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phanerozoic
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Coq-QuickChick

statement stringlengths 1 1.39k	proof stringlengths 0 4.58k	type stringclasses 21 values	symbolic_name stringlengths 1 49	library stringclasses 18 values	filename stringclasses 100 values	imports listlengths 0 26	deps listlengths 0 23	docstring stringlengths 0 2.01k	source_url stringclasses 1 value	commit stringclasses 1 value
Tree	:= \| Leaf : Tree \| Node : nat -> Tree -> Tree -> Tree.	Inductive	Tree	benchmarks.BST	benchmarks/BST/BST.v	[ "QuickChick", "QcNotation", "List", "ListNotations", "String", "ExtLib", "Monad", "MonadNotation" ]	[ "nat" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
between : nat -> nat -> nat -> Prop	:= \| between_n : forall n m, le n m -> between n (S n) (S (S m)) \| between_S : forall n m o, between n m o -> between n (S m) (S o).	Inductive	between	benchmarks.BST	benchmarks/BST/BST.v	[ "QuickChick", "QcNotation", "List", "ListNotations", "String", "ExtLib", "Monad", "MonadNotation" ]	[ "le", "nat" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
bst : nat -> nat -> Tree -> Prop	:= \| bst_leaf : forall lo hi, bst lo hi Leaf \| bst_node : forall lo hi x l r, between lo x hi -> bst lo x l -> bst x hi r -> bst lo hi (Node x l r).	Inductive	bst	benchmarks.BST	benchmarks/BST/BST.v	[ "QuickChick", "QcNotation", "List", "ListNotations", "String", "ExtLib", "Monad", "MonadNotation" ]	[ "Tree", "between", "nat" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
gen_bst (s : nat) (lo hi : nat) : G Tree	:= match s with \| O => ret Leaf \| S s' => freq [(1, ret Leaf) ;(if hi - lo < 2? then 0 else s, x <- choose (lo+1, hi-1);; l <- gen_bst s' lo x;; r <- gen_bst s' x hi;; ret (Node x l r))] end.	Fixpoint	gen_bst	benchmarks.BST	benchmarks/BST/BST.v	[ "QuickChick", "QcNotation", "List", "ListNotations", "String", "ExtLib", "Monad", "MonadNotation" ]	[ "Tree", "choose", "nat" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
is_bst (lo hi : nat) (t : Tree)	:= match t with \| Leaf => true \| Node x l r => andb ((lo < x /\ x < hi) ?) (andb (is_bst lo x l) (is_bst x hi r)) end.	Fixpoint	is_bst	benchmarks.BST	benchmarks/BST/BST.v	[ "QuickChick", "QcNotation", "List", "ListNotations", "String", "ExtLib", "Monad", "MonadNotation" ]	[ "Tree", "andb", "nat" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
insert (x : nat) (t : Tree)	:= match t with \| Leaf => Node x Leaf Leaf \| Node y l r => (! ) if x < y ? then (!! IF-LE-L ) (! if x <= y ? then ) Node y (insert x l) r (! ) else if x > y ? then (!! IF-LE-R ) (! else if x >= y ? then ) Node y l (insert x r) else...	Fixpoint	insert	benchmarks.BST	benchmarks/BST/BST.v	[ "QuickChick", "QcNotation", "List", "ListNotations", "String", "ExtLib", "Monad", "MonadNotation" ]	[ "Tree", "nat" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
insert_bst	:= forAll (gen_bst 5 0 10) (fun t => forAll (choose (1, 9)) (fun x => is_bst 0 10 (insert x t))).	Definition	insert_bst	benchmarks.BST	benchmarks/BST/BST.v	[ "QuickChick", "QcNotation", "List", "ListNotations", "String", "ExtLib", "Monad", "MonadNotation" ]	[ "choose", "forAll", "gen_bst", "insert", "is_bst" ]	! Section base	https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
insert_bst_derived_checker	:= forAll (gen_bst 5 0 10) (fun t => forAll (choose (1, 9)) (fun x => bst 0 10 (insert x t) ?? 10)).	Definition	insert_bst_derived_checker	benchmarks.BST	benchmarks/BST/BST.v	[ "QuickChick", "QcNotation", "List", "ListNotations", "String", "ExtLib", "Monad", "MonadNotation" ]	[ "bst", "choose", "forAll", "gen_bst", "insert" ]	! Section derived-dec	https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
insert_bst_derived_gen	:= forAllMaybe (@arbitrarySizeST _ (fun t => bst 0 10 t) _ 5) (fun t => forAll (choose (1, 9)) (fun x => is_bst 0 10 (insert x t))).	Definition	insert_bst_derived_gen	benchmarks.BST	benchmarks/BST/BST.v	[ "QuickChick", "QcNotation", "List", "ListNotations", "String", "ExtLib", "Monad", "MonadNotation" ]	[ "bst", "choose", "forAll", "forAllMaybe", "insert", "is_bst" ]	! Section derived-gen	https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
type : Type	:= \| N : type \| Arrow : type -> type -> type.	Inductive	type	benchmarks.stlc	benchmarks/stlc/stlc.v	[ "mathcomp", "ssreflect", "ssrbool", "eqtype", "Arith", "List", "String", "Lia", "QuickChick", "ListNotations" ]	[]	Types	https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
dec_type (t1 t2 : type) : Dec (t1 = t2).	Proof. dec_eq. Defined.	Instance	dec_type	benchmarks.stlc	benchmarks/stlc/stlc.v	[ "mathcomp", "ssreflect", "ssrbool", "eqtype", "Arith", "List", "String", "Lia", "QuickChick", "ListNotations" ]	[ "Dec", "dec_eq", "type" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
var	:= nat.	Definition	var	benchmarks.stlc	benchmarks/stlc/stlc.v	[ "mathcomp", "ssreflect", "ssrbool", "eqtype", "Arith", "List", "String", "Lia", "QuickChick", "ListNotations" ]	[ "nat" ]	Terms	https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
term : Type	:= \| Const : nat -> term \| Id : var -> term \| App : term -> term -> term \| Abs : type -> term -> term.	Inductive	term	benchmarks.stlc	benchmarks/stlc/stlc.v	[ "mathcomp", "ssreflect", "ssrbool", "eqtype", "Arith", "List", "String", "Lia", "QuickChick", "ListNotations" ]	[ "nat", "type", "var" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
env	:= list type.	Definition	env	benchmarks.stlc	benchmarks/stlc/stlc.v	[ "mathcomp", "ssreflect", "ssrbool", "eqtype", "Arith", "List", "String", "Lia", "QuickChick", "ListNotations" ]	[ "type" ]	Environments	https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
bind : env -> nat -> type -> Prop	:= \| BindNow : forall t G, bind (t :: G) 0 t \| BindLater : forall t t' x G, bind G x t -> bind (t' :: G) (S x) t.	Inductive	bind	benchmarks.stlc	benchmarks/stlc/stlc.v	[ "mathcomp", "ssreflect", "ssrbool", "eqtype", "Arith", "List", "String", "Lia", "QuickChick", "ListNotations" ]	[ "env", "nat", "type" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
typing (G : env) : term -> type -> Prop	:= \| TId : forall x t, bind G x t -> typing G (Id x) t \| TConst : forall n, typing G (Const n) N \| TAbs : forall e t1 t2, typing (t1 :: G) e t2 -> typing G (Abs t1 e) (Arrow t1 t2) \| TApp : forall e1 e2 t1 t2, typing G e2 t1 -> typing G e1 (Arrow t1 t2) -> ...	Inductive	typing	benchmarks.stlc	benchmarks/stlc/stlc.v	[ "mathcomp", "ssreflect", "ssrbool", "eqtype", "Arith", "List", "String", "Lia", "QuickChick", "ListNotations" ]	[ "bind", "env", "term", "type" ]	Typing	https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
typeOf G e : option type	:= match e with \| Id x => nth_error G x \| Const n => Some N \| Abs t e' => match typeOf (t::G) e' with \| Some t' => Some (Arrow t t') \| None => None end \| App e1 e2 => match typeOf G e1, typeOf G e2 with \| Some (Arrow t1 t2), Some t1' => if t1 = t1'? then Some t2 else None \| _...	Fixpoint	typeOf	benchmarks.stlc	benchmarks/stlc/stlc.v	[ "mathcomp", "ssreflect", "ssrbool", "eqtype", "Arith", "List", "String", "Lia", "QuickChick", "ListNotations" ]	[ "nth_error", "type" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
vars (Γ : env) (t : type) (g : G term) : G term	:= let vs := map (fun p => Id (snd p)) (filter (fun p => t = fst p?) (combine Γ (seq 0 (List.length Γ)))) in match vs with \| [] => g \| _ => oneOf_ (ret (Const 0)) [elems_ (Const 0) vs; g] end.	Definition	vars	benchmarks.stlc	benchmarks/stlc/stlc.v	[ "mathcomp", "ssreflect", "ssrbool", "eqtype", "Arith", "List", "String", "Lia", "QuickChick", "ListNotations" ]	[ "combine", "elems_", "env", "filter", "fst", "length", "map", "oneOf_", "snd", "term", "type" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
gen_base (Γ : env) (t : type) : G term	:= match t with \| N => vars Γ t (bindGen (choose (0,10)) (fun n => returnGen (Const n))) \| Arrow t1 t2 => bindGen (gen_base (t1::Γ) t2) (fun e => returnGen (Abs t1 e)) end.	Fixpoint	gen_base	benchmarks.stlc	benchmarks/stlc/stlc.v	[ "mathcomp", "ssreflect", "ssrbool", "eqtype", "Arith", "List", "String", "Lia", "QuickChick", "ListNotations" ]	[ "bindGen", "choose", "env", "returnGen", "term", "type", "vars" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
gen_typed (sz : nat) (Γ : env) (t : type) : G term	:= match sz with \| O => gen_base Γ t \| S sz' => let app := bindGen (@arbitrarySized type _ 3) (fun t' => bindGen (gen_typed sz' Γ (Arrow t' t)) (fun e1 => bindGen (gen_typed sz' Γ t') (fun e2 => returnGen (App e1 e2)))) in match t with \| N => vars Γ t (oneOf_ app ...	Fixpoint	gen_typed	benchmarks.stlc	benchmarks/stlc/stlc.v	[ "mathcomp", "ssreflect", "ssrbool", "eqtype", "Arith", "List", "String", "Lia", "QuickChick", "ListNotations" ]	[ "app", "bindGen", "env", "gen_base", "liftGen", "nat", "oneOf_", "returnGen", "term", "type", "vars" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
value : term -> Prop	:= \| VConst : forall n, value (Const n) \| VAbs : forall t e, value (Abs t e).	Inductive	value	benchmarks.stlc	benchmarks/stlc/stlc.v	[ "mathcomp", "ssreflect", "ssrbool", "eqtype", "Arith", "List", "String", "Lia", "QuickChick", "ListNotations" ]	[ "term" ]	Small step CBV semantics	https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
is_value (e : term) : bool	:= match e with \| Const _ \| Abs _ _ => true \| _ => false end.	Definition	is_value	benchmarks.stlc	benchmarks/stlc/stlc.v	[ "mathcomp", "ssreflect", "ssrbool", "eqtype", "Arith", "List", "String", "Lia", "QuickChick", "ListNotations" ]	[ "term" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
subst (y : var) (e1 : term) (e2 : term) : term	:= match e2 with \| Const n => Const n \| Id x => (! ) if eq_nat_dec x y then e1 else e2 (!! SUBST-swap ) (! if eq_nat_dec x y then e2 else e1 ) \| App e e' => App (subst y e1 e) (subst y e1 e') \| Abs t e => (! ) Abs t (subst (S y) e1 e) (*!! SUBST-no-lift ...	Fixpoint	subst	benchmarks.stlc	benchmarks/stlc/stlc.v	[ "mathcomp", "ssreflect", "ssrbool", "eqtype", "Arith", "List", "String", "Lia", "QuickChick", "ListNotations" ]	[ "term", "var" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
step (e : term) : option term	:= match e with \| Const _ \| Id _ => None \| Abs _ x => None \| App (Abs t e1) e2 => if is_value e2 then Some (subst 0 e2 e1) else match step e2 with \| Some e2' => Some (App (Abs t e1) e2') \| None => None end \| App e1 e2 => match step e1 with \| Some e1'...	Fixpoint	step	benchmarks.stlc	benchmarks/stlc/stlc.v	[ "mathcomp", "ssreflect", "ssrbool", "eqtype", "Arith", "List", "String", "Lia", "QuickChick", "ListNotations" ]	[ "is_value", "subst", "term" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
show_type (tau : type)	:= match tau with \| N => "N" \| Arrow tau1 tau2 => "(Arrow " ++ show_type tau1 ++ " -> " ++ show_type tau2 ++ ")" end.	Fixpoint	show_type	benchmarks.stlc	benchmarks/stlc/stlc.v	[ "mathcomp", "ssreflect", "ssrbool", "eqtype", "Arith", "List", "String", "Lia", "QuickChick", "ListNotations" ]	[ "type" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
showType : Show type	:= { show := show_type }.	Instance	showType	benchmarks.stlc	benchmarks/stlc/stlc.v	[ "mathcomp", "ssreflect", "ssrbool", "eqtype", "Arith", "List", "String", "Lia", "QuickChick", "ListNotations" ]	[ "Show", "show_type", "type" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
show_term (e : term)	:= match e with \| Const n => "(Const " ++ show n ++ ")" \| Id x => "(Id " ++ show x ++ ")" \| App e1 e2 => "(App " ++ show_term e1 ++ " " ++ show_term e2 ++ ")" \| Abs t e => "(Abs " ++ show t ++ " " ++ show_term e ++ ")" end.	Fixpoint	show_term	benchmarks.stlc	benchmarks/stlc/stlc.v	[ "mathcomp", "ssreflect", "ssrbool", "eqtype", "Arith", "List", "String", "Lia", "QuickChick", "ListNotations" ]	[ "term" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
showTerm : Show term	:= { show := show_term }.	Instance	showTerm	benchmarks.stlc	benchmarks/stlc/stlc.v	[ "mathcomp", "ssreflect", "ssrbool", "eqtype", "Arith", "List", "String", "Lia", "QuickChick", "ListNotations" ]	[ "Show", "show_term", "term" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
dec_eq_opt_type : Dec_Eq (option type).	Proof. dec_eq. Defined.	Instance	dec_eq_opt_type	benchmarks.stlc	benchmarks/stlc/stlc.v	[ "mathcomp", "ssreflect", "ssrbool", "eqtype", "Arith", "List", "String", "Lia", "QuickChick", "ListNotations" ]	[ "Dec_Eq", "dec_eq", "type" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
preservation (e : term) (t: type) : Checker	:= match step e with \| Some e' => checker ((typeOf nil e' = Some t)?) \| None => checker true end.	Definition	preservation	benchmarks.stlc	benchmarks/stlc/stlc.v	[ "mathcomp", "ssreflect", "ssrbool", "eqtype", "Arith", "List", "String", "Lia", "QuickChick", "ListNotations" ]	[ "Checker", "step", "term", "type", "typeOf" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
preservation_derived (e : term) (t: type) : Checker	:= match step e with \| Some e' => checker (typing nil e' t ?? 10) \| None => checker true end.	Definition	preservation_derived	benchmarks.stlc	benchmarks/stlc/stlc.v	[ "mathcomp", "ssreflect", "ssrbool", "eqtype", "Arith", "List", "String", "Lia", "QuickChick", "ListNotations" ]	[ "Checker", "step", "term", "type", "typing" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
preservation_check (e : term) : Checker	:= match typeOf nil e, step e with \| Some t, Some e' => checker ((typeOf nil e' = Some t)?) \| None, _ => checker tt \| _, _ => checker true end.	Definition	preservation_check	benchmarks.stlc	benchmarks/stlc/stlc.v	[ "mathcomp", "ssreflect", "ssrbool", "eqtype", "Arith", "List", "String", "Lia", "QuickChick", "ListNotations" ]	[ "Checker", "step", "term", "typeOf" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
prop_preservation	:= forAll (@arbitrary type _) (fun t => forAll (gen_typed 5 nil t) (fun e => preservation e t)).	Definition	prop_preservation	benchmarks.stlc	benchmarks/stlc/stlc.v	[ "mathcomp", "ssreflect", "ssrbool", "eqtype", "Arith", "List", "String", "Lia", "QuickChick", "ListNotations" ]	[ "forAll", "gen_typed", "preservation", "type" ]	! Section base	https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
prop_preservation_derived_checker	:= forAll (@arbitrary type _) (fun t => forAll (gen_typed 5 nil t) (fun e => preservation_derived e t)).	Definition	prop_preservation_derived_checker	benchmarks.stlc	benchmarks/stlc/stlc.v	[ "mathcomp", "ssreflect", "ssrbool", "eqtype", "Arith", "List", "String", "Lia", "QuickChick", "ListNotations" ]	[ "forAll", "gen_typed", "preservation_derived", "type" ]	! Section derived-dec	https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
prop_preservation_derived_gen	:= forAll (@arbitrary type _) (fun t => forAllMaybe (@arbitrarySizeST _ (fun e => typing nil e t) _ 5) (fun e => preservation e t)).	Definition	prop_preservation_derived_gen	benchmarks.stlc	benchmarks/stlc/stlc.v	[ "mathcomp", "ssreflect", "ssrbool", "eqtype", "Arith", "List", "String", "Lia", "QuickChick", "ListNotations" ]	[ "forAll", "forAllMaybe", "preservation", "type", "typing" ]	! Section derived-gen	https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
prop_preservation_naive_gen	:= forAll (@arbitrary term _) (fun e => preservation_check e).	Definition	prop_preservation_naive_gen	benchmarks.stlc	benchmarks/stlc/stlc.v	[ "mathcomp", "ssreflect", "ssrbool", "eqtype", "Arith", "List", "String", "Lia", "QuickChick", "ListNotations" ]	[ "forAll", "preservation_check", "term" ]	! Section naive-gen	https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
RandomSeed	:= RandomSeed.	Definition	RandomSeed	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
G	:= @G.	Definition	G	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
semGen	:= @semProd G ProducerGen.	Definition	semGen	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[ "ProducerGen" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
semGenSize	:= @semGenSize.	Definition	semGenSize	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
Functor_G	:= @Functor_Monad _ (@super _ ProducerGen).	Definition	Functor_G	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[ "ProducerGen" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
Applicative_G	:= @Applicative_Monad _ (@super _ ProducerGen).	Definition	Applicative_G	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[ "ProducerGen" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
Monad_G	:= @super _ ProducerGen.	Definition	Monad_G	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[ "ProducerGen" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
bindGen'	:= @bindPf G ProducerGen.	Definition	bindGen'	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[ "ProducerGen" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
bindGenOpt	:= @bindOpt G ProducerGen.	Definition	bindGenOpt	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[ "ProducerGen", "bindOpt" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
run	:= @Generators.run.	Definition	run	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
listOf	:= @listOf G ProducerGen.	Definition	listOf	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[ "ProducerGen" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
vectorOf	:= @vectorOf G ProducerGen.	Definition	vectorOf	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[ "ProducerGen" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
elems_	:= @elems_ G ProducerGen.	Definition	elems_	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[ "ProducerGen" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
oneOf_	:= @oneOf_ G ProducerGen.	Definition	oneOf_	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[ "ProducerGen" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
freq_	:= @freq_.	Definition	freq_	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
backtrack	:= @backtrack.	Definition	backtrack	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
resize	:= @resize G ProducerGen.	Definition	resize	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[ "ProducerGen" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
sized	:= @sized G ProducerGen.	Definition	sized	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[ "ProducerGen" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
suchThatMaybe	:= @suchThatMaybe.	Definition	suchThatMaybe	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
suchThatMaybeOpt	:= @suchThatMaybeOpt.	Definition	suchThatMaybeOpt	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
ChoosableFromInterval (A : Type) (le : relation A) : Type	:= { randomR : A * A -> RandomSeed -> A * RandomSeed; randomRCorrect : forall (a a1 a2 : A), le a1 a2 -> (le a1 a /\ le a a2 <-> exists seed, fst (randomR (a1, a2) seed) = a); enumR : A * A -> LazyList A; enumRCorrect : forall (a a1 a2 : A), le a1 a2 -> (le a1 a /\ le a ...	Class	ChoosableFromInterval	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[ "In_ll", "LazyList", "RandomSeed", "fst", "le", "relation" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
ChooseN	:= ChooseN.	Definition	ChooseN	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
ChooseNat	:= ChooseNat.	Definition	ChooseNat	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
ChooseZ	:= ChooseZ.	Definition	ChooseZ	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
choose	:= @choose G ProducerGen.	Definition	choose	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[ "ProducerGen" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
"'do!' X <- A ; B"	:= (bindGen A (fun X => B)) (at level 200, X name, A at level 100, B at level 200).	Notation	'do!' X <- A ; B	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[ "bindGen" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
"'do\'' X <- A ; B"	:= (bindGen' A (fun X H => B)) (at level 200, X name, A at level 100, B at level 200).	Notation	'do\'' X <- A ; B	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[ "bindGen'" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
"'doM!' X <- A ; B"	:= (bindGenOpt A (fun X => B)) (at level 200, X name, A at level 100, B at level 200).	Notation	'doM!' X <- A ; B	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[ "bindGenOpt" ]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
showNat	:= showNat .	Definition	showNat	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
showBool	:= showBool .	Definition	showBool	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
showZ	:= showZ .	Definition	showZ	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
showString	:= showString .	Definition	showString	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
showList	:= @showList .	Definition	showList	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
showPair	:= @showPair .	Definition	showPair	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
showOpt	:= @showOpt .	Definition	showOpt	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
showEx	:= @showEx .	Definition	showEx	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
nl	:= nl.	Definition	nl	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
GenOfGenSized	:= @GenOfGenSized.	Definition	GenOfGenSized	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
genBoolSized	:= @genBoolSized .	Definition	genBoolSized	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
genNatSized	:= @genNatSized .	Definition	genNatSized	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
genZSized	:= @genZSized .	Definition	genZSized	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
genListSized	:= @genListSized .	Definition	genListSized	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
genList	:= @genList .	Definition	genList	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
genOption	:= @genOption .	Definition	genOption	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
genPairSized	:= @genPairSized .	Definition	genPairSized	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
genPair	:= @Instances.genPair .	Definition	genPair	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
shrinkBool	:= shrinkBool.	Definition	shrinkBool	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]	TODO: Strings?	https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
shrinkNat	:= shrinkNat .	Definition	shrinkNat	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
shrinkZ	:= shrinkZ .	Definition	shrinkZ	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
shrinkList	:= @shrinkList .	Definition	shrinkList	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
shrinkPair	:= @shrinkPair .	Definition	shrinkPair	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
shrinkOption	:= @shrinkOption .	Definition	shrinkOption	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
ArbitraryOfGenShrink	:= @ArbitraryOfGenShrink.	Definition	ArbitraryOfGenShrink	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
Checker	:= @Checker.	Definition	Checker	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
testBool	:= testBool .	Definition	testBool	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
testUnit	:= testUnit .	Definition	testUnit	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
forAll	:= @forAll.	Definition	forAll	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
forAllProof	:= @forAllProof.	Definition	forAllProof	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
forAllShrink	:= @forAllShrink.	Definition	forAllShrink	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
testFun	:= @testFun .	Definition	testFun	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
testProd	:= @testProd.	Definition	testProd	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
testPolyFun	:= @testPolyFun.	Definition	testPolyFun	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
whenFail	:= @whenFail.	Definition	whenFail	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129
expectFailure	:= @expectFailure.	Definition	expectFailure	doc	doc/DocumentationCheck.v	[ "mathcomp", "ssreflect", "ssrfun", "ssrbool", "Coq", "Relations", "ZArith", "Strings.Ascii", "Strings.String", "QuickChick", "LazyList", "doc", "QuickChickInterface", "QcDefaultNotation" ]	[]		https://github.com/QuickChick/QuickChick	5a6c291b11e9affe059c0e1812612bc474d0a129

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Coq-QuickChick

Randomized property-based testing plugin for Coq, inspired by QuickCheck.

Source

Repository: https://github.com/QuickChick/QuickChick
Commit: 5a6c291b11e9affe059c0e1812612bc474d0a129
Files: 109
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: 2,753
With proof: 2,655 (96.4%)
With docstring: 752 (27.3%)
Libraries: 18

By type

Type	Count
Definition	675
Lemma	575
Instance	380
Inductive	210
Fixpoint	188
Theorem	186
Notation	133
Ltac2	132
Class	82
Example	71
Parameter	34
Ltac	33
Axiom	31
Record	11
Coercion	3
Function	3
CoInductive	2
Corollary	1
Fact	1
Hypothesis	1
CoFixpoint	1

Example

between : nat -> nat -> nat -> Prop
:=
| between_n : forall n m, le n m -> between n (S n) (S (S m))
| between_S : forall n m o, between n m o -> between n (S m) (S o).

type: Inductive | symbolic_name: between | benchmarks/BST/BST.v

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{coq_quickchick_dataset,
  title  = {Coq-QuickChick},
  author = {Norton, Charles},
  year   = {2026},
  note   = {Extracted from https://github.com/QuickChick/QuickChick, commit 5a6c291b11e9},
  url    = {https://huggingface.co/datasets/phanerozoic/Coq-QuickChick}
}

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Proof Assistant Projects

Collection

Digesting proof assistant libraries for AI ingestion. • 103 items • Updated 3 days ago • 3