Search is not available for this dataset
fact
string | imports
string | filename
string | symbolic_name
string | __index_level_0__
int64 |
|---|---|---|---|---|
Fixpoint foldr {R} (o: T → R) (f: T → R → R) (a: L): R := match a with | one x => o x | cons x y => f x (foldr o f y) end.
|
Coq.Unicode.Utf8 Coq.Lists.List Coq.Setoids.Setoid Coq.Classes.Morphisms Coq.Sorting.Permutation
|
coq-community-math-classes/implementations/ne_list
|
coq-community-math-classes
| 1,060 |
Fixpoint foldr1 (f: T → T → T) (a: L): T := match a with | one x => x | cons x y => f x (foldr1 f y) end.
|
Coq.Unicode.Utf8 Coq.Lists.List Coq.Setoids.Setoid Coq.Classes.Morphisms Coq.Sorting.Permutation
|
coq-community-math-classes/implementations/ne_list
|
coq-community-math-classes
| 1,061 |
Definition head (l: L): T := match l with one x => x | cons x _ => x end.
|
Coq.Unicode.Utf8 Coq.Lists.List Coq.Setoids.Setoid Coq.Classes.Morphisms Coq.Sorting.Permutation
|
coq-community-math-classes/implementations/ne_list
|
coq-community-math-classes
| 1,062 |
Fixpoint to_list (l: L): list T := match l with | one x => x :: nil | cons x xs => x :: to_list xs end.
|
Coq.Unicode.Utf8 Coq.Lists.List Coq.Setoids.Setoid Coq.Classes.Morphisms Coq.Sorting.Permutation
|
coq-community-math-classes/implementations/ne_list
|
coq-community-math-classes
| 1,063 |
Fixpoint from_list (x: T) (xs: list T): L := match xs with | nil => one x | List.cons h t => cons x (from_list h t) end.
|
Coq.Unicode.Utf8 Coq.Lists.List Coq.Setoids.Setoid Coq.Classes.Morphisms Coq.Sorting.Permutation
|
coq-community-math-classes/implementations/ne_list
|
coq-community-math-classes
| 1,064 |
Definition tail (l: L): list T := match l with one _ => nil | cons _ x => to_list x end.
|
Coq.Unicode.Utf8 Coq.Lists.List Coq.Setoids.Setoid Coq.Classes.Morphisms Coq.Sorting.Permutation
|
coq-community-math-classes/implementations/ne_list
|
coq-community-math-classes
| 1,065 |
Definition last: L → T := foldr1 (fun x y => y).
|
Coq.Unicode.Utf8 Coq.Lists.List Coq.Setoids.Setoid Coq.Classes.Morphisms Coq.Sorting.Permutation
|
coq-community-math-classes/implementations/ne_list
|
coq-community-math-classes
| 1,066 |
Fixpoint replicate_Sn (x: T) (n: nat): L := match n with | 0 => one x | S n' => cons x (replicate_Sn x n') end.
|
Coq.Unicode.Utf8 Coq.Lists.List Coq.Setoids.Setoid Coq.Classes.Morphisms Coq.Sorting.Permutation
|
coq-community-math-classes/implementations/ne_list
|
coq-community-math-classes
| 1,067 |
Fixpoint take (n: nat) (l: L): L := match l, n with | cons x xs, S n' => take n' xs | _, _ => one (head l) end.
|
Coq.Unicode.Utf8 Coq.Lists.List Coq.Setoids.Setoid Coq.Classes.Morphisms Coq.Sorting.Permutation
|
coq-community-math-classes/implementations/ne_list
|
coq-community-math-classes
| 1,068 |
Definition Permutation (x y: L): Prop := ListPermutation x y.
|
Coq.Unicode.Utf8 Coq.Lists.List Coq.Setoids.Setoid Coq.Classes.Morphisms Coq.Sorting.Permutation
|
coq-community-math-classes/implementations/ne_list
|
coq-community-math-classes
| 1,069 |
Fixpoint tails {A} (l: L A): L (L A) := match l with | one x => one (one x) | cons x y => cons l (tails y) end.
|
Coq.Unicode.Utf8 Coq.Lists.List Coq.Setoids.Setoid Coq.Classes.Morphisms Coq.Sorting.Permutation
|
coq-community-math-classes/implementations/ne_list
|
coq-community-math-classes
| 1,070 |
Fixpoint map {A B} (f: A → B) (l: L A): L B := match l with | one x => one (f x) | cons h t => cons (f h) (map f t) end.
|
Coq.Unicode.Utf8 Coq.Lists.List Coq.Setoids.Setoid Coq.Classes.Morphisms Coq.Sorting.Permutation
|
coq-community-math-classes/implementations/ne_list
|
coq-community-math-classes
| 1,071 |
Fixpoint inits {A} (l: L A): L (L A) := match l with | one x => one (one x) | cons h t => cons (one h) (map (cons h) (inits t)) end.
|
Coq.Unicode.Utf8 Coq.Lists.List Coq.Setoids.Setoid Coq.Classes.Morphisms Coq.Sorting.Permutation
|
coq-community-math-classes/implementations/ne_list
|
coq-community-math-classes
| 1,072 |
Fixpoint ne_zip {A B: Type} (l: ne_list A) (m: ne_list B) {struct l} : ne_list (A * B) := match l with | one a => one (a, head m) | a ::: l => match m with | one b => one (a, b) | b ::: m => (a, b) ::: ne_zip l m end end.
|
Coq.Unicode.Utf8 Coq.Lists.List Coq.Setoids.Setoid Coq.Classes.Morphisms Coq.Sorting.Permutation
|
coq-community-math-classes/implementations/ne_list
|
coq-community-math-classes
| 1,073 |
Definition g : N → R := f ∘ cast N (SRpair N).
|
Coq.setoid_ring.Ring MathClasses.interfaces.abstract_algebra MathClasses.theory.categories MathClasses.interfaces.naturals MathClasses.interfaces.integers MathClasses.theory.jections MathClasses.implementations.semiring_pairs
|
coq-community-math-classes/implementations/natpair_integers
|
coq-community-math-classes
| 1,074 |
Definition is_multiple `{Equiv Z} `{Mult Z} (b x : Z) := ∃ k, x = b * k.
|
Coq.setoid_ring.Ring MathClasses.interfaces.abstract_algebra MathClasses.interfaces.integers MathClasses.theory.integers MathClasses.theory.ring_ideals
|
coq-community-math-classes/implementations/modular_ring
|
coq-community-math-classes
| 1,075 |
Definition NonZero_inject (x : F ₀) : F := `x.
|
Coq.setoid_ring.Ring MathClasses.interfaces.abstract_algebra MathClasses.theory.fields
|
coq-community-math-classes/implementations/nonzero_field_elements
|
coq-community-math-classes
| 1,076 |
Definition fset_map `(f : A → B) `{SetType A} `{SetType B} `{EmptySet B} `{SetJoin B} `{SetSingleton B} `{U : !FSetExtend A} : set_type A → set_type B := fset_extend (singleton ∘ f).
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders
|
coq-community-math-classes/interfaces/finite_sets
|
coq-community-math-classes
| 1,077 |
Fixpoint map_var `(f: V → W) `(t: Term V o): Term W o := match t in Term _ o return Term W o with | Var v s => Var (f v) s | App _ _ _ x y => App _ _ _ (map_var f x) (map_var f y) | Op _ s => Op _ s end.
|
Coq.Lists.List MathClasses.interfaces.abstract_algebra MathClasses.misc.util MathClasses.theory.jections MathClasses.interfaces.ua_basic
|
coq-community-math-classes/interfaces/universal_algebra
|
coq-community-math-classes
| 1,079 |
Definition Term0 v sort := Term v (ne_list.one sort).
|
Coq.Lists.List MathClasses.interfaces.abstract_algebra MathClasses.misc.util MathClasses.theory.jections MathClasses.interfaces.ua_basic
|
coq-community-math-classes/interfaces/universal_algebra
|
coq-community-math-classes
| 1,080 |
Fixpoint applications {ot}: Term V ot → Type := match ot with | ne_list.one x => @P x | ne_list.cons x y => λ z, ∀ v, P v → applications (App V _ _ z v) end.
|
Coq.Lists.List MathClasses.interfaces.abstract_algebra MathClasses.misc.util MathClasses.theory.jections MathClasses.interfaces.ua_basic
|
coq-community-math-classes/interfaces/universal_algebra
|
coq-community-math-classes
| 1,081 |
Definition T := Term nat.
|
Coq.Lists.List MathClasses.interfaces.abstract_algebra MathClasses.misc.util MathClasses.theory.jections MathClasses.interfaces.ua_basic
|
coq-community-math-classes/interfaces/universal_algebra
|
coq-community-math-classes
| 1,082 |
Definition T0 := Term0 nat.
|
Coq.Lists.List MathClasses.interfaces.abstract_algebra MathClasses.misc.util MathClasses.theory.jections MathClasses.interfaces.ua_basic
|
coq-community-math-classes/interfaces/universal_algebra
|
coq-community-math-classes
| 1,083 |
Definition Identity t := prod (T t) (T t).
|
Coq.Lists.List MathClasses.interfaces.abstract_algebra MathClasses.misc.util MathClasses.theory.jections MathClasses.interfaces.ua_basic
|
coq-community-math-classes/interfaces/universal_algebra
|
coq-community-math-classes
| 1,084 |
Definition Identity0 sort := Identity (ne_list.one sort).
|
Coq.Lists.List MathClasses.interfaces.abstract_algebra MathClasses.misc.util MathClasses.theory.jections MathClasses.interfaces.ua_basic
|
coq-community-math-classes/interfaces/universal_algebra
|
coq-community-math-classes
| 1,085 |
Definition mkIdentity0 {sort}: T (ne_list.one sort) → T (ne_list.one sort) → Identity0 sort := pair.
|
Coq.Lists.List MathClasses.interfaces.abstract_algebra MathClasses.misc.util MathClasses.theory.jections MathClasses.interfaces.ua_basic
|
coq-community-math-classes/interfaces/universal_algebra
|
coq-community-math-classes
| 1,086 |
Record Entailment (P: Type): Type := { entailment_premises: list P; entailment_conclusion: P }.
|
Coq.Lists.List MathClasses.interfaces.abstract_algebra MathClasses.misc.util MathClasses.theory.jections MathClasses.interfaces.ua_basic
|
coq-community-math-classes/interfaces/universal_algebra
|
coq-community-math-classes
| 1,087 |
Definition EqEntailment := Entailment (sigT Identity0).
|
Coq.Lists.List MathClasses.interfaces.abstract_algebra MathClasses.misc.util MathClasses.theory.jections MathClasses.interfaces.ua_basic
|
coq-community-math-classes/interfaces/universal_algebra
|
coq-community-math-classes
| 1,088 |
Definition identity_as_eq (s: sigT Identity0): Statement := Eq _ (projT2 s).
|
Coq.Lists.List MathClasses.interfaces.abstract_algebra MathClasses.misc.util MathClasses.theory.jections MathClasses.interfaces.ua_basic
|
coq-community-math-classes/interfaces/universal_algebra
|
coq-community-math-classes
| 1,089 |
Definition entailment_as_conjunctive_statement (e: EqEntailment): Statement := Impl (fold_right Conj (Ext True) (map identity_as_eq (entailment_premises _ e))) (identity_as_eq (entailment_conclusion _ e)).
|
Coq.Lists.List MathClasses.interfaces.abstract_algebra MathClasses.misc.util MathClasses.theory.jections MathClasses.interfaces.ua_basic
|
coq-community-math-classes/interfaces/universal_algebra
|
coq-community-math-classes
| 1,090 |
Definition Vars := ∀ a, V → A a.
|
Coq.Lists.List MathClasses.interfaces.abstract_algebra MathClasses.misc.util MathClasses.theory.jections MathClasses.interfaces.ua_basic
|
coq-community-math-classes/interfaces/universal_algebra
|
coq-community-math-classes
| 1,091 |
Definition no_vars x: Vars x False := λ _, False_rect _.
|
Coq.Lists.List MathClasses.interfaces.abstract_algebra MathClasses.misc.util MathClasses.theory.jections MathClasses.interfaces.ua_basic
|
coq-community-math-classes/interfaces/universal_algebra
|
coq-community-math-classes
| 1,092 |
Fixpoint close {V} {o} (v: Vars (λ x, Term False (ne_list.one x)) V) (t: Term V o): Term False o := match t in Term _ o return Term False o with | Var x y => v y x | App _ x y z r => App _ x y (close v z) (close v r) | Op _ o => Op _ o end.
|
Coq.Lists.List MathClasses.interfaces.abstract_algebra MathClasses.misc.util MathClasses.theory.jections MathClasses.interfaces.ua_basic
|
coq-community-math-classes/interfaces/universal_algebra
|
coq-community-math-classes
| 1,093 |
Fixpoint eval {V} {n: OpType} (vars: Vars A V) (t: Term V n) {struct t}: op_type A n := match t with | Var v a => vars a v | Op _ o => algebra_op o | App _ n a f p => eval vars f (eval vars p) end.
|
Coq.Lists.List MathClasses.interfaces.abstract_algebra MathClasses.misc.util MathClasses.theory.jections MathClasses.interfaces.ua_basic
|
coq-community-math-classes/interfaces/universal_algebra
|
coq-community-math-classes
| 1,094 |
Fixpoint app_tree {V} {o}: Term V o → op_type (Term0 V) o := match o with | ne_list.one _ => id | ne_list.cons _ _ => λ x y, app_tree (App _ _ _ x y) end.
|
Coq.Lists.List MathClasses.interfaces.abstract_algebra MathClasses.misc.util MathClasses.theory.jections MathClasses.interfaces.ua_basic
|
coq-community-math-classes/interfaces/universal_algebra
|
coq-community-math-classes
| 1,095 |
Definition eval_stmt (vars: Vars A nat): Statement → Prop := fix F (s: Statement) := match s with | Eq _ i => eval vars (fst i) = eval vars (snd i) | Impl a b => F a → F b | Ext P => P | Conj a b => F a ∧ F b | Disj a b => F a ∨ F b end.
|
Coq.Lists.List MathClasses.interfaces.abstract_algebra MathClasses.misc.util MathClasses.theory.jections MathClasses.interfaces.ua_basic
|
coq-community-math-classes/interfaces/universal_algebra
|
coq-community-math-classes
| 1,096 |
Definition boring_eval_entailment (vars: Vars A nat) (ee: EqEntailment): eval_stmt vars ee ↔ eval_stmt vars (entailment_as_conjunctive_statement ee).
|
Coq.Lists.List MathClasses.interfaces.abstract_algebra MathClasses.misc.util MathClasses.theory.jections MathClasses.interfaces.ua_basic
|
coq-community-math-classes/interfaces/universal_algebra
|
coq-community-math-classes
| 1,097 |
Record EquationalTheory := { et_sig:> Signature ; et_laws:> EqEntailment et_sig → Prop }.
|
Coq.Lists.List MathClasses.interfaces.abstract_algebra MathClasses.misc.util MathClasses.theory.jections MathClasses.interfaces.ua_basic
|
coq-community-math-classes/interfaces/universal_algebra
|
coq-community-math-classes
| 1,098 |
Definition OpType := ne_list Sorts.
|
Coq.Lists.List MathClasses.interfaces.abstract_algebra
|
coq-community-math-classes/interfaces/ua_basic
|
coq-community-math-classes
| 1,100 |
Definition result: OpType → Sorts := @ne_list.last _.
|
Coq.Lists.List MathClasses.interfaces.abstract_algebra
|
coq-community-math-classes/interfaces/ua_basic
|
coq-community-math-classes
| 1,101 |
Variable carrier: Sorts → Type.
|
Coq.Lists.List MathClasses.interfaces.abstract_algebra
|
coq-community-math-classes/interfaces/ua_basic
|
coq-community-math-classes
| 1,102 |
Fixpoint op_type (o: OpType): Type := match o with | ne_list.one a => carrier a | ne_list.cons a g => carrier a → op_type g end.
|
Coq.Lists.List MathClasses.interfaces.abstract_algebra
|
coq-community-math-classes/interfaces/ua_basic
|
coq-community-math-classes
| 1,103 |
Fixpoint op_type_equiv o: Equiv (op_type o) := match o with | ne_list.one _ => _: Equiv (carrier _) | ne_list.cons A g => (e A ==> op_type_equiv g)%signature end.
|
Coq.Lists.List MathClasses.interfaces.abstract_algebra
|
coq-community-math-classes/interfaces/ua_basic
|
coq-community-math-classes
| 1,104 |
Definition single_sorted_signature {Op: Set} (arities: Op → nat): Signature := Build_Signature unit Op (ne_list.replicate_Sn tt ∘ arities).
|
Coq.Lists.List MathClasses.interfaces.abstract_algebra
|
coq-community-math-classes/interfaces/ua_basic
|
coq-community-math-classes
| 1,105 |
Definition fold `{MonUnit M} `{SgOp M}: free M → M := extend id.
|
Coq.Lists.List MathClasses.interfaces.abstract_algebra MathClasses.theory.categories MathClasses.theory.forget_algebra MathClasses.theory.forget_variety MathClasses.theory.rings MathClasses.interfaces.universal_algebra MathClasses.interfaces.functors MathClasses.categories.setoids MathClasses.categories.varieties
|
coq-community-math-classes/interfaces/sequences
|
coq-community-math-classes
| 1,106 |
Definition nat_distance `{nd : NatDistance N} (x y : N) := match nat_distance_sig x y with | inl (n↾_) => n | inr (n↾_) => n end.
|
MathClasses.interfaces.abstract_algebra MathClasses.theory.categories MathClasses.varieties.semirings MathClasses.categories.varieties
|
coq-community-math-classes/interfaces/naturals
|
coq-community-math-classes
| 1,108 |
Definition int_abs `{ia : IntAbs} (x : Z) : N := match int_abs_sig x with | inl (n↾_) => n | inr (n↾_) => n end.
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.naturals MathClasses.theory.categories MathClasses.categories.varieties
|
coq-community-math-classes/interfaces/integers
|
coq-community-math-classes
| 1,110 |
Definition int_to_nat `{Zero N} `{ia : IntAbs} (x : Z) : N := match int_abs_sig x with | inl (n↾_) => n | inr (n↾_) => 0 end.
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.naturals MathClasses.theory.categories MathClasses.categories.varieties
|
coq-community-math-classes/interfaces/integers
|
coq-community-math-classes
| 1,111 |
Definition id {A : Type} (a : A) := a.
|
MathClasses.theory.CoqStreams Coq.Classes.Morphisms Coq.Setoids.Setoid Coq.Program.Program Coq.Unicode.Utf8 Coq.Unicode.Utf8_core MathClasses.misc.stdlib_hints
|
coq-community-math-classes/interfaces/canonical_names
|
coq-community-math-classes
| 1,112 |
Definition ext_equiv `{Equiv A} `{Equiv B} : Equiv (A → B) := ((=) ==> (=))%signature.
|
MathClasses.theory.CoqStreams Coq.Classes.Morphisms Coq.Setoids.Setoid Coq.Program.Program Coq.Unicode.Utf8 Coq.Unicode.Utf8_core MathClasses.misc.stdlib_hints
|
coq-community-math-classes/interfaces/canonical_names
|
coq-community-math-classes
| 1,113 |
Definition sig_equiv `{Equiv A} (P: A → Prop) : Equiv (sig P) := λ x y, `x = `y.
|
MathClasses.theory.CoqStreams Coq.Classes.Morphisms Coq.Setoids.Setoid Coq.Program.Program Coq.Unicode.Utf8 Coq.Unicode.Utf8_core MathClasses.misc.stdlib_hints
|
coq-community-math-classes/interfaces/canonical_names
|
coq-community-math-classes
| 1,114 |
Definition sigT_equiv `{Equiv A} (P: A → Type) : Equiv (sigT P) := λ a b, projT1 a = projT1 b.
|
MathClasses.theory.CoqStreams Coq.Classes.Morphisms Coq.Setoids.Setoid Coq.Program.Program Coq.Unicode.Utf8 Coq.Unicode.Utf8_core MathClasses.misc.stdlib_hints
|
coq-community-math-classes/interfaces/canonical_names
|
coq-community-math-classes
| 1,115 |
Definition sig_apart `{Apart A} (P: A → Prop) : Apart (sig P) := λ x y, `x ≶ `y.
|
MathClasses.theory.CoqStreams Coq.Classes.Morphisms Coq.Setoids.Setoid Coq.Program.Program Coq.Unicode.Utf8 Coq.Unicode.Utf8_core MathClasses.misc.stdlib_hints
|
coq-community-math-classes/interfaces/canonical_names
|
coq-community-math-classes
| 1,116 |
Definition ApartZero R `{Zero R} `{Apart R} := sig (≶ zero).
|
MathClasses.theory.CoqStreams Coq.Classes.Morphisms Coq.Setoids.Setoid Coq.Program.Program Coq.Unicode.Utf8 Coq.Unicode.Utf8_core MathClasses.misc.stdlib_hints
|
coq-community-math-classes/interfaces/canonical_names
|
coq-community-math-classes
| 1,117 |
Definition NonNeg R `{Zero R} `{Le R} := sig (le zero).
|
MathClasses.theory.CoqStreams Coq.Classes.Morphisms Coq.Setoids.Setoid Coq.Program.Program Coq.Unicode.Utf8 Coq.Unicode.Utf8_core MathClasses.misc.stdlib_hints
|
coq-community-math-classes/interfaces/canonical_names
|
coq-community-math-classes
| 1,118 |
Definition Pos R `{Zero R} `{Equiv R} `{Lt R} := sig (lt zero).
|
MathClasses.theory.CoqStreams Coq.Classes.Morphisms Coq.Setoids.Setoid Coq.Program.Program Coq.Unicode.Utf8 Coq.Unicode.Utf8_core MathClasses.misc.stdlib_hints
|
coq-community-math-classes/interfaces/canonical_names
|
coq-community-math-classes
| 1,119 |
Definition NonPos R `{Zero R} `{Le R} := sig (λ y, le y zero).
|
MathClasses.theory.CoqStreams Coq.Classes.Morphisms Coq.Setoids.Setoid Coq.Program.Program Coq.Unicode.Utf8 Coq.Unicode.Utf8_core MathClasses.misc.stdlib_hints
|
coq-community-math-classes/interfaces/canonical_names
|
coq-community-math-classes
| 1,120 |
Definition abs `{Abs A} := λ x : A, ` (abs_sig x).
|
MathClasses.theory.CoqStreams Coq.Classes.Morphisms Coq.Setoids.Setoid Coq.Program.Program Coq.Unicode.Utf8 Coq.Unicode.Utf8_core MathClasses.misc.stdlib_hints
|
coq-community-math-classes/interfaces/canonical_names
|
coq-community-math-classes
| 1,121 |
Record Object := object { obj:> Type ; Arrows_inst: Arrows obj ; Equiv_inst: ∀ x y: obj, Equiv (x ⟶ y) ; CatId_inst: CatId obj ; CatComp_inst: CatComp obj ; Category_inst: Category obj }.
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.functors MathClasses.theory.categories
|
coq-community-math-classes/categories/JMcat
|
coq-community-math-classes
| 1,122 |
Record Arrow (x y: Object): Type := arrow { map_obj:> obj x → obj y ; Fmap_inst: Fmap map_obj ; Functor_inst: Functor map_obj _ }.
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.functors MathClasses.theory.categories
|
coq-community-math-classes/categories/JMcat
|
coq-community-math-classes
| 1,123 |
Variables (w x y z: Object) (a: w ⟶ x) (b: x ⟶ y) (c: y ⟶ z).
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.functors MathClasses.theory.categories
|
coq-community-math-classes/categories/categories
|
coq-community-math-classes
| 1,126 |
Record Object A `{Arrows A} `{∀ x y : A, Equiv (x ⟶ y)} `{!CatId A} `{!CatComp A} B `{Arrows B} `{∀ x y : B, Equiv (x ⟶ y)} `{!CatId B} `{!CatComp B} : Type := object { map_obj:> A → B ; Fmap_inst:> Fmap map_obj ; Functor_inst: Functor map_obj _ }.
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.functors MathClasses.theory.categories
|
coq-community-math-classes/categories/functors
|
coq-community-math-classes
| 1,127 |
Record Arrow `{Arrows A} `{∀ x y : A, Equiv (x ⟶ y)} `{!CatId A} `{!CatComp A} `{Arrows B} `{∀ x y : B, Equiv (x ⟶ y)} `{!CatId B} `{!CatComp B} (F G : Object A B) : Type := arrow { eta:> map_obj F ⇛ map_obj G ; NaturalTransformation_inst: NaturalTransformation eta }.
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.functors MathClasses.theory.categories
|
coq-community-math-classes/categories/functors
|
coq-community-math-classes
| 1,128 |
Record Object (et: EquationalTheory) : Type := object { variety_carriers:> sorts et → Type ; variety_equiv: ∀ a, Equiv (variety_carriers a) ; variety_ops: AlgebraOps et variety_carriers ; variety_proof: InVariety et variety_carriers }.
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.universal_algebra MathClasses.theory.ua_homomorphisms
|
coq-community-math-classes/categories/varieties
|
coq-community-math-classes
| 1,129 |
Definition forget (O: Object) : setoids.Object := setoids.object O.
|
MathClasses.interfaces.abstract_algebra MathClasses.theory.categories MathClasses.orders.maps MathClasses.interfaces.orders MathClasses.orders.orders MathClasses.interfaces.functors
|
coq-community-math-classes/categories/orders
|
coq-community-math-classes
| 1,131 |
Definition Object := ∀ i, O i.
|
MathClasses.interfaces.abstract_algebra Coq.Logic.ChoiceFacts MathClasses.interfaces.functors MathClasses.theory.categories MathClasses.categories.categories
|
coq-community-math-classes/categories/product
|
coq-community-math-classes
| 1,132 |
Definition e (x y: Object): Equiv (x ⟶ y) := λ f g, ∀ i, f i = g i.
|
MathClasses.interfaces.abstract_algebra Coq.Logic.ChoiceFacts MathClasses.interfaces.functors MathClasses.theory.categories MathClasses.categories.categories
|
coq-community-math-classes/categories/product
|
coq-community-math-classes
| 1,133 |
Variables (C: categories.Object) (X: ∀ i, C ⟶ ith_obj i).
|
MathClasses.interfaces.abstract_algebra Coq.Logic.ChoiceFacts MathClasses.interfaces.functors MathClasses.theory.categories MathClasses.categories.categories
|
coq-community-math-classes/categories/product
|
coq-community-math-classes
| 1,134 |
Record Object (sign: Signature) : Type := object { algebra_carriers:> sorts sign → Type ; algebra_equiv: ∀ a, Equiv (algebra_carriers a) ; algebra_ops: AlgebraOps sign algebra_carriers ; algebra_proof: Algebra sign algebra_carriers }.
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.universal_algebra MathClasses.theory.ua_homomorphisms MathClasses.theory.categories
|
coq-community-math-classes/categories/algebras
|
coq-community-math-classes
| 1,135 |
Definition fmap_op: @Fmap _ flipA _ flipA F := fun v w => @fmap _ _ _ _ F _ w v.
|
Coq.Relations.Relation_Definitions MathClasses.interfaces.abstract_algebra MathClasses.theory.categories MathClasses.interfaces.functors
|
coq-community-math-classes/categories/dual
|
coq-community-math-classes
| 1,137 |
Definition Empty_map {A: Empty_set → Type} : ∀ x : Empty_set, A x := λ x, match x with end.
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.functors
|
coq-community-math-classes/categories/empty
|
coq-community-math-classes
| 1,138 |
Definition sort (x y: A) : A * A := if decide_rel (≤) x y then (x, y) else (y, x).
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders MathClasses.orders.orders MathClasses.orders.lattices MathClasses.theory.setoids
|
coq-community-math-classes/orders/minmax
|
coq-community-math-classes
| 1,139 |
Definition default_join_sl_le `{JoinSemiLattice L} : Le L := λ x y, x ⊔ y = y.
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders MathClasses.orders.maps MathClasses.theory.lattices
|
coq-community-math-classes/orders/lattices
|
coq-community-math-classes
| 1,140 |
Definition default_meet_sl_le `{MeetSemiLattice L} : Le L := λ x y, x ⊓ y = x.
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders MathClasses.orders.maps MathClasses.theory.lattices
|
coq-community-math-classes/orders/lattices
|
coq-community-math-classes
| 1,141 |
Definition lt_dec_slow `{!TrivialApart A} `{∀ x y, Decision (x ≤ y)} : ∀ x y, Decision (x < y).
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders MathClasses.theory.strong_setoids
|
coq-community-math-classes/orders/orders
|
coq-community-math-classes
| 1,142 |
Definition dec_lt: Lt A := λ x y, x ≤ y ∧ x ≠ y.
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders MathClasses.theory.strong_setoids
|
coq-community-math-classes/orders/orders
|
coq-community-math-classes
| 1,143 |
Definition pointwise_dependent_relation: relation (∀ a, B a) := λ f f', ∀ a, R _ (f a) (f' a).
|
Coq.Program.Program Coq.Classes.Morphisms Coq.Setoids.Setoid MathClasses.interfaces.canonical_names
|
coq-community-math-classes/misc/util
|
coq-community-math-classes
| 1,144 |
Definition iffT (A B: Type): Type := prod (A → B) (B → A).
|
Coq.Program.Program Coq.Classes.Morphisms Coq.Setoids.Setoid MathClasses.interfaces.canonical_names
|
coq-community-math-classes/misc/util
|
coq-community-math-classes
| 1,145 |
Definition uncurry {A B C} (f: A → B → C) (p: A * B): C := f (fst p) (snd p).
|
Coq.Program.Program Coq.Classes.Morphisms Coq.Setoids.Setoid MathClasses.interfaces.canonical_names
|
coq-community-math-classes/misc/util
|
coq-community-math-classes
| 1,146 |
Definition is_sole `{Equiv T} (P: T → Prop) (x: T) : Prop := P x ∧ ∀ y, P y → y = x.
|
Coq.Program.Program Coq.Classes.Morphisms Coq.Setoids.Setoid MathClasses.interfaces.canonical_names
|
coq-community-math-classes/misc/util
|
coq-community-math-classes
| 1,147 |
Definition DN (T: Type): Prop := (T → False) → False.
|
Coq.Program.Program Coq.Classes.Morphisms Coq.Setoids.Setoid MathClasses.interfaces.canonical_names
|
coq-community-math-classes/misc/util
|
coq-community-math-classes
| 1,148 |
Definition is_Some `(x : option A) := match x with | None => False | Some _ => True end.
|
Coq.Program.Program Coq.Classes.Morphisms Coq.Setoids.Setoid MathClasses.interfaces.canonical_names
|
coq-community-math-classes/misc/util
|
coq-community-math-classes
| 1,149 |
Definition is_None `(x : option A) := match x with | None => True | Some _ => False end.
|
Coq.Program.Program Coq.Classes.Morphisms Coq.Setoids.Setoid MathClasses.interfaces.canonical_names
|
coq-community-math-classes/misc/util
|
coq-community-math-classes
| 1,150 |
Definition bool_decide (P : Prop) `{dec : !Decision P} : bool := if dec then true else false.
|
MathClasses.interfaces.canonical_names MathClasses.misc.util
|
coq-community-math-classes/misc/decision
|
coq-community-math-classes
| 1,151 |
Definition decide_rel `(R : A → B → Prop) {dec : ∀ x y, Decision (R x y)} (x : A) (y : B) : Decision (R x y) := dec x y.
|
MathClasses.interfaces.canonical_names MathClasses.misc.util
|
coq-community-math-classes/misc/decision
|
coq-community-math-classes
| 1,152 |
Definition bool_decide_rel `(R : relation A) {dec : ∀ x y, Decision (R x y)} : A → A → bool := λ x y, if dec x y then true else false.
|
MathClasses.interfaces.canonical_names MathClasses.misc.util
|
coq-community-math-classes/misc/decision
|
coq-community-math-classes
| 1,153 |
Fixpoint root_loop (x : Dyadic Z) (n : nat) : Dyadic Z * Dyadic Z := match n with | O => (x, 0) | S n => let (r, s) := root_loop x n in if decide_rel (≤) (s + 1) r then ((r - (s + 1)) ≪ 2, (s + 2) ≪ 1) else (r ≪ 2, s ≪ 1) end.
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.integers MathClasses.interfaces.additional_operations MathClasses.implementations.dyadics MathClasses.implementations.fast_integers
|
coq-community-math-classes/misc/benchmarks_nobuild
|
coq-community-math-classes
| 1,154 |
Definition fast_root_loop := root_loop (Z:=fastZ).
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.integers MathClasses.interfaces.additional_operations MathClasses.implementations.dyadics MathClasses.implementations.fast_integers
|
coq-community-math-classes/misc/benchmarks_nobuild
|
coq-community-math-classes
| 1,155 |
Definition BigD_0 : bigD := (0 ▼ 0).
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.integers MathClasses.interfaces.additional_operations MathClasses.implementations.dyadics MathClasses.implementations.fast_integers BigZ
|
coq-community-math-classes/misc/benchmarks_nobuild
|
coq-community-math-classes
| 1,156 |
Definition BigD_1 : bigD := (1 ▼ 0).
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.integers MathClasses.interfaces.additional_operations MathClasses.implementations.dyadics MathClasses.implementations.fast_integers BigZ
|
coq-community-math-classes/misc/benchmarks_nobuild
|
coq-community-math-classes
| 1,157 |
Definition BigD_2 : bigD := (2 ▼ 0).
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.integers MathClasses.interfaces.additional_operations MathClasses.implementations.dyadics MathClasses.implementations.fast_integers BigZ
|
coq-community-math-classes/misc/benchmarks_nobuild
|
coq-community-math-classes
| 1,158 |
Definition BigD_plus (x y : bigD) : bigD := match BigZ.compare (expo x) (expo y) with | Gt => BigZ.shiftl (mant x) (expo x - expo y) + mant y ▼ BigZ.min (expo x) (expo y) | _ => mant x + BigZ.shiftl (mant y) (expo y - expo x) ▼ BigZ.min (expo x) (expo y) end.
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.integers MathClasses.interfaces.additional_operations MathClasses.implementations.dyadics MathClasses.implementations.fast_integers BigZ
|
coq-community-math-classes/misc/benchmarks_nobuild
|
coq-community-math-classes
| 1,159 |
Definition BigD_opp (x : bigD) : bigD := -mant x ▼ expo x.
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.integers MathClasses.interfaces.additional_operations MathClasses.implementations.dyadics MathClasses.implementations.fast_integers BigZ
|
coq-community-math-classes/misc/benchmarks_nobuild
|
coq-community-math-classes
| 1,160 |
Definition BigD_mult (x y : bigD) : bigD := mant x * mant y ▼ expo x + expo y.
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.integers MathClasses.interfaces.additional_operations MathClasses.implementations.dyadics MathClasses.implementations.fast_integers BigZ
|
coq-community-math-classes/misc/benchmarks_nobuild
|
coq-community-math-classes
| 1,161 |
Definition BigD_shiftl (x : bigD) (n : bigZ) : bigD := mant x ▼ expo x + n.
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.integers MathClasses.interfaces.additional_operations MathClasses.implementations.dyadics MathClasses.implementations.fast_integers BigZ
|
coq-community-math-classes/misc/benchmarks_nobuild
|
coq-community-math-classes
| 1,162 |
Definition BigD_compare (x y : bigD) : comparison := match BigZ.compare (expo x) (expo y) with | Gt => BigZ.compare (BigZ.shiftl (mant x) (expo x - expo y)) (mant y) | _ => BigZ.compare (mant x) (BigZ.shiftl (mant y) (expo y - expo x)) end.
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.integers MathClasses.interfaces.additional_operations MathClasses.implementations.dyadics MathClasses.implementations.fast_integers BigZ
|
coq-community-math-classes/misc/benchmarks_nobuild
|
coq-community-math-classes
| 1,163 |
Fixpoint root_loop_alt (x : bigD) (n : nat) : bigD * bigD := match n with | O => (x, BigD_0) | S n => let (r, s) := root_loop_alt x n in match BigD_compare (BigD_plus s BigD_1) r with | Gt => (BigD_shiftl r 2, BigD_shiftl s 1) | _ => (BigD_shiftl (BigD_plus r (BigD_opp (BigD_plus s BigD_1))) 2, BigD_shiftl (BigD_plus s BigD_2) 1) end end.
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.integers MathClasses.interfaces.additional_operations MathClasses.implementations.dyadics MathClasses.implementations.fast_integers BigZ
|
coq-community-math-classes/misc/benchmarks_nobuild
|
coq-community-math-classes
| 1,164 |
Definition BigD_4 : bigD := (4 ▼ 0).
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.integers MathClasses.interfaces.additional_operations MathClasses.implementations.dyadics MathClasses.implementations.fast_integers BigZ
|
coq-community-math-classes/misc/benchmarks_nobuild
|
coq-community-math-classes
| 1,165 |
Fixpoint root_loop_alt_mult (x : bigD) (n : nat) : bigD * bigD := match n with | O => (x, BigD_0) | S n => let (r, s) := root_loop_alt_mult x n in match BigD_compare (BigD_plus s BigD_1) r with | Gt => (BigD_mult BigD_4 r, BigD_mult BigD_2 s) | _ => (BigD_mult BigD_4 (BigD_plus r (BigD_opp (BigD_plus s BigD_1))), BigD_mult BigD_2 (BigD_plus s BigD_2)) end end.
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.integers MathClasses.interfaces.additional_operations MathClasses.implementations.dyadics MathClasses.implementations.fast_integers BigZ
|
coq-community-math-classes/misc/benchmarks_nobuild
|
coq-community-math-classes
| 1,166 |
Fixpoint eval (e: Expr): nat := match e with | Plus a b => eval a + eval b | Mult a b => eval a * eval b | Zero => 0 | One => 1 end.
|
Coq.Classes.Morphisms Coq.Program.Program Coq.Unicode.Utf8
|
coq-community-math-classes/quote/classquote
|
coq-community-math-classes
| 1,167 |
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