Proof Assistant Projects
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Digesting proof assistant libraries for AI ingestion. • 84 items • Updated • 3
fact stringlengths 9 2.92k | type stringclasses 20
values | library stringclasses 6
values | imports listlengths 1 4 | filename stringclasses 63
values | symbolic_name stringlengths 1 35 | docstring stringclasses 1
value |
|---|---|---|---|---|---|---|
option_mul {T : Mul.type} (o1 o2 : option T) : option T := match o1, o2 with | Some n, Some m => Some (mul n m) | _, _ => None end. HB.instance Definition _ (T : Mul.type) := HasMul.Build (option T) option_mul. | Definition | examples | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | examples/hulk.v | option_mul | |
option_square {T : Sq.type} (o : option T) : option T := match o with | Some n => Some (sq n) | None => None end. HB.instance Definition _ (T : Sq.type) := HasSq.Build (option T) option_square. (* Now we mix the two unrelated structures by building Sq out of Mul. *** This breaks Non Forgetful Inheritance *** https://ma... | Definition | examples | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | examples/hulk.v | option_square | |
sq_mul (V : Mul.type) (v : V) : sq v = mul v v. Proof. by reflexivity. Qed. | Lemma | examples | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | examples/hulk.v | sq_mul | |
problem (W : Mul.type) (w : option W) : sq w = mul w w. Proof. Fail reflexivity. (* What? It used to work! *) Fail rewrite sq_mul. (* Lemmas don't cross the container either! *) (* Let's investigate *) rewrite /mul/= /sq/=. (* As we expect, we are on the option type. In the LHS it is the Sq built using the NFI instance... | Lemma | examples | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | examples/hulk.v | problem | |
option_mul {T : Mul.type} (o1 o2 : option T) : option T := match o1, o2 with | Some n, Some m => Some (mul n m) | _, _ => None end. HB.instance Definition _ (T : Mul.type) := HasMul.Build (option T) option_mul. | Definition | examples | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | examples/hulk.v | option_mul | |
option_square {T : Sq.type} (o : option T) : option T := match o with | Some n => Some (sq n) | None => None end. | Definition | examples | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | examples/hulk.v | option_square | |
option_sq_mul {T : Sq.type} (o : option T) : option_square o = mul o o. Proof. by rewrite /option_square; case: o => [x|//]; rewrite sq_mul. Qed. HB.instance Definition _ (T : Sq.type) := HasSq.Build (option T) option_square option_sq_mul. | Lemma | examples | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | examples/hulk.v | option_sq_mul | |
problem (W : Sq.type) (w : option W) : sq w = mul w w. Proof. by rewrite sq_mul. Qed. | Lemma | examples | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | examples/hulk.v | problem | |
link {xT T : Type} {f : xT -> T} {g : T -> xT} (canfg : forall x, f (g x) = x) := T. (* (link canfg) is convertible to T *) (* We explain HB how to transfer Equality over link *) | Definition | examples | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | examples/hulk.v | link | |
link_eqtest (x y : T) : bool := eqtest (g x) (g y). | Definition | examples | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | examples/hulk.v | link_eqtest | |
link_eqOK (x y : T) : reflect (x = y) (link_eqtest x y). Proof. rewrite /link_eqtest; case: (eqOK (g x) (g y)) => [E|abs]. by constructor; rewrite -[x]canfg -[y]canfg E canfg. by constructor=> /(f_equal g)/abs. Qed. (* (link canfg) is now an Equality instance *) HB.instance Definition link_HasEqDec := HasEqDec.Build (l... | Lemma | examples | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | examples/hulk.v | link_eqOK | |
link_def : link canfg := f def. | Definition | examples | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | examples/hulk.v | link_def | |
link_all_def x : eqtest x link_def = true. Proof. rewrite /link_def; have /eqOK <- := all_def (g x). by rewrite canfg; case: (eqOK x x). Qed. (* (link canfg) is now a Signleton instance *) HB.instance Definition _ := IsContractible.Build (link canfg) link_def link_all_def. | Lemma | examples | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | examples/hulk.v | link_all_def | |
B : Type. | Axiom | examples | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | examples/hulk.v | B | |
testB : B -> B -> bool. | Axiom | examples | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | examples/hulk.v | testB | |
testOKB : forall x y, reflect (x = y) (testB x y). HB.instance Definition _ := HasEqDec.Build B testB testOKB. | Axiom | examples | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | examples/hulk.v | testOKB | |
defB : B. | Axiom | examples | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | examples/hulk.v | defB | |
all_defB : forall x, eqtest x defB = true. HB.instance Definition _ := IsContractible.Build B defB all_defB. (* Now we copy all instances from B to A via link *) | Axiom | examples | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | examples/hulk.v | all_defB | |
A : Type. | Axiom | examples | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | examples/hulk.v | A | |
f : B -> A. | Axiom | examples | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | examples/hulk.v | f | |
g : A -> B. | Axiom | examples | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | examples/hulk.v | g | |
canfg : forall x, f (g x) = x. (* We take all the instances up to Singleton on (link canfg) and we copy them on A. Recall (link canfg) is convertible to A *) HB.instance Definition _ := Singleton.copy A (link canfg). HB.about A. (* both Equality and Singleton have been copied *) | Axiom | examples | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | examples/hulk.v | canfg | |
new_concept := 999999. | Definition | examples | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | examples/hulk.v | new_concept | |
test x : new_concept ^ x ^ new_concept = x ^ new_concept ^ new_concept. Proof. (* this goal is not trivial, and maybe even false, but you may call some automation on it anyway *) Time Fail reflexivity. (* takes 7s, note that both by and // call reflexivity *) Abort. | Lemma | examples | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | examples/hulk.v | test | |
test x : new_concept ^ x ^ new_concept = x ^ new_concept ^ new_concept. Time Fail reflexivity. (* takes 0s *) rewrite new_concept.unlock. Time Fail reflexivity. (* takes 7s, the original body is restored *) Abort. Print Module Type new_concept_Locked. Print Module new_concept. (* | Lemma | examples | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | examples/hulk.v | test | |
body : nat. | Parameter | examples | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | examples/hulk.v | body | |
unlock : body = 999999 | Parameter | examples | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | examples/hulk.v | unlock | |
new_concept := new_concept.body *) | Notation | examples | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | examples/hulk.v | new_concept | |
unlock_new_concept := Unlockable new_concept.unlock. | Canonical | examples | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | examples/hulk.v | unlock_new_concept | |
example (G : AbelianGrp.type) (x : G) : x + (- x) = - 0. Proof. by rewrite addrC addNr -[LHS](addNr zero) addrC add0r. Qed. | Lemma | examples | [
"From HB Require Import structures.",
"From Corelib Require Import ssreflect BinNums IntDef."
] | examples/readme.v | example | |
Z_add_assoc : forall x y z, Z.add x (Z.add y z) = Z.add (Z.add x y) z. | Axiom | examples | [
"From HB Require Import structures.",
"From Corelib Require Import ssreflect BinNums IntDef."
] | examples/readme.v | Z_add_assoc | |
Z_add_comm : forall x y, Z.add x y = Z.add y x. | Axiom | examples | [
"From HB Require Import structures.",
"From Corelib Require Import ssreflect BinNums IntDef."
] | examples/readme.v | Z_add_comm | |
Z_add_0_l : forall x, Z.add Z0 x = x. | Axiom | examples | [
"From HB Require Import structures.",
"From Corelib Require Import ssreflect BinNums IntDef."
] | examples/readme.v | Z_add_0_l | |
Z_add_opp_diag_l : forall x, Z.add (Z.opp x) x = Z0. HB.instance Definition Z_CoMoid := AddComoid_of_Type.Build Z Z0 Z.add Z_add_assoc Z_add_comm Z_add_0_l. HB.instance Definition Z_AbGrp := AbelianGrp_of_AddComoid.Build Z Z.opp Z_add_opp_diag_l. | Axiom | examples | [
"From HB Require Import structures.",
"From Corelib Require Import ssreflect BinNums IntDef."
] | examples/readme.v | Z_add_opp_diag_l | |
example2 (x : Z) : x + (- x) = - 0. Proof. by rewrite example. Qed. Check AbelianGrp.on Z. HB.graph "readme.dot". HB.about Z. | Lemma | examples | [
"From HB Require Import structures.",
"From Corelib Require Import ssreflect BinNums IntDef."
] | examples/readme.v | example2 | |
Search Blacklist "Builders_". | Add | HB | [
"From Corelib Require Import ssreflect ssrfun.",
"From elpi Require Import elpi.",
"From elpi.apps Require Import locker."
] | HB/structures.v | Search | |
Search Blacklist "__canonical__". | Add | HB | [
"From Corelib Require Import ssreflect ssrfun.",
"From elpi Require Import elpi.",
"From elpi.apps Require Import locker."
] | HB/structures.v | Search | |
Search Blacklist "__to__". | Add | HB | [
"From Corelib Require Import ssreflect ssrfun.",
"From elpi Require Import elpi.",
"From elpi.apps Require Import locker."
] | HB/structures.v | Search | |
Search Blacklist "_between_". | Add | HB | [
"From Corelib Require Import ssreflect ssrfun.",
"From elpi Require Import elpi.",
"From elpi.apps Require Import locker."
] | HB/structures.v | Search | |
Search Blacklist "_mixin". | Add | HB | [
"From Corelib Require Import ssreflect ssrfun.",
"From elpi Require Import elpi.",
"From elpi.apps Require Import locker."
] | HB/structures.v | Search | |
error_msg := NoMsg | IsNotCanonicallyA (x : Type). | Variant | HB | [
"From Corelib Require Import ssreflect ssrfun.",
"From elpi Require Import elpi.",
"From elpi.apps Require Import locker."
] | HB/structures.v | error_msg | |
unify T1 T2 (t1 : T1) (t2 : T2) (s : error_msg) := phantom T1 t1 -> phantom T2 t2. | Definition | HB | [
"From Corelib Require Import ssreflect ssrfun.",
"From elpi Require Import elpi.",
"From elpi.apps Require Import locker."
] | HB/structures.v | unify | |
id_phant {T} {t : T} (x : phantom T t) := x. | Definition | HB | [
"From Corelib Require Import ssreflect ssrfun.",
"From elpi Require Import elpi.",
"From elpi.apps Require Import locker."
] | HB/structures.v | id_phant | |
id_phant_disabled {T T'} {t : T} {t' : T'} (x : phantom T t) := Phantom T' t'. | Definition | HB | [
"From Corelib Require Import ssreflect ssrfun.",
"From elpi Require Import elpi.",
"From elpi.apps Require Import locker."
] | HB/structures.v | id_phant_disabled | |
nomsg : error_msg := NoMsg. | Definition | HB | [
"From Corelib Require Import ssreflect ssrfun.",
"From elpi Require Import elpi.",
"From elpi.apps Require Import locker."
] | HB/structures.v | nomsg | |
is_not_canonically_a x := IsNotCanonicallyA x. | Definition | HB | [
"From Corelib Require Import ssreflect ssrfun.",
"From elpi Require Import elpi.",
"From elpi.apps Require Import locker."
] | HB/structures.v | is_not_canonically_a | |
new {T} (x : T) := x. | Definition | HB | [
"From Corelib Require Import ssreflect ssrfun.",
"From elpi Require Import elpi.",
"From elpi.apps Require Import locker."
] | HB/structures.v | new | |
eta {T} (x : T) := x. | Definition | HB | [
"From Corelib Require Import ssreflect ssrfun.",
"From elpi Require Import elpi.",
"From elpi.apps Require Import locker."
] | HB/structures.v | eta | |
ignore {T} (x: T) := x. | Definition | HB | [
"From Corelib Require Import ssreflect ssrfun.",
"From elpi Require Import elpi.",
"From elpi.apps Require Import locker."
] | HB/structures.v | ignore | |
ignore_disabled {T T'} (x : T) (x' : T') := x'. (* ********************* structures ****************************** *) From elpi Require Import elpi. Register unify as hb.unify. Register id_phant as hb.id. Register id_phant_disabled as hb.id_disabled. Register ignore as hb.ignore. Register ignore_disabled as hb.ignore_d... | Definition | HB | [
"From Corelib Require Import ssreflect ssrfun.",
"From elpi Require Import elpi.",
"From elpi.apps Require Import locker."
] | HB/structures.v | ignore_disabled | |
indexed T := T (only parsing). Declare Scope HB_scope. | Notation | HB | [
"From Corelib Require Import ssreflect ssrfun.",
"From elpi Require Import elpi.",
"From elpi.apps Require Import locker."
] | HB/structures.v | indexed | |
aux_fact : .... HB.export aux_fact. ... HB.end. ... | Lemma | HB | [
"From Corelib Require Import ssreflect ssrfun.",
"From elpi Require Import elpi.",
"From elpi.apps Require Import locker."
] | HB/structures.v | aux_fact | |
error_msg := NoMsg | IsNotCanonicallyA (x : Type). | Variant | shim | [
"From Coq Require Import String ssreflect ssrfun."
] | shim/structures.v | error_msg | |
unify T1 T2 (t1 : T1) (t2 : T2) (s : error_msg) := phantom T1 t1 -> phantom T2 t2. | Definition | shim | [
"From Coq Require Import String ssreflect ssrfun."
] | shim/structures.v | unify | |
id_phant {T} {t : T} (x : phantom T t) := x. | Definition | shim | [
"From Coq Require Import String ssreflect ssrfun."
] | shim/structures.v | id_phant | |
nomsg : error_msg := NoMsg. | Definition | shim | [
"From Coq Require Import String ssreflect ssrfun."
] | shim/structures.v | nomsg | |
is_not_canonically_a x := IsNotCanonicallyA x. | Definition | shim | [
"From Coq Require Import String ssreflect ssrfun."
] | shim/structures.v | is_not_canonically_a | |
new {T} (x : T) := x. | Definition | shim | [
"From Coq Require Import String ssreflect ssrfun."
] | shim/structures.v | new | |
eta {T} (x : T) := x. | Definition | shim | [
"From Coq Require Import String ssreflect ssrfun."
] | shim/structures.v | eta | |
testTy := A | B. HB.mixin Record Stack1 T := { prop1 : unit }. HB.structure Definition JustStack1 := { T of Stack1 T }. HB.mixin Record Stack1Param R T := { prop2 : unit }. HB.structure Definition JustStack1Param R := { T of Stack1Param R T }. HB.mixin Record Stack2 T := { prop3 : unit }. HB.structure Definition JustSt... | Variant | tests | [
"From HB Require Import structures."
] | tests/bug_447.v | testTy | |
unit' := unit. HB.instance Definition _ := isInhab.Build unit' tt. Check Inhab.of unit'. Fail Check Inhab.of unit. HB.instance Definition _ := Inhab.copy unit unit'. Check Inhab.of unit. (* with params *) HB.mixin Record isInhabIf (b : bool) (T : Type) := { y : forall ph : phant T, (match b with true => T | false => un... | Definition | tests | [
"From Coq Require Import ssreflect ssrfun ssrbool.",
"From HB Require Import structures."
] | tests/class_for.v | unit' | |
bool' := bool. HB.instance Definition _ := isInhabIf.Build true bool' (fun=> false). Check InhabIf.of bool'. Fail Check InhabIf.of bool. HB.instance Definition _ := InhabIf.copy bool bool'. Check InhabIf.of bool. Check (y (Phant bool) : bool). | Definition | tests | [
"From Coq Require Import ssreflect ssrfun ssrbool.",
"From HB Require Import structures."
] | tests/class_for.v | bool' | |
test := [the C.type _ _ of T]. | Definition | tests | [
"From Corelib Require Import ssreflect ssrfun.",
"From HB Require Import structures."
] | tests/declare.v | test | |
test2 := [the C.type _ _ of T]. | Definition | tests | [
"From Corelib Require Import ssreflect ssrfun.",
"From HB Require Import structures."
] | tests/declare.v | test2 | |
copy : Type -> Type := id. HB.declare Context p T of hasABC p tt (copy T). | Definition | tests | [
"From Corelib Require Import ssreflect ssrfun.",
"From HB Require Import structures."
] | tests/declare.v | copy | |
test3 := [the C.type _ _ of copy T]. | Definition | tests | [
"From Corelib Require Import ssreflect ssrfun.",
"From HB Require Import structures."
] | tests/declare.v | test3 | |
comb A op := forall x : A, op (op x) = x. HB.mixin Record Foo A := { op : A -> A; ax : comb A op }. HB.structure Definition S1 := { A of Foo A }. Fail HB.structure Definition S2 := { A of Foo A }. | Definition | tests | [
"From HB Require Import structures."
] | tests/duplicate_structure.v | comb | |
x := (fun x : nat => true). HB.mixin Record m T := {x : T}. HB.factory Record f T := { x : T }. HB.builders Context T of f T. HB.instance Definition _ := m.Build T x. HB.end. | Notation | tests | [
"From HB Require Import structures."
] | tests/factory_when_notation.v | x | |
pred T := T -> bool. HB.mixin Record isPredNat (f : pred nat) := {}. HB.structure Definition PredNat := {f of isPredNat f}. | Definition | tests | [
"From HB Require Import structures."
] | tests/grefclass.v | pred | |
xxx := HB.pack_for AB.type T (hasB.Build T b) (hasA.Build T a). HB.instance Definition _ := AB.copy T xxx. HB.end. About hasAB.type. HB.factory Definition hasA' T := hasA T. About hasA'.type. | Definition | tests | [
"Require Import ssreflect ssrfun ssrbool.",
"From elpi Require Import elpi.",
"From HB Require Import structures."
] | tests/hb_pack.v | xxx | |
prop := Prop. HB.instance Definition Xprop := X_of_Type.Build prop. HB.instance Definition XSet := X_of_Type.Build Set. | Definition | tests | [
"From HB Require Import structures."
] | tests/issue284.v | prop | |
set := Set. HB.instance Definition Xset := X_of_Type.Build set. HB.instance Definition XType := X_of_Type.Build Type. | Definition | tests | [
"From HB Require Import structures."
] | tests/issue284.v | set | |
type := Type. HB.instance Definition Xtype := X_of_Type.Build type. | Definition | tests | [
"From HB Require Import structures."
] | tests/issue284.v | type | |
nat1 := nat. HB.lock Definition bar : nat1 := 3. HB.lock Definition baz n : nat := 3 + n. | Definition | tests | [
"From HB Require Import structures."
] | tests/lock.v | nat1 | |
bigbody : Type -> Type -> Type. | Axiom | tests | [
"From HB Require Import structures."
] | tests/lock.v | bigbody | |
bigop : forall R I : Type, R -> list I -> (I -> bigbody R I) -> R. HB.lock Definition big := bigop. | Axiom | tests | [
"From HB Require Import structures."
] | tests/lock.v | bigop | |
A T := { a : T; f : T -> T; p : forall x : T, f x = x -> True; q : forall h : f a = a, p _ h = p _ h; }. HB.structure Definition S := { T of A T }. About A.p. | Record | tests | [
"From HB Require Import structures."
] | tests/log_impargs_record.v | A | |
option_mul {T : Mul.type} (o1 o2 : option T) : option T := match o1, o2 with | Some n, Some m => Some (mul n m) | _, _ => None end. HB.instance Definition _ (T : Mul.type) := HasMul.Build (option T) option_mul. | Definition | tests | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | tests/non_forgetful_inheritance.v | option_mul | |
option_square {T : Sq.type} (o : option T) : option T := match o with | Some n => Some (sq n) | None => None end. HB.instance Definition _ (T : Sq.type) := HasSq.Build (option T) option_square. (* Now we mix the two unrelated structures by building Sq out of Mul. *** This breaks Forgetful Inheritance *** https://math-c... | Definition | tests | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | tests/non_forgetful_inheritance.v | option_square | |
sq_mul (V : Mul.type) (v : V) : sq v = mul v v. Proof. by reflexivity. Qed. | Lemma | tests | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | tests/non_forgetful_inheritance.v | sq_mul | |
problem (W : Mul.type) (w : option W) : sq w = mul w w. Proof. Fail reflexivity. (* What? It used to work! *) Fail rewrite sq_mul. (* Lemmas don't cross the container either! *) (* Let's investigate *) rewrite /mul/= /sq/=. (* As we expect, we are on the option type. In the LHS it is the Sq built using the NFI instance... | Lemma | tests | [
"From HB Require Import structures.",
"Require Import ssreflect ssrfun ssrbool."
] | tests/non_forgetful_inheritance.v | problem | |
to_AddComoid_of_TYPE := AddComoid_of_TYPE.Build A zero add addrA addrC add0r. HB.instance | Definition | tests | [
"From Coq Require Import ssreflect ssrfun.",
"From HB Require Import structures."
] | tests/packable.v | to_AddComoid_of_TYPE | |
to_Ring_of_AddComoid := Ring_of_AddComoid.Build A _ _ _ addNr mulrA mul1r mulr1 mulrDl mulrDr. HB.end. (* End change *) HB.structure Definition Ring := { A of Ring_of_TYPE A }. | Definition | tests | [
"From Coq Require Import ssreflect ssrfun.",
"From HB Require Import structures."
] | tests/packable.v | to_Ring_of_AddComoid | |
xxx := ABType T (hasB.Build T b) (hasA.Build T a). HB.instance Definition _ := AB.copy T xxx. HB.end. About hasAB.type. HB.factory Definition hasA' T := hasA T. About hasA'.type. | Definition | tests | [
"From Corelib Require Import ssreflect ssrfun.",
"From HB Require Import structures."
] | tests/short.v | xxx | |
pred T := T -> Prop. #[key="sub_sort"] HB.mixin Record is_SUB (T : Type) (P : pred T) (sub_sort : Type) := SubType { val : sub_sort -> T; Sub : forall x, P x -> sub_sort; Sub_rect : forall K (_ : forall x Px, K (@Sub x Px)) u, K u; SubK : forall x Px, val (@Sub x Px) = x }. HB.structure Definition SUB (T : Type) (P : p... | Definition | tests | [
"From HB Require Import structures."
] | tests/subtype.v | pred | |
xxx : P (default : T). HB.instance Definition SubInhabMix := is_inhab.Build sT (Sub (default : T) xxx). HB.end. | Axiom | tests | [
"From HB Require Import structures."
] | tests/subtype.v | xxx | |
ix : Type. | Axiom | tests | [
"From HB Require Import structures."
] | tests/test_CS_db_filtering.v | ix | |
vec T := ix -> T. | Definition | tests | [
"From HB Require Import structures."
] | tests/test_CS_db_filtering.v | vec | |
dual (T : Type) := T. | Definition | tests | [
"From HB Require Import structures."
] | tests/test_synthesis_params.v | dual | |
dd (d:unit) : unit. exact d. Qed. HB.instance Definition _ d (T : POrder.type d) := IsDualPOrdered.Build (dd d) (dual T) (fun x y => @le d T y x) (fun x y => @le d T y x). HB.instance Definition _ d (T : TPOrder.type d) := HasBottom.Build (dd d) (dual T) (@top _ T). HB.instance Definition _ d (T : BPOrder.type d) := Ha... | Definition | tests | [
"From HB Require Import structures."
] | tests/test_synthesis_params.v | dd | |
comb A op := forall x : A, op (op x) = x. HB.mixin Record Foo A := { op : A -> A; ax : comb A op }. HB.structure Definition S := { A of Foo A }. Set Printing All. | Definition | tests | [
"From HB Require Import structures."
] | tests/type_of_exported_ops.v | comb | |
test1 : True. Proof. pose proof @ax as H. match goal with | H : forall x : S.type, comb (S.sort x) op |- _ => trivial | H : ?T |- _ => fail "type of ax not as nice as expected:" T end. Qed. HB.mixin Record HasMul T := { mul : T -> T -> T; mulC: forall x y : T, mul x y = mul y x; mulA: forall x y z : T, mul x (mul y z) ... | Lemma | tests | [
"From HB Require Import structures."
] | tests/type_of_exported_ops.v | test1 | |
test2 : True. Proof. pose proof @mulA as H. match goal with | H : forall s : Mul.type, forall x y z : Mul.sort s, mul x (mul y z) = mul (mul x y) z |- _ => trivial | H : ?T |- _ => fail "type of mulA not as nice as expected:" T end. Qed. | Lemma | tests | [
"From HB Require Import structures."
] | tests/type_of_exported_ops.v | test2 | |
_ := AddAG_of_TYPE.Build Z 0%Z Z.add Z.opp Z.add_assoc Z.add_comm Z.add_0_l Z.add_opp_diag_l. HB.instance | Definition | tests_stdlib | [
"From Coq Require Import ZArith ssrfun ssreflect.",
"From HB Require Import structures.",
"From HB Require Import demo1."
] | tests_stdlib/about.v | _ | |
_ := Ring_of_TYPE.Build Z 0%Z 1%Z Z.add Z.opp Z.mul Z.add_assoc Z.add_comm Z.add_0_l Z.add_opp_diag_l Z.mul_assoc Z.mul_1_l Z.mul_1_r Z.mul_add_distr_r Z.mul_add_distr_l. (* mixin *) HB.about AddMonoid_of_TYPE. (* mixin constructor *) HB.about AddMonoid_of_TYPE.Build. (* structure *) HB.about AddAG.type. (* class *) HB... | Definition | tests_stdlib | [
"From Coq Require Import ZArith ssrfun ssreflect.",
"From HB Require Import structures.",
"From HB Require Import demo1."
] | tests_stdlib/about.v | _ | |
addr0 : right_id (@zero R) add. Proof. by move=> x; rewrite addrC add0r. Qed. HB.export addr0. | Lemma | tests_stdlib | [
"From Coq Require Import ssreflect ssrfun ZArith.",
"From HB Require Import structures."
] | tests_stdlib/exports.v | addr0 | |
addrN : right_inverse (@zero R) opp add. Proof. by move=> x; rewrite addrC addNr. Qed. | Lemma | tests_stdlib | [
"From Coq Require Import ssreflect ssrfun ZArith.",
"From HB Require Import structures."
] | tests_stdlib/exports.v | addrN | |
subrr x : x - x = 0. Proof. by rewrite addrN. Qed. | Lemma | tests_stdlib | [
"From Coq Require Import ssreflect ssrfun ZArith.",
"From HB Require Import structures."
] | tests_stdlib/exports.v | subrr | |
addrNK x y : x + y - y = x. Proof. by rewrite -addrA subrr addr0. Qed. | Lemma | tests_stdlib | [
"From Coq Require Import ssreflect ssrfun ZArith.",
"From HB Require Import structures."
] | tests_stdlib/exports.v | addrNK | |
addrNK := addrNK. HB.export addrNK. HB.end. | Definition | tests_stdlib | [
"From Coq Require Import ssreflect ssrfun ZArith.",
"From HB Require Import structures."
] | tests_stdlib/exports.v | addrNK |
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Coq-HierarchyBuilder
Structured dataset from Hierarchy Builder — High-level commands for packed class hierarchies.
752 declarations extracted from Coq source files.
Applications
- Training language models on formal proofs
- Fine-tuning theorem provers
- Retrieval-augmented generation for proof assistants
- Learning proof embeddings and representations
Source
- Repository: https://github.com/math-comp/hierarchy-builder
Schema
| Column | Type | Description |
|---|---|---|
| fact | string | Declaration body |
| type | string | Lemma, Definition, Theorem, etc. |
| library | string | Source module |
| imports | list | Required imports |
| filename | string | Source file path |
| symbolic_name | string | Identifier |
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