Datasets:

phanerozoic
/

Coq-Stdlib

fact stringlengths 6 2.88k	type stringclasses 17 values	library stringclasses 2 values	imports listlengths 0 16	filename stringclasses 89 values	symbolic_name stringlengths 1 36
lowlevel_sub(arr : 'a array) (start : int) (len : int) : 'a array := let l := length arr in match Int.equal l 0 with \| true => empty \| false => let newarr:=make len (get arr 0) in lowlevel_blit arr start newarr 0 len; newarr end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	lowlevel_sub
init(l : int) (f : int -> 'a) : 'a array := let rec init_aux (dst : 'a array) (pos : int) (len : int) (f : int->'a) := match Int.equal len 0 with \| true => () \| false => set dst pos (f pos); init_aux dst (Int.add pos 1) (Int.sub len 1) f end in match Int.le l 0 with \| true => empty \| false => let arr:=make l (f 0) in init_aux arr 1 (Int.sub l 1) f; arr end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	init
make_matrix(sx : int) (sy : int) (v : 'a) : 'a array array := let initr _ := make sy v in init sx initr.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	make_matrix
copy(a : 'a array) : 'a array := lowlevel_sub a 0 (length a).	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	copy
append(a1 : 'a array) (a2 : 'a array) : 'a array := match Int.equal (length a1) 0 with \| true => copy a2 \| false => match Int.equal (length a2) 0 with \| true => copy a1 \| false => let newarr:=make (Int.add (length a1) (length a2)) (get a1 0) in lowlevel_blit a1 0 newarr 0 (length a1); lowlevel_blit a2 0 newarr (length a1) (length a2); newarr end end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	append
sub(a : 'a array) (ofs : int) (len : int) : 'a array := Control.assert_valid_argument "Array.sub ofs<0" (Int.ge ofs 0); Control.assert_valid_argument "Array.sub len<0" (Int.ge len 0); Control.assert_bounds "Array.sub" (Int.le ofs (Int.sub (length a) len)); lowlevel_sub a ofs len.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	sub
fill(a : 'a array) (ofs : int) (len : int) (v : 'a) : unit := Control.assert_valid_argument "Array.fill ofs<0" (Int.ge ofs 0); Control.assert_valid_argument "Array.fill len<0" (Int.ge len 0); Control.assert_bounds "Array.fill" (Int.le ofs (Int.sub (length a) len)); lowlevel_fill a ofs len v.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	fill
blit(a1 : 'a array) (ofs1 : int) (a2 : 'a array) (ofs2 : int) (len : int) : unit := Control.assert_valid_argument "Array.blit ofs1<0" (Int.ge ofs1 0); Control.assert_valid_argument "Array.blit ofs2<0" (Int.ge ofs2 0); Control.assert_valid_argument "Array.blit len<0" (Int.ge len 0); Control.assert_bounds "Array.blit ofs1+len>len a1" (Int.le ofs1 (Int.sub (length a1) len)); Control.assert_bounds "Array.blit ofs2+len>len a2" (Int.le ofs2 (Int.sub (length a2) len)); lowlevel_blit a1 ofs1 a2 ofs2 len.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	blit
reciter_aux (f : 'a -> unit) (a : 'a array) (pos : int) (len : int) : unit := match Int.equal len 0 with \| true => () \| false => f (get a pos); iter_aux f a (Int.add pos 1) (Int.sub len 1) end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	rec
iter(f : 'a -> unit) (a : 'a array) : unit := iter_aux f a 0 (length a).	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	iter
reciter2_aux (f : 'a -> 'b -> unit) (a : 'a array) (b : 'b array) (pos : int) (len : int) : unit := match Int.equal len 0 with \| true => () \| false => f (get a pos) (get b pos); iter2_aux f a b (Int.add pos 1) (Int.sub len 1) end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	rec
reciter2 (f : 'a -> 'b -> unit) (a : 'a array) (b : 'b array) : unit := Control.assert_valid_argument "Array.iter2" (Int.equal (length a) (length b)); iter2_aux f a b 0 (length a).	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	rec
map(f : 'a -> 'b) (a : 'a array) : 'b array := init (length a) (fun i => f (get a i)).	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	map
map2(f : 'a -> 'b -> 'c) (a : 'a array) (b : 'b array) : 'c array := Control.assert_valid_argument "Array.map2" (Int.equal (length a) (length b)); init (length a) (fun i => f (get a i) (get b i)).	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	map2
reciteri_aux (f : int -> 'a -> unit) (a : 'a array) (pos : int) (len : int) : unit := match Int.equal len 0 with \| true => () \| false => f pos (get a pos); iteri_aux f a (Int.add pos 1) (Int.sub len 1) end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	rec
iteri(f : int -> 'a -> unit) (a : 'a array) : unit := iteri_aux f a 0 (length a).	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	iteri
mapi(f : int -> 'a -> 'b) (a : 'a array) : 'b array := init (length a) (fun i => f i (get a i)).	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	mapi
recto_list_aux (a : 'a array) (pos : int) (len : int) : 'a list := match Int.equal len 0 with \| true => [] \| false => get a pos :: to_list_aux a (Int.add pos 1) (Int.sub len 1) end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	rec
to_list(a : 'a array) : 'a list := to_list_aux a 0 (length a).	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	to_list
recof_list_aux (ls : 'a list) (dst : 'a array) (pos : int) : unit := match ls with \| [] => () \| hd::tl => set dst pos hd; of_list_aux tl dst (Int.add pos 1) end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	rec
of_list(ls : 'a list) : 'a array :=	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	of_list
recfold_left_aux (f : 'a -> 'b -> 'a) (x : 'a) (a : 'b array) (pos : int) (len : int) : 'a := match Int.equal len 0 with \| true => x \| false => fold_left_aux f (f x (get a pos)) a (Int.add pos 1) (Int.sub len 1) end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	rec
fold_left(f : 'a -> 'b -> 'a) (x : 'a) (a : 'b array) : 'a := fold_left_aux f x a 0 (length a).	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	fold_left
recfold_right_aux (f : 'a -> 'b -> 'b) (a : 'a array) (x : 'b) (pos : int) (len : int) : 'b :=	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	rec
fold_right(f : 'a -> 'b -> 'b) (a : 'a array) (x : 'b) : 'b := fold_right_aux f a x (Int.sub (length a) 1) (length a).	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	fold_right
recexist_aux (p : 'a -> bool) (a : 'a array) (pos : int) (len : int) : bool := match Int.equal len 0 with \| true => false \| false => match p (get a pos) with \| true => true \| false => exist_aux p a (Int.add pos 1) (Int.sub len 1) end end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	rec
exist(p : 'a -> bool) (a : 'a array) : bool := exist_aux p a 0 (length a).	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	exist
recfor_all_aux (p : 'a -> bool) (a : 'a array) (pos : int) (len : int) : bool := match Int.equal len 0 with \| true => true \| false => match p (get a pos) with \| true => for_all_aux p a (Int.add pos 1) (Int.sub len 1) \| false => false end end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	rec
for_all(p : 'a -> bool) (a : 'a array) : bool := for_all_aux p a 0 (length a).	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	for_all
mem(eq : 'a -> 'a -> bool) (x : 'a) (a : 'a array) : bool := exist (eq x) a.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	mem
recfor_all2_aux (p : 'a -> 'b -> bool) (a : 'a array) (b : 'b array) (pos : int) (len : int) : bool := if Int.equal len 0 then true else if p (get a pos) (get b pos) then for_all2_aux p a b (Int.add pos 1) (Int.sub len 1) else false.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	rec
for_all2(p : 'a -> 'b -> bool) (a : 'a array) (b : 'b array) : bool := let lena := length a in let lenb := length b in if Int.equal lena lenb then for_all2_aux p a b 0 lena else Control.throw_invalid_argument "Array.for_all2".	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	for_all2
equal(p : 'a -> 'b -> bool) (a : 'a array) (b : 'b array) : bool := let lena := length a in let lenb := length b in if Int.equal lena lenb then for_all2_aux p a b 0 lena else false.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	equal
rev(ar : 'a array) : 'a array := let len := length ar in init len (fun i => get ar (Int.sub (Int.sub len i) 1)).	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int", "Require Ltac2.Control", "Require Ltac2.Bool", "Require Ltac2.Message" ]	Ltac2/Array.v	rev
andx y := match x with \| true => y \| false => false end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init" ]	Ltac2/Bool.v	and
orx y := match x with \| true => true \| false => y end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init" ]	Ltac2/Bool.v	or
implx y := match x with \| true => y \| false => true end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init" ]	Ltac2/Bool.v	impl
negx := match x with \| true => false \| false => true end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init" ]	Ltac2/Bool.v	neg
xorx y := match x with \| true => match y with \| true => false \| false => true end \| false => match y with \| true => true \| false => false end end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init" ]	Ltac2/Bool.v	xor
equalx y := match x with \| true => match y with \| true => true \| false => false end \| false => match y with \| true => false \| false => true end end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init" ]	Ltac2/Bool.v	equal
Notationx(self) "&&" y(thunk(self)) : 2 := match x with \| true => y () \| false => false end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init" ]	Ltac2/Bool.v	Notation
Notationx(self) "\|\|" y(thunk(self)) : 3 := match x with \| true => true \| false => y () end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init" ]	Ltac2/Bool.v	Notation
equal(x : char) (y : char) : bool := Int.equal (to_int x) (to_int y).	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int" ]	Ltac2/Char.v	equal
compare(x : char) (y : char) : int := Int.compare (to_int x) (to_int y).	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Int" ]	Ltac2/Char.v	compare
Typet := constant.	Ltac2	Ltac2	[ "Require Import Ltac2.Init" ]	Ltac2/Constant.v	Type
Typerelevance_var.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	Type
Typerelevance := [ Relevant \| Irrelevant \| RelevanceVar (relevance_var) ].	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	Type
Typet := Binder.relevance.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	Type
Typecase.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	Type
Typecase_invert	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	Type
Typekind := [ \| Rel (int)	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	Type
reckind_nocast c := match kind c with \| Cast c _ _ => kind_nocast c \| k => k end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	rec
is_closed(c : constr) : bool := closedn 0 c.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	is_closed
occur_between:= noccur_between.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	occur_between
noccurn(n : int) (c : constr) : bool := noccur_between n 1 c.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	noccurn
occurn(n : int) (c : constr) : bool := noccur_between n 1 c.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	occurn
constructor(ind : inductive) (i : int) : constructor := Ind.get_constructor (Ind.data ind) i.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	constructor
iter(f : constr -> unit) (c : constr) : unit := match kind c with \| Rel _ \| Meta _ \| Var _ \| Sort _ \| Constant _ _ \| Ind _ _ \| Constructor _ _ \| Uint63 _ \| Float _ \| String _ => () \| Cast c _ t => f c; f t \| Prod b c => f (Binder.type b); f c \| Lambda b c => f (Binder.type b); f c \| LetIn b t c => f (Binder.type b); f t; f c \| App c l => f c; Array.iter f l \| Evar _ l => Array.iter f l \| Case _ x iv y bl => match x with (x,_) => f x end; iter_invert f iv; f y; Array.iter f bl \| Proj _p _ c => f c \| Fix _ _ tl bl => Array.iter (fun b => f (Binder.type b)) tl; Array.iter f bl \| CoFix _ tl bl => Array.iter (fun b => f (Binder.type b)) tl; Array.iter f bl \| Array _u t def ty => f ty; Array.iter f t; f def end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	iter
iter_with_binders(g : 'a -> binder -> 'a) (f : 'a -> constr -> unit) (n : 'a) (c : constr) : unit := match kind c with \| Rel _ \| Meta _ \| Var _ \| Sort _ \| Constant _ _ \| Ind _ _ \| Constructor _ _ \| Uint63 _ \| Float _ \| String _ => () \| Cast c _ t => f n c; f n t \| Prod b c => f n (Binder.type b); f (g n b) c \| Lambda b c => f n (Binder.type b); f (g n b) c \| LetIn b t c => f n (Binder.type b); f n t; f (g n b) c \| App c l => f n c; Array.iter (f n) l \| Evar _ l => Array.iter (f n) l \| Case _ x iv y bl => match x with (x,_) => f n x end; iter_invert (f n) iv; f n y; Array.iter (f n) bl \| Proj _p _ c => f n c \| Fix _ _ tl bl => Array.iter (fun b => f n (Binder.type b)) tl; let n := Array.fold_left g n tl in Array.iter (f n) bl \| CoFix _ tl bl => Array.iter (fun b => f n (Binder.type b)) tl; let n := Array.fold_left g n tl in Array.iter (f n) bl \| Array _u t def ty => f n ty; Array.iter (f n) t; f n def end. Local Ltac2 binder_map (f : constr -> constr) (b : binder) : binder := Binder.unsafe_make (Binder.name b) (Binder.relevance b) (f (Binder.type b)). Local Ltac2 map_invert (f : constr -> constr) (iv : case_invert) : case_invert := match iv with \| NoInvert => NoInvert \| CaseInvert indices => CaseInvert (Array.map f indices) end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	iter_with_binders
map(f : constr -> constr) (c : constr) : constr := match kind c with \| Rel _ \| Meta _ \| Var _ \| Sort _ \| Constant _ _ \| Ind _ _ \| Constructor _ _ \| Uint63 _ \| Float _ \| String _ => c \| Cast c k t => let c := f c with t := f t in make (Cast c k t) \| Prod b c => let b := binder_map f b with c := f c in make (Prod b c) \| Lambda b c => let b := binder_map f b with c := f c in make (Lambda b c) \| LetIn b t c => let b := binder_map f b with t := f t with c := f c in make (LetIn b t c) \| App c l => let c := f c with l := Array.map f l in make (App c l) \| Evar e l => let l := Array.map f l in make (Evar e l) \| Case info x iv y bl => let x := match x with (x,x') => (f x, x') end with iv := map_invert f iv with y := f y with bl := Array.map f bl in make (Case info x iv y bl) \| Proj p r c => let c := f c in make (Proj p r c) \| Fix structs which tl bl => let tl := Array.map (binder_map f) tl with bl := Array.map f bl in make (Fix structs which tl bl) \| CoFix which tl bl => let tl := Array.map (binder_map f) tl with bl := Array.map f bl in make (CoFix which tl bl) \| Array u t def ty => let ty := f ty with t := Array.map f t with def := f def in make (Array u t def ty) ...	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	map
map_with_binders(lift : 'a -> binder -> 'a) (f : 'a -> constr -> constr) (n : 'a) (c : constr) : constr := match kind c with \| Rel _ \| Meta _ \| Var _ \| Sort _ \| Constant _ _ \| Ind _ _ \| Constructor _ _ \| Uint63 _ \| Float _ \| String _ => c \| Cast c k t => let c := f n c with t := f n t in make (Cast c k t) \| Prod b c => let b := binder_map (f n) b with c := f (lift n b) c in make (Prod b c) \| Lambda b c => let b := binder_map (f n) b with c := f (lift n b) c in make (Lambda b c) \| LetIn b t c => let b := binder_map (f n) b with t := f n t with c := f (lift n b) c in make (LetIn b t c) \| App c l => let c := f n c with l := Array.map (f n) l in make (App c l) \| Evar e l => let l := Array.map (f n) l in make (Evar e l) \| Case info x iv y bl => let x := match x with (x,x') => (f n x, x') end with iv := map_invert (f n) iv with y := f n y with bl := Array.map (f n) bl in make (Case info x iv y bl) \| Proj p r c => let c := f n c in make (Proj p r c) \| Fix structs which tl bl => let tl := Array.map (binder_map (f n)) tl in let n_bl := Array.fold_left lift n tl in let bl := Array.map (f n_bl) bl in make (Fix structs which tl bl) \| CoFix which tl bl => let tl := Array.map (binder_map (f n)) tl in let n_bl := Array.fold_left lift n tl in let bl := Array.map (f n_bl) bl in make (CoFix which tl bl) \| Array u t def ty => let ty := f n ty with t := Array.map (f n) t ...	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	map_with_binders
Typet.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	Type
Abbreviationopen_constr_flags_with_tc := set_nf_evars false (set_allow_evars true constr_flags). Local Ltac2 open_constr_flags_with_tc_kn () := open_constr_flags_with_tc.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	Abbreviation
Abbreviationopen_constr_flags_no_tc := set_use_typeclasses false open_constr_flags_with_tc.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	Abbreviation
Abbreviationopen_constr_flags := open_constr_flags_with_tc.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	Abbreviation
Typeexpected_type.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	Type
pretype(c : preterm) : constr := Pretype.pretype Pretype.Flags.constr_flags Pretype.expected_without_type_constraint c.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	pretype
decompose_app_list(c : constr) := match Unsafe.kind c with \| Unsafe.App f cl => (f, Array.to_list cl) \| _ => (c,[]) end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	decompose_app_list
decompose_app(c : constr) := match Unsafe.kind c with \| Unsafe.App f cl => (f, cl) \| _ => (c,[\| \|]) end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	decompose_app
is_evar(c: constr) := match Unsafe.kind c with \| Unsafe.Evar _ _ => true \| _ => false end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	is_evar
is_var(c: constr) := match Unsafe.kind c with \| Unsafe.Var _ => true \| _ => false end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	is_var
is_fix(c: constr) := match Unsafe.kind c with \| Unsafe.Fix _ _ _ _ => true \| _ => false end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	is_fix
is_cofix(c: constr) := match Unsafe.kind c with \| Unsafe.CoFix _ _ _ => true \| _ => false end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	is_cofix
is_ind(c: constr) := match Unsafe.kind c with \| Unsafe.Ind _ _ => true \| _ => false end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	is_ind
is_constructor(c: constr) := match Unsafe.kind c with \| Unsafe.Constructor _ _ => true \| _ => false end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	is_constructor
is_proj(c: constr) := match Unsafe.kind c with \| Unsafe.Proj _ _ _ => true \| _ => false end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	is_proj
is_const(c: constr) := match Unsafe.kind c with \| Unsafe.Constant _ _ => true \| _ => false end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	is_const
is_float(c: constr) := match Unsafe.kind c with \| Unsafe.Float _ => true \| _ => false end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	is_float
is_uint63(c: constr) := match Unsafe.kind c with \| Unsafe.Uint63 _ => true \| _ => false end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	is_uint63
is_string(c: constr) := match Unsafe.kind c with \| Unsafe.String _ => true \| _ => false end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	is_string
is_array(c: constr) := match Unsafe.kind c with \| Unsafe.Array _ _ _ _ => true \| _ => false end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	is_array
is_sort(c: constr) := match Unsafe.kind c with \| Unsafe.Sort _ => true \| _ => false end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Ind Ltac2.Array" ]	Ltac2/Constr.v	is_sort
Typet := constructor.	Ltac2	Ltac2	[ "Require Import Ltac2.Init" ]	Ltac2/Constructor.v	Type
once_plus(run : unit -> 'a) (handle : exn -> 'a) : 'a := once (fun () => plus run handle).	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Message" ]	Ltac2/Control.v	once_plus
throw_invalid_argument(msg : string) := Control.throw (Invalid_argument (Some (Message.of_string msg))).	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Message" ]	Ltac2/Control.v	throw_invalid_argument
throw_out_of_bounds(msg : string) := Control.throw (Out_of_bounds (Some (Message.of_string msg))).	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Message" ]	Ltac2/Control.v	throw_out_of_bounds
assert_valid_argument(msg : string) (test : bool) := match test with \| true => () \| false => throw_invalid_argument msg end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Message" ]	Ltac2/Control.v	assert_valid_argument
assert_bounds(msg : string) (test : bool) := match test with \| true => () \| false => throw_out_of_bounds msg end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Message" ]	Ltac2/Control.v	assert_bounds
assert_trueb := if b then () else throw Assertion_failure.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Message" ]	Ltac2/Control.v	assert_true
assert_falseb := if b then throw Assertion_failure else ().	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Message" ]	Ltac2/Control.v	assert_false
backtrack_tactic_failure(msg : string) := Control.zero (Tactic_failure (Some (Message.of_string msg))).	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Message" ]	Ltac2/Control.v	backtrack_tactic_failure
once_plus_bt(run : unit -> 'a) (handle : exn -> exninfo -> 'a) : 'a := once (fun _ => plus_bt run handle).	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Message" ]	Ltac2/Control.v	once_plus_bt
clear_exn_info(e : exn) : exn := match e with \| Init.Internal err => Init.Internal (clear_err_info err) \| e => e end.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Message" ]	Ltac2/Control.v	clear_exn_info
Typet := evar.	Ltac2	Ltac2	[ "Require Import Ltac2.Init" ]	Ltac2/Evar.v	Type
Typet := float.	Ltac2	Ltac2	[ "Require Import Ltac2.Init" ]	Ltac2/Float.v	Type
Type('k, 'v) t.	Ltac2	Ltac2	[ "From Ltac2 Require Import Init", "From Ltac2 Require FSet" ]	Ltac2/FMap.v	Type
Typet.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Control", "Require Ltac2.List" ]	Ltac2/Fresh.v	Type
of_goal() := of_ids (List.map (fun (id, _, _) => id) (Control.hyps ())).	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Control", "Require Ltac2.List" ]	Ltac2/Fresh.v	of_goal
in_goalid := Fresh.fresh (Free.of_goal ()) id.	Ltac2	Ltac2	[ "Require Import Ltac2.Init", "Require Ltac2.Control", "Require Ltac2.List" ]	Ltac2/Fresh.v	in_goal
Type'a tag.	Ltac2	Ltac2	[ "From Ltac2 Require Import Init" ]	Ltac2/FSet.v	Type

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Coq-Stdlib

Structured dataset of definitions and theorems from the Coq standard library.

Schema

Column	Type	Description
fact	string	Declaration body (without type keyword)
type	string	Definition, Lemma, Theorem, Fixpoint, Inductive, Class, Instance, Ltac, Ltac2, etc.
library	string	Top-level module (Corelib, Ltac2)
imports	list	Require/Import statements
filename	string	Source file path
symbolic_name	string	Declaration identifier