include "nat/minus.ma".
include "list/list.ma".
-interpretation "list nth" 'nth = (nth _).
-interpretation "list nth" 'nth_appl l d i = (nth _ l d i).
+interpretation "list nth" 'nth = (nth ?).
+interpretation "list nth" 'nth_appl l d i = (nth ? l d i).
notation "\nth" with precedence 90 for @{'nth}.
notation < "\nth \nbsp term 90 l \nbsp term 90 d \nbsp term 90 i"
with precedence 69 for @{'nth_appl $l $d $i}.
match n with [ O ⇒ nil ? | S m ⇒ def m :: make_list m]
in make_list.
-interpretation "\mk_list appl" 'mk_list_appl f n = (make_list _ f n).
-interpretation "\mk_list" 'mk_list = (make_list _).
+interpretation "\mk_list appl" 'mk_list_appl f n = (make_list ? f n).
+interpretation "\mk_list" 'mk_list = (make_list ?).
notation "\mk_list" with precedence 90 for @{'mk_list}.
notation < "\mk_list \nbsp term 90 f \nbsp term 90 n"
with precedence 69 for @{'mk_list_appl $f $n}.
notation "\len" with precedence 90 for @{'len}.
-interpretation "len" 'len = (length _).
+interpretation "len" 'len = (length ?).
notation < "\len \nbsp term 90 l" with precedence 69 for @{'len_appl $l}.
-interpretation "len appl" 'len_appl l = (length _ l).
+interpretation "len appl" 'len_appl l = (length ? l).
lemma mk_list_ext: ∀T:Type.∀f1,f2:nat→T.∀n. (∀x.x<n → f1 x = f2 x) → \mk_list f1 n = \mk_list f2 n.
intros 4;elim n; [reflexivity] simplify; rewrite > H1; [2: apply le_n]
notation > "\last" non associative with precedence 90 for @{'last}.
notation < "\last d l" non associative with precedence 70 for @{'last2 $d $l}.
-interpretation "list last" 'last = (last _).
-interpretation "list last applied" 'last2 d l = (last _ d l).
+interpretation "list last" 'last = (last ?).
+interpretation "list last applied" 'last2 d l = (last ? d l).
definition head ≝
λT:Type.λd.λl:list T.\nth l d O.
notation > "\hd" non associative with precedence 90 for @{'hd}.
notation < "\hd d l" non associative with precedence 70 for @{'hd2 $d $l}.
-interpretation "list head" 'hd = (head _).
-interpretation "list head applied" 'hd2 d l = (head _ d l).
+interpretation "list head" 'hd = (head ?).
+interpretation "list head applied" 'hd2 d l = (head ? d l).