AST.Abstraction",
"Reflection.AST.Argument",
"Reflection.AST.Definition",
"Reflection.AST.Meta",
"Reflection.AST.Name",
"Reflection.AST.Literal",
"Reflection.AST.Pattern",
"Reflection.AST.Term",
"Reflection.AST.Argument.M... | [] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
_≟-Pattern_ = Pattern._≟_
{-# WARNING_ON_USAGE _≟-Pattern_
"Warning: _≟-Pattern_ was deprecated in v1.3.
Please use Reflection.AST.Pattern's _≟_ instead."
#-} | function | _≟-Pattern_ | Root | src/Reflection.agda | [
"Reflection.AST",
"Reflection.TCM",
"Reflection.TCM.Syntax",
"Reflection.AST.Abstraction",
"Reflection.AST.Argument",
"Reflection.AST.Definition",
"Reflection.AST.Meta",
"Reflection.AST.Name",
"Reflection.AST.Literal",
"Reflection.AST.Pattern",
"Reflection.AST.Term",
"Reflection.AST.Argument.M... | [] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
_≟-ArgPatterns_ = Pattern._≟s_
{-# WARNING_ON_USAGE _≟-ArgPatterns_
"Warning: _≟-ArgPatterns_ was deprecated in v1.3.
Please use Reflection.AST.Pattern's _≟s_ instead."
#-} | function | _≟-ArgPatterns_ | Root | src/Reflection.agda | [
"Reflection.AST",
"Reflection.TCM",
"Reflection.TCM.Syntax",
"Reflection.AST.Abstraction",
"Reflection.AST.Argument",
"Reflection.AST.Definition",
"Reflection.AST.Meta",
"Reflection.AST.Name",
"Reflection.AST.Literal",
"Reflection.AST.Pattern",
"Reflection.AST.Term",
"Reflection.AST.Argument.M... | [] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
map-Abs = Abstraction.map
{-# WARNING_ON_USAGE map-Abs
"Warning: map-Abs was deprecated in v1.3.
Please use Reflection.AST.Abstraction's map instead."
#-} | function | map-Abs | Root | src/Reflection.agda | [
"Reflection.AST",
"Reflection.TCM",
"Reflection.TCM.Syntax",
"Reflection.AST.Abstraction",
"Reflection.AST.Argument",
"Reflection.AST.Definition",
"Reflection.AST.Meta",
"Reflection.AST.Name",
"Reflection.AST.Literal",
"Reflection.AST.Pattern",
"Reflection.AST.Term",
"Reflection.AST.Argument.M... | [] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
map-Arg = Argument.map
{-# WARNING_ON_USAGE map-Arg
"Warning: map-Arg was deprecated in v1.3.
Please use Reflection.AST.Argument's map instead."
#-} | function | map-Arg | Root | src/Reflection.agda | [
"Reflection.AST",
"Reflection.TCM",
"Reflection.TCM.Syntax",
"Reflection.AST.Abstraction",
"Reflection.AST.Argument",
"Reflection.AST.Definition",
"Reflection.AST.Meta",
"Reflection.AST.Name",
"Reflection.AST.Literal",
"Reflection.AST.Pattern",
"Reflection.AST.Term",
"Reflection.AST.Argument.M... | [] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
map-Args = Argument.map-Args
{-# WARNING_ON_USAGE map-Args
"Warning: map-Args was deprecated in v1.3.
Please use Reflection.AST.Argument's map-Args instead."
#-} | function | map-Args | Root | src/Reflection.agda | [
"Reflection.AST",
"Reflection.TCM",
"Reflection.TCM.Syntax",
"Reflection.AST.Abstraction",
"Reflection.AST.Argument",
"Reflection.AST.Definition",
"Reflection.AST.Meta",
"Reflection.AST.Name",
"Reflection.AST.Literal",
"Reflection.AST.Pattern",
"Reflection.AST.Term",
"Reflection.AST.Argument.M... | [] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
visibility = Information.visibility
{-# WARNING_ON_USAGE visibility
"Warning: visibility was deprecated in v1.3.
Please use Reflection.AST.Argument.Information's visibility instead."
#-} | function | visibility | Root | src/Reflection.agda | [
"Reflection.AST",
"Reflection.TCM",
"Reflection.TCM.Syntax",
"Reflection.AST.Abstraction",
"Reflection.AST.Argument",
"Reflection.AST.Definition",
"Reflection.AST.Meta",
"Reflection.AST.Name",
"Reflection.AST.Literal",
"Reflection.AST.Pattern",
"Reflection.AST.Term",
"Reflection.AST.Argument.M... | [] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
relevance = Modality.relevance
{-# WARNING_ON_USAGE relevance
"Warning: relevance was deprecated in v1.3.
Please use Reflection.AST.Argument.Modality's relevance instead."
#-} | function | relevance | Root | src/Reflection.agda | [
"Reflection.AST",
"Reflection.TCM",
"Reflection.TCM.Syntax",
"Reflection.AST.Abstraction",
"Reflection.AST.Argument",
"Reflection.AST.Definition",
"Reflection.AST.Meta",
"Reflection.AST.Name",
"Reflection.AST.Literal",
"Reflection.AST.Pattern",
"Reflection.AST.Term",
"Reflection.AST.Argument.M... | [] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
_≟-AbsTerm_ = Term._≟-AbsTerm_
{-# WARNING_ON_USAGE _≟-AbsTerm_
"Warning: _≟-AbsTerm_ was deprecated in v1.3.
Please use Reflection.AST.Term's _≟-AbsTerm_ instead."
#-} | function | _≟-AbsTerm_ | Root | src/Reflection.agda | [
"Reflection.AST",
"Reflection.TCM",
"Reflection.TCM.Syntax",
"Reflection.AST.Abstraction",
"Reflection.AST.Argument",
"Reflection.AST.Definition",
"Reflection.AST.Meta",
"Reflection.AST.Name",
"Reflection.AST.Literal",
"Reflection.AST.Pattern",
"Reflection.AST.Term",
"Reflection.AST.Argument.M... | [] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
_≟-AbsType_ = Term._≟-AbsType_
{-# WARNING_ON_USAGE _≟-AbsType_
"Warning: _≟-AbsType_ was deprecated in v1.3.
Please use Reflection.AST.Term's _≟-AbsType_ instead."
#-} | function | _≟-AbsType_ | Root | src/Reflection.agda | [
"Reflection.AST",
"Reflection.TCM",
"Reflection.TCM.Syntax",
"Reflection.AST.Abstraction",
"Reflection.AST.Argument",
"Reflection.AST.Definition",
"Reflection.AST.Meta",
"Reflection.AST.Name",
"Reflection.AST.Literal",
"Reflection.AST.Pattern",
"Reflection.AST.Term",
"Reflection.AST.Argument.M... | [] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
_≟-ArgTerm_ = Term._≟-ArgTerm_
{-# WARNING_ON_USAGE _≟-ArgTerm_
"Warning: _≟-ArgTerm_ was deprecated in v1.3.
Please use Reflection.AST.Term's _≟-ArgTerm_ instead."
#-} | function | _≟-ArgTerm_ | Root | src/Reflection.agda | [
"Reflection.AST",
"Reflection.TCM",
"Reflection.TCM.Syntax",
"Reflection.AST.Abstraction",
"Reflection.AST.Argument",
"Reflection.AST.Definition",
"Reflection.AST.Meta",
"Reflection.AST.Name",
"Reflection.AST.Literal",
"Reflection.AST.Pattern",
"Reflection.AST.Term",
"Reflection.AST.Argument.M... | [] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
_≟-ArgType_ = Term._≟-ArgType_
{-# WARNING_ON_USAGE _≟-ArgType_
"Warning: _≟-ArgType_ was deprecated in v1.3.
Please use Reflection.AST.Term's _≟-ArgType_ instead."
#-} | function | _≟-ArgType_ | Root | src/Reflection.agda | [
"Reflection.AST",
"Reflection.TCM",
"Reflection.TCM.Syntax",
"Reflection.AST.Abstraction",
"Reflection.AST.Argument",
"Reflection.AST.Definition",
"Reflection.AST.Meta",
"Reflection.AST.Name",
"Reflection.AST.Literal",
"Reflection.AST.Pattern",
"Reflection.AST.Term",
"Reflection.AST.Argument.M... | [] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
_≟-Args_ = Term._≟-Args_
{-# WARNING_ON_USAGE _≟-Args_
"Warning: _≟-Args_ was deprecated in v1.3.
Please use Reflection.AST.Term's _≟-Args_ instead."
#-} | function | _≟-Args_ | Root | src/Reflection.agda | [
"Reflection.AST",
"Reflection.TCM",
"Reflection.TCM.Syntax",
"Reflection.AST.Abstraction",
"Reflection.AST.Argument",
"Reflection.AST.Definition",
"Reflection.AST.Meta",
"Reflection.AST.Name",
"Reflection.AST.Literal",
"Reflection.AST.Pattern",
"Reflection.AST.Term",
"Reflection.AST.Argument.M... | [] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
_≟-Clause_ = Term._≟-Clause_
{-# WARNING_ON_USAGE _≟-Clause_
"Warning: _≟-Clause_ was deprecated in v1.3.
Please use Reflection.AST.Term's _≟-Clause_ instead."
#-} | function | _≟-Clause_ | Root | src/Reflection.agda | [
"Reflection.AST",
"Reflection.TCM",
"Reflection.TCM.Syntax",
"Reflection.AST.Abstraction",
"Reflection.AST.Argument",
"Reflection.AST.Definition",
"Reflection.AST.Meta",
"Reflection.AST.Name",
"Reflection.AST.Literal",
"Reflection.AST.Pattern",
"Reflection.AST.Term",
"Reflection.AST.Argument.M... | [] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
_≟-Clauses_ = Term._≟-Clauses_
{-# WARNING_ON_USAGE _≟-Clauses_
"Warning: _≟-Clauses_ was deprecated in v1.3.
Please use Reflection.AST.Term's _≟-Clauses_ instead."
#-} | function | _≟-Clauses_ | Root | src/Reflection.agda | [
"Reflection.AST",
"Reflection.TCM",
"Reflection.TCM.Syntax",
"Reflection.AST.Abstraction",
"Reflection.AST.Argument",
"Reflection.AST.Definition",
"Reflection.AST.Meta",
"Reflection.AST.Name",
"Reflection.AST.Literal",
"Reflection.AST.Pattern",
"Reflection.AST.Term",
"Reflection.AST.Argument.M... | [] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
_≟_ = Term._≟_
{-# WARNING_ON_USAGE _≟_
"Warning: _≟_ was deprecated in v1.3.
Please use Reflection.AST.Term's _≟_ instead."
#-} | function | _≟_ | Root | src/Reflection.agda | [
"Reflection.AST",
"Reflection.TCM",
"Reflection.TCM.Syntax",
"Reflection.AST.Abstraction",
"Reflection.AST.Argument",
"Reflection.AST.Definition",
"Reflection.AST.Meta",
"Reflection.AST.Name",
"Reflection.AST.Literal",
"Reflection.AST.Pattern",
"Reflection.AST.Term",
"Reflection.AST.Argument.M... | [] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
_≟-Sort_ = Term._≟-Sort_
{-# WARNING_ON_USAGE _≟-Sort_
"Warning: _≟-Sort_ was deprecated in v1.3.
Please use Reflection.AST.Term's _≟-Sort_ instead."
#-} | function | _≟-Sort_ | Root | src/Reflection.agda | [
"Reflection.AST",
"Reflection.TCM",
"Reflection.TCM.Syntax",
"Reflection.AST.Abstraction",
"Reflection.AST.Argument",
"Reflection.AST.Definition",
"Reflection.AST.Meta",
"Reflection.AST.Name",
"Reflection.AST.Literal",
"Reflection.AST.Pattern",
"Reflection.AST.Term",
"Reflection.AST.Argument.M... | [] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
SizedSet : (ℓ : Level) → Set (suc ℓ) | SizedSet ℓ = Size → Set ℓ | function | SizedSet | Root | src/Size.agda | [
"Level",
"Agda.Builtin.Size"
] | [
"suc"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | |
SuccessorSet c ℓ : Set (suc (c ⊔ ℓ)) where
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
suc# : Op₁ Carrier
zero# : Carrier
isSuccessorSet : IsSuccessorSet _≈_ suc# zero#
open IsSuccessorSet isSuccessorSet public
rawSuccessorSet : Raw... | record | SuccessorSet | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"IsSuccessorSet",
"Op₁",
"RawSuccessorSet",
"Rel",
"_≈_",
"suc"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
Magma c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _∙_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_∙_ : Op₂ Carrier
isMagma : IsMagma _≈_ _∙_
open IsMagma isMagma public
rawMagma : RawMagma _ _
rawMagma = record { _≈_ = _≈_; _∙_ = _∙_ }
open RawMagma rawMagma public
us... | record | Magma | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"IsMagma",
"Op₂",
"RawMagma",
"Rel",
"_∙_",
"_≈_",
"_≉_",
"isMagma",
"rawMagma",
"suc"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
SelectiveMagma c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _∙_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_∙_ : Op₂ Carrier
isSelectiveMagma : IsSelectiveMagma _≈_ _∙_
open IsSelectiveMagma isSelectiveMagma public
magma : Magma c ℓ
magma = record {... | record | SelectiveMagma | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"IsSelectiveMagma",
"Magma",
"Op₂",
"Rel",
"_∙_",
"_≈_",
"isMagma",
"isSelectiveMagma",
"magma",
"rawMagma",
"suc"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
CommutativeMagma c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _∙_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_∙_ : Op₂ Carrier
isCommutativeMagma : IsCommutativeMagma _≈_ _∙_
open IsCommutativeMagma isCommutativeMagma public
magma : Magma c ℓ
... | record | CommutativeMagma | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"IsCommutativeMagma",
"Magma",
"Op₂",
"Rel",
"_∙_",
"_≈_",
"isMagma",
"magma",
"rawMagma",
"suc"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
IdempotentMagma c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _∙_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_∙_ : Op₂ Carrier
isIdempotentMagma : IsIdempotentMagma _≈_ _∙_
open IsIdempotentMagma isIdempotentMagma public
magma : Magma c ℓ
magma = record { isMagma = isMagma }
... | record | IdempotentMagma | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"IsIdempotentMagma",
"Magma",
"Op₂",
"Rel",
"_∙_",
"_≈_",
"isMagma",
"magma",
"rawMagma",
"suc"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
AlternativeMagma c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _∙_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_∙_ : Op₂ Carrier
isAlternativeMagma : IsAlternativeMagma _≈_ _∙_
open IsAlternativeMagma isAlternativeMagma public
magma : Magma c ℓ
magma = record { isMagma = isMag... | record | AlternativeMagma | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"IsAlternativeMagma",
"Magma",
"Op₂",
"Rel",
"_∙_",
"_≈_",
"isMagma",
"magma",
"rawMagma",
"suc"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
FlexibleMagma c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _∙_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_∙_ : Op₂ Carrier
isFlexibleMagma : IsFlexibleMagma _≈_ _∙_
open IsFlexibleMagma isFlexibleMagma public
magma : Magma c ℓ
magma = record { isMagma = isMagma }
open Ma... | record | FlexibleMagma | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"IsFlexibleMagma",
"Magma",
"Op₂",
"Rel",
"_∙_",
"_≈_",
"isMagma",
"magma",
"rawMagma",
"suc"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
MedialMagma c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _∙_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_∙_ : Op₂ Carrier
isMedialMagma : IsMedialMagma _≈_ _∙_
open IsMedialMagma isMedialMagma public
magma : Magma c ℓ
magma = record { isMagma = isMagma }
open Magma magma ... | record | MedialMagma | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"IsMedialMagma",
"Magma",
"Op₂",
"Rel",
"_∙_",
"_≈_",
"isMagma",
"magma",
"rawMagma",
"suc"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
SemimedialMagma c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _∙_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_∙_ : Op₂ Carrier
isSemimedialMagma : IsSemimedialMagma _≈_ _∙_
open IsSemimedialMagma isSemimedialMagma public
magma : Magma c ℓ
magma = record { isMagma = isMagma }
... | record | SemimedialMagma | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"IsSemimedialMagma",
"Magma",
"Op₂",
"Rel",
"_∙_",
"_≈_",
"isMagma",
"magma",
"rawMagma",
"suc"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
Semigroup c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _∙_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_∙_ : Op₂ Carrier
isSemigroup : IsSemigroup _≈_ _∙_
open IsSemigroup isSemigroup public
magma : Magma c ℓ
magma = record { isMagma = isMagma }
open Magma magma... | record | Semigroup | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"IsSemigroup",
"Magma",
"Op₂",
"Rel",
"_∙_",
"_≈_",
"_≉_",
"isMagma",
"isSemigroup",
"magma",
"rawMagma",
"suc"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
Band c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _∙_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_∙_ : Op₂ Carrier
isBand : IsBand _≈_ _∙_
open IsBand isBand public
semigroup : Semigroup c ℓ
semigroup = record { isSemigroup = isSemigroup }
open Semigroup semigroup public
... | record | Band | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"IsBand",
"Op₂",
"Rel",
"Semigroup",
"_∙_",
"_≈_",
"_≉_",
"isBand",
"isSemigroup",
"magma",
"rawMagma",
"semigroup",
"suc"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
CommutativeSemigroup c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _∙_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_∙_ : Op₂ Carrier
isCommutativeSemigroup : IsCommutativeSemigroup _≈_ _∙_
open IsCommutativeSemigroup isCommutativeSemi... | record | CommutativeSemigroup | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"CommutativeMagma",
"IsCommutativeSemigroup",
"Op₂",
"Rel",
"Semigroup",
"_∙_",
"_≈_",
"_≉_",
"commutativeMagma",
"isCommutativeSemigroup",
"isSemigroup",
"magma",
"rawMagma",
"semigroup",
"suc"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
CommutativeBand c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _∙_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_∙_ : Op₂ Carrier
isCommutativeBand : IsCommutativeBand _≈_ _∙_
open IsCommutativeBand isCommutativeBand public
band : Band _ _
band =... | record | CommutativeBand | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"Band",
"CommutativeSemigroup",
"IsCommutativeBand",
"Op₂",
"Rel",
"_∙_",
"_≈_",
"_≉_",
"band",
"commutativeMagma",
"commutativeSemigroup",
"isBand",
"isCommutativeSemigroup",
"magma",
"rawMagma",
"semigroup",
"suc"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
UnitalMagma c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _∙_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_∙_ : Op₂ Carrier
ε : Carrier
isUnitalMagma : IsUnitalMagma _≈_ _∙_ ε
open IsUnitalMagma isUnitalMagma public
magma : Magma c ℓ
magma = record { isMagma = isM... | record | UnitalMagma | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"IsUnitalMagma",
"Magma",
"Op₂",
"Rel",
"_∙_",
"_≈_",
"_≉_",
"isMagma",
"magma",
"rawMagma",
"suc"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
Monoid c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _∙_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_∙_ : Op₂ Carrier
ε : Carrier
isMonoid : IsMonoid _≈_ _∙_ ε
open IsMonoid isMonoid public
semigroup : Semigroup _ _
semigroup = record { isSemigroup = isSemigroup ... | record | Monoid | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"IsMonoid",
"Op₂",
"RawMonoid",
"Rel",
"Semigroup",
"UnitalMagma",
"_∙_",
"_≈_",
"_≉_",
"isMonoid",
"isSemigroup",
"magma",
"rawMagma",
"rawMonoid",
"semigroup",
"suc",
"unitalMagma"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
CommutativeMonoid c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _∙_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_∙_ : Op₂ Carrier
ε : Carrier
isCommutativeMonoid : IsCommutativeMonoid _≈_ _∙_ ε
open IsCommutativeMonoid isComm... | record | CommutativeMonoid | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"CommutativeSemigroup",
"IsCommutativeMonoid",
"Monoid",
"Op₂",
"Rel",
"_∙_",
"_≈_",
"_≉_",
"commutativeMagma",
"commutativeSemigroup",
"isCommutativeMonoid",
"isCommutativeSemigroup",
"isMonoid",
"magma",
"monoid",
"rawMagma",
"rawMonoid",
"semigroup",
"suc",
"unitalMagma"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
IdempotentMonoid c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _∙_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_∙_ : Op₂ Carrier
ε : Carrier
isIdempotentMonoid : IsIdempotentMonoid _≈_ _∙_ ε
open IsIdempotentMonoid isIdempotentMo... | record | IdempotentMonoid | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"Band",
"IsIdempotentMonoid",
"Monoid",
"Op₂",
"Rel",
"_∙_",
"_≈_",
"_≉_",
"band",
"isBand",
"isMonoid",
"magma",
"monoid",
"rawMagma",
"rawMonoid",
"semigroup",
"suc",
"unitalMagma"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
IdempotentCommutativeMonoid c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _∙_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_∙_ : Op₂ Carrier
ε : Carrier
isIdempotentCommutativeMonoid : IsId... | record | IdempotentCommutativeMonoid | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"CommutativeBand",
"CommutativeMonoid",
"IdempotentMonoid",
"IsIdempotentCommutativeMonoid",
"Op₂",
"Rel",
"_∙_",
"_≈_",
"_≉_",
"band",
"commutativeMagma",
"commutativeMonoid",
"commutativeSemigroup",
"isCommutativeMonoid",
"isIdempotentCommutativeMonoid",
"magma",
"monoid",
"rawMa... | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
InvertibleMagma c ℓ : Set (suc (c ⊔ ℓ)) where
infix 8 _⁻¹
infixl 7 _∙_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_∙_ : Op₂ Carrier
ε : Carrier
_⁻¹ : Op₁ Carrier
isInvertibleMagma : IsInvertibleMagma _≈_ _∙_ ε _⁻¹
open IsInvertibleMagma isInvertibleMagma... | record | InvertibleMagma | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"IsInvertibleMagma",
"Magma",
"Op₁",
"Op₂",
"Rel",
"_⁻¹",
"_∙_",
"_≈_",
"_≉_",
"isMagma",
"magma",
"rawMagma",
"suc"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
InvertibleUnitalMagma c ℓ : Set (suc (c ⊔ ℓ)) where
infix 8 _⁻¹
infixl 7 _∙_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_∙_ : Op₂ Carrier
ε : Carrier
_⁻¹ : Op₁ Carrier
isIn... | record | InvertibleUnitalMagma | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"InvertibleMagma",
"IsInvertibleUnitalMagma",
"Op₁",
"Op₂",
"Rel",
"_⁻¹",
"_∙_",
"_≈_",
"_≉_",
"invertibleMagma",
"magma",
"rawMagma",
"suc"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
Group c ℓ : Set (suc (c ⊔ ℓ)) where
infix 8 _⁻¹
infixl 7 _∙_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_∙_ : Op₂ Carrier
ε : Carrier
_⁻¹ : Op₁ Carrier
isGroup : IsGroup _≈_ _∙_ ε _⁻¹
open IsGroup isGroup public
rawGroup : RawGroup _ _
rawGroup = re... | record | Group | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"InvertibleMagma",
"InvertibleUnitalMagma",
"IsGroup",
"Monoid",
"Op₁",
"Op₂",
"RawGroup",
"Rel",
"_⁻¹",
"_∙_",
"_≈_",
"_≉_",
"invertibleMagma",
"invertibleUnitalMagma",
"isGroup",
"isMonoid",
"magma",
"monoid",
"rawGroup",
"rawMagma",
"rawMonoid",
"semigroup",
"suc",
"... | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
AbelianGroup c ℓ : Set (suc (c ⊔ ℓ)) where
infix 8 _⁻¹
infixl 7 _∙_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_∙_ : Op₂ Carrier
ε : Carrier
_⁻¹ : Op₁ Carrier
isAbelianGroup : IsAbelianGroup _≈_ _∙_ ε _⁻¹
open IsAbelian... | record | AbelianGroup | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"CommutativeMonoid",
"Group",
"IsAbelianGroup",
"Op₁",
"Op₂",
"Rel",
"_⁻¹",
"_∙_",
"_≈_",
"_≉_",
"commutativeMagma",
"commutativeMonoid",
"commutativeSemigroup",
"group",
"invertibleMagma",
"invertibleUnitalMagma",
"isAbelianGroup",
"isCommutativeMonoid",
"isGroup",
"magma",
... | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
NearSemiring c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _*_
infixl 6 _+_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_+_ : Op₂ Carrier
_*_ : Op₂ Carrier
0# : Carrier
isNearSemiring : IsNearSemiring _≈_ _+_ _*_ 0#
open IsNearSe... | record | NearSemiring | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"*-isSemigroup",
"*-magma",
"*-rawMagma",
"*-semigroup",
"+-magma",
"+-rawMagma",
"+-rawMonoid",
"+-semigroup",
"0#",
"IsNearSemiring",
"Monoid",
"Op₂",
"RawNearSemiring",
"Rel",
"Semigroup",
"_*_",
"_+_",
"_≈_",
"_≉_",
"isMonoid",
"isNearSemiring",
"isSemigroup",
"magma"... | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
SemiringWithoutOne c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _*_
infixl 6 _+_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_+_ : Op₂ Carrier
_*_ : Op₂ Carrier
0# : Carrier
isSemiringWithoutOne : IsSe... | record | SemiringWithoutOne | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"*-magma",
"*-rawMagma",
"*-semigroup",
"+-commutativeSemigroup",
"+-magma",
"+-rawMagma",
"+-rawMonoid",
"+-semigroup",
"0#",
"CommutativeMonoid",
"IsSemiringWithoutOne",
"NearSemiring",
"Op₂",
"Rel",
"_*_",
"_+_",
"_≈_",
"commutativeMagma",
"commutativeSemigroup",
"isCommutat... | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
CommutativeSemiringWithoutOne c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _*_
infixl 6 _+_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_+_ : Op₂ Carrier
_*_ : Op₂ Carrier
0# ... | record | CommutativeSemiringWithoutOne | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"*-magma",
"*-rawMagma",
"*-semigroup",
"+-commutativeSemigroup",
"+-magma",
"+-rawMagma",
"+-rawMonoid",
"+-semigroup",
"0#",
"IsCommutativeSemiringWithoutOne",
"Op₂",
"Rel",
"SemiringWithoutOne",
"_*_",
"_+_",
"_≈_",
"isCommutativeSemiringWithoutOne",
"isSemiringWithoutOne",
"n... | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
SemiringWithoutAnnihilatingZero c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _*_
infixl 6 _+_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_+_ : Op₂ Carrier
_*_ : Op₂ Carrier
... | record | SemiringWithoutAnnihilatingZero | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"*-isMonoid",
"*-magma",
"*-monoid",
"*-rawMagma",
"*-rawMonoid",
"*-semigroup",
"+-commutativeSemigroup",
"+-magma",
"+-rawMagma",
"+-rawMonoid",
"+-semigroup",
"0#",
"1#",
"CommutativeMonoid",
"IsSemiringWithoutAnnihilatingZero",
"Monoid",
"Op₂",
"RawSemiring",
"Rel",
"_*_",
... | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
Semiring c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _*_
infixl 6 _+_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_+_ : Op₂ Carrier
_*_ : Op₂ Carrier
0# : Carrier
1# : Carrier
isSemiring : IsSemiring _≈_ _+_ _*_ 0# 1#
open IsSemiring i... | record | Semiring | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"*-magma",
"*-monoid",
"*-rawMagma",
"*-rawMonoid",
"*-semigroup",
"+-commutativeSemigroup",
"+-magma",
"+-rawMagma",
"+-rawMonoid",
"+-semigroup",
"0#",
"1#",
"IsSemiring",
"Op₂",
"Rel",
"SemiringWithoutAnnihilatingZero",
"SemiringWithoutOne",
"_*_",
"_+_",
"_≈_",
"_≉_",
"... | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
CommutativeSemiring c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _*_
infixl 6 _+_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_+_ : Op₂ Carrier
_*_ : Op₂ Carrier
0# : Carrier
1# ... | record | CommutativeSemiring | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"*-commutativeMonoid",
"*-commutativeSemigroup",
"*-isCommutativeMonoid",
"*-magma",
"*-monoid",
"*-rawMagma",
"*-rawMonoid",
"*-semigroup",
"+-commutativeSemigroup",
"+-magma",
"+-rawMagma",
"+-rawMonoid",
"+-semigroup",
"0#",
"1#",
"CommutativeMonoid",
"CommutativeSemiringWithoutOn... | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
CancellativeCommutativeSemiring c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _*_
infixl 6 _+_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_+_ : Op₂ Carrier
_*_ : Op₂ Carrier
... | record | CancellativeCommutativeSemiring | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"*-commutativeMonoid",
"*-commutativeSemigroup",
"*-magma",
"*-monoid",
"*-rawMagma",
"*-rawMonoid",
"*-semigroup",
"+-commutativeSemigroup",
"+-magma",
"+-rawMagma",
"+-rawMonoid",
"+-semigroup",
"0#",
"1#",
"CommutativeSemiring",
"IsCancellativeCommutativeSemiring",
"Op₂",
"Rel",... | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
IdempotentSemiring c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _*_
infixl 6 _+_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_+_ : Op₂ Carrier
_*_ : Op₂ Carrier
0# : Carrier
1# ... | record | IdempotentSemiring | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"*-magma",
"*-monoid",
"*-rawMagma",
"*-rawMonoid",
"*-semigroup",
"+-commutativeSemigroup",
"+-magma",
"+-rawMagma",
"+-rawMonoid",
"+-semigroup",
"0#",
"1#",
"IdempotentCommutativeMonoid",
"IsIdempotentSemiring",
"Op₂",
"Rel",
"Semiring",
"_*_",
"_+_",
"_≈_",
"_≉_",
"band... | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
KleeneAlgebra c ℓ : Set (suc (c ⊔ ℓ)) where
infix 8 _⋆
infixl 7 _*_
infixl 6 _+_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_+_ : Op₂ Carrier
_*_ : Op₂ Carrier
_⋆ : Op₁ Carrier
0# ... | record | KleeneAlgebra | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"*-magma",
"*-monoid",
"*-rawMagma",
"*-rawMonoid",
"*-semigroup",
"+-commutativeSemigroup",
"+-magma",
"+-rawMagma",
"+-rawMonoid",
"+-semigroup",
"0#",
"1#",
"IdempotentSemiring",
"IsKleeneAlgebra",
"Op₁",
"Op₂",
"RawKleeneAlgebra",
"Rel",
"_*_",
"_+_",
"_≈_",
"_≉_",
"_... | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
Quasiring c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _*_
infixl 6 _+_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_+_ : Op₂ Carrier
_*_ : Op₂ Carrier
0# : Carrier
1# : Carrier
isQuasiring : IsQuasiring _≈_ _+_ _*_ 0# ... | record | Quasiring | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"*-isMonoid",
"*-magma",
"*-monoid",
"*-rawMagma",
"*-rawMonoid",
"*-semigroup",
"+-magma",
"+-rawMagma",
"+-rawMonoid",
"+-semigroup",
"0#",
"1#",
"IsQuasiring",
"Monoid",
"Op₂",
"Rel",
"_*_",
"_+_",
"_≈_",
"_≉_",
"isMonoid",
"isQuasiring",
"magma",
"rawMagma",
"rawM... | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
BooleanSemiring c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _*_
infixl 6 _+_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_+_ : Op₂ Carrier
_*_ : Op₂ Carrier
0# : Carrier
1# : Carrier
isBooleanSemi... | record | BooleanSemiring | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"*-magma",
"*-monoid",
"*-rawMagma",
"*-rawMonoid",
"*-semigroup",
"+-commutativeSemigroup",
"+-magma",
"+-rawMagma",
"+-rawMonoid",
"+-semigroup",
"0#",
"1#",
"IdempotentMonoid",
"IsBooleanSemiring",
"Op₂",
"Rel",
"Semiring",
"_*_",
"_+_",
"_≈_",
"_≉_",
"band",
"isBoolea... | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
RingWithoutOne c ℓ : Set (suc (c ⊔ ℓ)) where
infix 8 -_
infixl 7 _*_
infixl 6 _+_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_+_ : Op₂ Carrier
_*_ : Op₂ Carrier
-_ : Op₁ Carrier
0# : Carrier
... | record | RingWithoutOne | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"*-magma",
"*-rawMagma",
"*-semigroup",
"+-isAbelianGroup",
"-_",
"0#",
"AbelianGroup",
"IsRingWithoutOne",
"NearSemiring",
"Op₁",
"Op₂",
"RawRingWithoutOne",
"Rel",
"_*_",
"_+_",
"_≈_",
"group",
"invertibleMagma",
"invertibleUnitalMagma",
"isAbelianGroup",
"isNearSemiring",
... | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
NonAssociativeRing c ℓ : Set (suc (c ⊔ ℓ)) where
infix 8 -_
infixl 7 _*_
infixl 6 _+_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_+_ : Op₂ Carrier
_*_ : Op₂ Carrier
-_ : Op₁ Carrier
0# ... | record | NonAssociativeRing | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"*-identity",
"*-magma",
"+-isAbelianGroup",
"-_",
"0#",
"1#",
"AbelianGroup",
"IsNonAssociativeRing",
"Op₁",
"Op₂",
"Rel",
"UnitalMagma",
"_*_",
"_+_",
"_≈_",
"group",
"identity",
"invertibleMagma",
"invertibleUnitalMagma",
"isAbelianGroup",
"magma",
"suc"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
Nearring c ℓ : Set (suc (c ⊔ ℓ)) where
infix 8 -_
infixl 7 _*_
infixl 6 _+_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_+_ : Op₂ Carrier
_*_ : Op₂ Carrier
-_ : Op₁ Carrier
0# : Carrier
1# : Carrier
... | record | Nearring | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"*-magma",
"*-monoid",
"*-rawMagma",
"*-semigroup",
"+-magma",
"+-rawMagma",
"+-rawMonoid",
"+-semigroup",
"-_",
"0#",
"1#",
"IsNearring",
"Op₁",
"Op₂",
"Quasiring",
"Rel",
"_*_",
"_+_",
"_≈_",
"_≉_",
"isQuasiring",
"quasiring",
"suc"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
Ring c ℓ : Set (suc (c ⊔ ℓ)) where
infix 8 -_
infixl 7 _*_
infixl 6 _+_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_+_ : Op₂ Carrier
_*_ : Op₂ Carrier
-_ : Op₁ Carrier
0# : Carrier
1# : Carrier
isRing : IsRing _≈_ _+_ _*_ -_ 0# 1#
ope... | record | Ring | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"*-magma",
"*-monoid",
"*-rawMagma",
"*-rawMonoid",
"*-semigroup",
"+-commutativeSemigroup",
"+-isAbelianGroup",
"+-magma",
"+-rawMagma",
"+-rawMonoid",
"+-semigroup",
"-_",
"0#",
"1#",
"AbelianGroup",
"IsRing",
"NearSemiring",
"Op₁",
"Op₂",
"RawRing",
"Rel",
"RingWithoutOn... | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
CommutativeRing c ℓ : Set (suc (c ⊔ ℓ)) where
infix 8 -_
infixl 7 _*_
infixl 6 _+_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_+_ : Op₂ Carrier
_*_ : Op₂ Carrier
-_ : Op₁ Carrier
0# : Carrier... | record | CommutativeRing | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"*-commutativeMonoid",
"*-commutativeSemigroup",
"*-magma",
"*-monoid",
"*-rawMagma",
"*-rawMonoid",
"*-semigroup",
"+-commutativeSemigroup",
"+-magma",
"+-rawMagma",
"+-rawMonoid",
"+-semigroup",
"-_",
"0#",
"1#",
"CommutativeSemiring",
"IsCommutativeRing",
"Op₁",
"Op₂",
"Rel"... | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
BooleanRing c ℓ : Set (suc (c ⊔ ℓ)) where
infix 8 -_
infixl 7 _*_
infixl 6 _+_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_+_ : Op₂ Carrier
_*_ : Op₂ Carrier
-_ : Op₁ Carrier
0# : Carrier
1# : Carrier... | record | BooleanRing | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"*-commutativeMonoid",
"*-commutativeSemigroup",
"*-idem",
"*-magma",
"*-monoid",
"*-rawMagma",
"*-rawMonoid",
"*-semigroup",
"+-commutativeSemigroup",
"+-magma",
"+-rawMagma",
"+-rawMonoid",
"+-semigroup",
"-_",
"0#",
"1#",
"CommutativeRing",
"IsBooleanRing",
"IsCommutativeRing"... | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
Quasigroup c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _∙_
infixl 7 _\\_
infixl 7 _//_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_∙_ : Op₂ Carrier
_\\_ : Op₂ Carrier
_//_ : Op₂ Carrier
isQuasigroup : IsQuasigroup _≈_ _∙_ _\\_ _//_
open... | record | Quasigroup | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"IsQuasigroup",
"Magma",
"Op₂",
"RawQuasigroup",
"Rel",
"_//_",
"_\\\\_",
"_∙_",
"_≈_",
"_≉_",
"isMagma",
"isQuasigroup",
"magma",
"rawMagma",
"rawQuasigroup",
"suc"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
Loop c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _∙_
infixl 7 _\\_
infixl 7 _//_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_∙_ : Op₂ Carrier
_\\_ : Op₂ Carrier
_//_ : Op₂ Carrier
ε : Carrier
isLoop : IsLoop _≈_ _∙_ _\\_ _//_ ε
open IsLoop isLoop pu... | record | Loop | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"IsLoop",
"Op₂",
"Quasigroup",
"RawLoop",
"Rel",
"_//_",
"_\\\\_",
"_∙_",
"_≈_",
"_≉_",
"isLoop",
"isQuasigroup",
"quasigroup",
"rawLoop",
"suc"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
LeftBolLoop c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _∙_
infixl 7 _\\_
infixl 7 _//_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_∙_ : Op₂ Carrier
_\\_ : Op₂ Carrier
_//_ : Op₂ Carrier
ε : Carrier
isLeftBolLoop : IsLeftBolLoop _≈_ _∙_ _\\_ _//_ ε
op... | record | LeftBolLoop | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"IsLeftBolLoop",
"Loop",
"Op₂",
"Rel",
"_//_",
"_\\\\_",
"_∙_",
"_≈_",
"isLoop",
"loop",
"quasigroup",
"suc"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
RightBolLoop c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _∙_
infixl 7 _\\_
infixl 7 _//_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_∙_ : Op₂ Carrier
_\\_ : Op₂ Carrier
_//_ : Op₂ Carrier
ε : Carrier
isRightBolLoop : IsRightBolLoop _≈_ _∙_ _\\_ _//_ ε
... | record | RightBolLoop | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"IsRightBolLoop",
"Loop",
"Op₂",
"Rel",
"_//_",
"_\\\\_",
"_∙_",
"_≈_",
"isLoop",
"loop",
"quasigroup",
"suc"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
MoufangLoop c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _∙_
infixl 7 _\\_
infixl 7 _//_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_∙_ : Op₂ Carrier
_\\_ : Op₂ Carrier
_//_ : Op₂ Carrier
ε : Carrier
isMoufangLoop : IsMoufangLoop _≈_ _∙_ _\\_ _//_ ε
op... | record | MoufangLoop | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"IsMoufangLoop",
"LeftBolLoop",
"Op₂",
"Rel",
"_//_",
"_\\\\_",
"_∙_",
"_≈_",
"leftBolLoop",
"loop",
"suc"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
MiddleBolLoop c ℓ : Set (suc (c ⊔ ℓ)) where
infixl 7 _∙_
infixl 7 _\\_
infixl 7 _//_
infix 4 _≈_
field
Carrier : Set c
_≈_ : Rel Carrier ℓ
_∙_ : Op₂ Carrier
_\\_ : Op₂ Carrier
_//_ : Op₂ Carrier
ε : Carrier
isMidd... | record | MiddleBolLoop | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"IsMiddleBolLoop",
"Loop",
"Op₂",
"Rel",
"_//_",
"_\\\\_",
"_∙_",
"_≈_",
"isLoop",
"loop",
"quasigroup",
"suc"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
BoundedLattice = IdempotentCommutativeMonoid | function | BoundedLattice | Algebra | src/Algebra/Bundles.agda | [
"Algebra.Bundles.Raw",
"Algebra.Core",
"Algebra.Structures",
"Relation.Binary.Core",
"Level"
] | [
"IdempotentCommutativeMonoid"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | ||
Op₁ : ∀ {ℓ} → Set ℓ → Set ℓ | Op₁ A = A → A | function | Op₁ | Algebra | src/Algebra/Core.agda | [
"Level"
] | [] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | |
Op₂ : ∀ {ℓ} → Set ℓ → Set ℓ | Op₂ A = A → A → A | function | Op₂ | Algebra | src/Algebra/Core.agda | [
"Level"
] | [] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | |
Congruent₁ : Op₁ A → Set _ | Congruent₁ = Monotonic₁ _≈_ _≈_ | function | Congruent₁ | Algebra | src/Algebra/Definitions.agda | [
"Relation.Binary.Core",
"Algebra.Core",
"Data.Product.Base",
"Data.Sum.Base",
"Relation.Binary.Definitions",
"Relation.Nullary.Negation.Core"
] | [
"Monotonic₁",
"Op₁",
"_≈_"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | |
Congruent₂ : Op₂ A → Set _ | Congruent₂ = Monotonic₂ _≈_ _≈_ _≈_ | function | Congruent₂ | Algebra | src/Algebra/Definitions.agda | [
"Relation.Binary.Core",
"Algebra.Core",
"Data.Product.Base",
"Data.Sum.Base",
"Relation.Binary.Definitions",
"Relation.Nullary.Negation.Core"
] | [
"Monotonic₂",
"Op₂",
"_≈_"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | |
LeftCongruent : Op₂ A → Set _ | LeftCongruent _∙_ = ∀ {x} → Congruent₁ (x ∙_) | function | LeftCongruent | Algebra | src/Algebra/Definitions.agda | [
"Relation.Binary.Core",
"Algebra.Core",
"Data.Product.Base",
"Data.Sum.Base",
"Relation.Binary.Definitions",
"Relation.Nullary.Negation.Core"
] | [
"Congruent₁",
"Op₂",
"_∙_"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | |
RightCongruent : Op₂ A → Set _ | RightCongruent _∙_ = ∀ {x} → Congruent₁ (_∙ x) | function | RightCongruent | Algebra | src/Algebra/Definitions.agda | [
"Relation.Binary.Core",
"Algebra.Core",
"Data.Product.Base",
"Data.Sum.Base",
"Relation.Binary.Definitions",
"Relation.Nullary.Negation.Core"
] | [
"Congruent₁",
"Op₂",
"_∙_"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | |
Associative : Op₂ A → Set _ | Associative _∙_ = ∀ x y z → ((x ∙ y) ∙ z) ≈ (x ∙ (y ∙ z)) | function | Associative | Algebra | src/Algebra/Definitions.agda | [
"Relation.Binary.Core",
"Algebra.Core",
"Data.Product.Base",
"Data.Sum.Base",
"Relation.Binary.Definitions",
"Relation.Nullary.Negation.Core"
] | [
"Op₂",
"_∙_"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | |
Commutative : Op₂ A → Set _ | Commutative _∙_ = ∀ x y → (x ∙ y) ≈ (y ∙ x)
-- An element is called `Central` for a binary operation
-- if it commutes with all other elements. | function | Commutative | Algebra | src/Algebra/Definitions.agda | [
"Relation.Binary.Core",
"Algebra.Core",
"Data.Product.Base",
"Data.Sum.Base",
"Relation.Binary.Definitions",
"Relation.Nullary.Negation.Core"
] | [
"Op₂",
"_∙_"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | |
Central : Op₂ A → A → Set _ | Central _∙_ x = ∀ y → (x ∙ y) ≈ (y ∙ x) | function | Central | Algebra | src/Algebra/Definitions.agda | [
"Relation.Binary.Core",
"Algebra.Core",
"Data.Product.Base",
"Data.Sum.Base",
"Relation.Binary.Definitions",
"Relation.Nullary.Negation.Core"
] | [
"Op₂",
"_∙_"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | |
LeftIdentity : A → Op₂ A → Set _ | LeftIdentity e _∙_ = ∀ x → (e ∙ x) ≈ x | function | LeftIdentity | Algebra | src/Algebra/Definitions.agda | [
"Relation.Binary.Core",
"Algebra.Core",
"Data.Product.Base",
"Data.Sum.Base",
"Relation.Binary.Definitions",
"Relation.Nullary.Negation.Core"
] | [
"Op₂",
"_∙_"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | |
RightIdentity : A → Op₂ A → Set _ | RightIdentity e _∙_ = ∀ x → (x ∙ e) ≈ x | function | RightIdentity | Algebra | src/Algebra/Definitions.agda | [
"Relation.Binary.Core",
"Algebra.Core",
"Data.Product.Base",
"Data.Sum.Base",
"Relation.Binary.Definitions",
"Relation.Nullary.Negation.Core"
] | [
"Op₂",
"_∙_"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | |
Identity : A → Op₂ A → Set _ | Identity e ∙ = (LeftIdentity e ∙) × (RightIdentity e ∙) | function | Identity | Algebra | src/Algebra/Definitions.agda | [
"Relation.Binary.Core",
"Algebra.Core",
"Data.Product.Base",
"Data.Sum.Base",
"Relation.Binary.Definitions",
"Relation.Nullary.Negation.Core"
] | [
"LeftIdentity",
"Op₂",
"RightIdentity"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | |
LeftZero : A → Op₂ A → Set _ | LeftZero z _∙_ = ∀ x → (z ∙ x) ≈ z | function | LeftZero | Algebra | src/Algebra/Definitions.agda | [
"Relation.Binary.Core",
"Algebra.Core",
"Data.Product.Base",
"Data.Sum.Base",
"Relation.Binary.Definitions",
"Relation.Nullary.Negation.Core"
] | [
"Op₂",
"_∙_"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | |
RightZero : A → Op₂ A → Set _ | RightZero z _∙_ = ∀ x → (x ∙ z) ≈ z | function | RightZero | Algebra | src/Algebra/Definitions.agda | [
"Relation.Binary.Core",
"Algebra.Core",
"Data.Product.Base",
"Data.Sum.Base",
"Relation.Binary.Definitions",
"Relation.Nullary.Negation.Core"
] | [
"Op₂",
"_∙_"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | |
Zero : A → Op₂ A → Set _ | Zero z ∙ = (LeftZero z ∙) × (RightZero z ∙) | function | Zero | Algebra | src/Algebra/Definitions.agda | [
"Relation.Binary.Core",
"Algebra.Core",
"Data.Product.Base",
"Data.Sum.Base",
"Relation.Binary.Definitions",
"Relation.Nullary.Negation.Core"
] | [
"LeftZero",
"Op₂",
"RightZero"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | |
LeftInverse : A → Op₁ A → Op₂ A → Set _ | LeftInverse e _⁻¹ _∙_ = ∀ x → ((x ⁻¹) ∙ x) ≈ e | function | LeftInverse | Algebra | src/Algebra/Definitions.agda | [
"Relation.Binary.Core",
"Algebra.Core",
"Data.Product.Base",
"Data.Sum.Base",
"Relation.Binary.Definitions",
"Relation.Nullary.Negation.Core"
] | [
"Op₁",
"Op₂",
"_⁻¹",
"_∙_"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | |
RightInverse : A → Op₁ A → Op₂ A → Set _ | RightInverse e _⁻¹ _∙_ = ∀ x → (x ∙ (x ⁻¹)) ≈ e | function | RightInverse | Algebra | src/Algebra/Definitions.agda | [
"Relation.Binary.Core",
"Algebra.Core",
"Data.Product.Base",
"Data.Sum.Base",
"Relation.Binary.Definitions",
"Relation.Nullary.Negation.Core"
] | [
"Op₁",
"Op₂",
"_⁻¹",
"_∙_"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | |
Inverse : A → Op₁ A → Op₂ A → Set _ | Inverse e ⁻¹ ∙ = (LeftInverse e ⁻¹) ∙ × (RightInverse e ⁻¹ ∙)
-- For structures in which not every element has an inverse (e.g. Fields) | function | Inverse | Algebra | src/Algebra/Definitions.agda | [
"Relation.Binary.Core",
"Algebra.Core",
"Data.Product.Base",
"Data.Sum.Base",
"Relation.Binary.Definitions",
"Relation.Nullary.Negation.Core"
] | [
"LeftInverse",
"Op₁",
"Op₂",
"RightInverse"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 | |
LeftInvertible : A → Op₂ A → A → Set _ | LeftInvertible e _∙_ x = ∃[ x⁻¹ ] (x⁻¹ ∙ x) ≈ e | function | LeftInvertible | Algebra | src/Algebra/Definitions.agda | [
"Relation.Binary.Core",
"Algebra.Core",
"Data.Product.Base",
"Data.Sum.Base",
"Relation.Binary.Definitions",
"Relation.Nullary.Negation.Core"
] | [
"Op₂",
"_∙_"
] | https://github.com/agda/agda-stdlib | 2a5a0dec0a3cb5c87468ce101388a513d39dbf10 |
End of preview. Expand in Data Studio
Agda-Stdlib
Structured dataset of definitions and types from the Agda standard library v2.3.
Source
- Repository: https://github.com/agda/agda-stdlib
- Commit:
2a5a0dec0a3cb5c87468ce101388a513d39dbf10 - Files: 1187
- License: mit
Schema
| Column | Type | Description |
|---|---|---|
| statement | string | Declaration signature/claim with the leading keyword removed (verbatim slice); the full declaration minus its proof |
| proof | string | Verbatim proof/body, empty if the declaration has none |
| type | string | Declaration keyword |
| symbolic_name | string | Declaration identifier |
| library | string | Sub-library |
| filename | string | Repository-relative source path |
| imports | list[string] | File-level Require/Import modules |
| deps | list[string] | Intra-corpus identifiers referenced |
| docstring | string | Preceding documentation comment, empty if absent |
| source_url | string | Upstream repository |
| commit | string | Upstream commit extracted |
Statistics
- Entries: 10,757
- With proof: 8,382 (77.9%)
- With docstring: 0 (0.0%)
- Libraries: 373
By type
| Type | Count |
|---|---|
| function | 10,097 |
| record | 441 |
| data | 219 |
Example
RecStruct : Set a → (ℓ₁ ℓ₂ : Level) → Set _
RecStruct A = PT A A
-- A recursor builder constructs an instance of a recursion structure
-- for a given input.
- type: function | symbolic_name:
RecStruct| src/Induction.agda
Use
Each declaration is split into a statement (signature/claim) and a proof (body) that are disjoint
and together form the complete declaration, for proof modeling, autoformalization, retrieval, and
dependency analysis via deps.
Citation
@misc{agda_stdlib_dataset,
title = {Agda-Stdlib},
author = {Norton, Charles},
year = {2026},
note = {Extracted from https://github.com/agda/agda-stdlib, commit 2a5a0dec0a3c},
url = {https://huggingface.co/datasets/phanerozoic/Agda-Stdlib}
}
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