# Library Coq.Lists.ListTactics

Require Import BinPos.
Require Import List.

Ltac list_fold_right fcons fnil l :=
match l with
| ?x :: ?tl => fcons x ltac:(list_fold_right fcons fnil tl)
| nil => fnil
end.

Ltac lazy_list_fold_right fcons fnil l :=
let f :=
match l with
| ?x :: ?tl =>
fun _ =>
fcons x ltac:(fun _ => lazy_list_fold_right fcons fnil tl)
| nil => fun _ => fnil()
end in
f().

Ltac list_fold_left fcons fnil l :=
match l with
| ?x :: ?tl => list_fold_left fcons ltac:(fcons x fnil) tl
| nil => fnil
end.

Ltac list_iter f l :=
match l with
| ?x :: ?tl => f x; list_iter f tl
| nil => idtac
end.

Ltac list_iter_gen seq f l :=
match l with
| ?x :: ?tl =>
let t1 _ := f x in
let t2 _ := list_iter_gen seq f tl in
seq t1 t2
| nil => idtac
end.

match l with
| nil => constr:(a::nil)
| a :: _ => l
| ?x :: ?l => let l' := AddFvTail a l in constr:(x::l')
end.

Ltac Find_at a l :=
let rec find n l :=
match l with
| nil => fail 100 "anomaly: Find_at"
| a :: _ => eval compute in n
| _ :: ?l => find (Pos.succ n) l
end
in find 1%positive l.

Ltac check_is_list t :=
match t with
| _ :: ?l => check_is_list l
| nil => idtac
| _ => fail 100 "anomaly: failed to build a canonical list"
end.

Ltac check_fv l :=
check_is_list l;
match type of l with
| list _ => idtac
| _ => fail 100 "anomaly: built an ill-typed list"
end.