mod change (-x)

[helm.git] / helm / software / matita / contribs / assembly / compiler / utility.ma

diff --git a/helm/software/matita/contribs/assembly/compiler/utility.ma b/helm/software/matita/contribs/assembly/compiler/utility.ma
old mode 100755 (executable)
new mode 100644 (file)
index aef219e..94adb3c
--- a/helm/software/matita/contribs/assembly/compiler/utility.ma
+++ b/helm/software/matita/contribs/assembly/compiler/utility.ma
@@ -40,7 +40,7 @@ notation "hvbox(hd break §§ tl)"
   right associative with precedence 46
   for @{'ne_cons $hd $tl}.
 
-notation "« y break £ list0 x sep ; break »"
+notation "« list0 x sep ; break £ y break »"
   non associative with precedence 90
   for ${fold right @{'ne_nil $y } rec acc @{'ne_cons $x $acc}}.
 
@@ -48,9 +48,9 @@ notation "hvbox(l1 break & l2)"
   right associative with precedence 47
   for @{'ne_append $l1 $l2 }.
 
-interpretation "ne_nil" 'ne_nil hd = (ne_nil _ hd).
-interpretation "ne_cons" 'ne_cons hd tl = (ne_cons _ hd tl).
-interpretation "ne_append" 'ne_append l1 l2 = (ne_append _ l1 l2).
+interpretation "ne_nil" 'ne_nil hd = (ne_nil ? hd).
+interpretation "ne_cons" 'ne_cons hd tl = (ne_cons ? hd tl).
+interpretation "ne_append" 'ne_append l1 l2 = (ne_append ? l1 l2).
 
 (* ************ *)
 (* List Utility *)
@@ -61,18 +61,14 @@ let rec neList_to_list (T:Type) (p_l:ne_list T) on p_l ≝
  match p_l with [ ne_nil h ⇒ [h] | ne_cons h t ⇒ [h]@neList_to_list T t ].
 
 let rec list_to_neList (T:Type) (p_l:list T) on p_l ≝
- match p_l with [ nil ⇒ None (ne_list T) | cons h t ⇒ match list_to_neList T t with [ None ⇒ Some ? «h£» | Some t' ⇒ Some ? («h£»&t') ]].
+ match p_l with [ nil ⇒ None (ne_list T) | cons h t ⇒ match list_to_neList T t with [ None ⇒ Some ? «£h» | Some t' ⇒ Some ? («£h»&t') ]].
 
 (* listlen *)
-let rec len_list_aux (T:Type) (p_l:list T) (c:nat) on p_l ≝
- match p_l with [ nil ⇒ c | cons _ t ⇒ len_list_aux T t (S c) ].
+let rec len_list (T:Type) (p_l:list T) on p_l ≝
+ match p_l with [ nil ⇒ O | cons _ t ⇒ S (len_list T t) ].
 
-definition len_list ≝ λT:Type.λl:list T.len_list_aux T l O.
-
-let rec len_neList_aux (T:Type) (p_l:ne_list T) (c:nat) on p_l ≝
- match p_l with [ ne_nil _ ⇒ (S c) | ne_cons _ t ⇒ len_neList_aux T t (S c) ].
-
-definition len_neList ≝ λT:Type.λl:ne_list T.len_neList_aux T l O.
+let rec len_neList (T:Type) (p_l:ne_list T) on p_l ≝
+ match p_l with [ ne_nil _ ⇒ 1 | ne_cons _ t ⇒ S (len_neList T t) ].
 
 (* nth elem *)
 let rec nth_list (T:Type) (l:list T) (n:nat) on l ≝
@@ -202,6 +198,37 @@ lemma isbemptylist_to_isemptylist : ∀T,l.isb_empty_list T l = true → is_empt
    normalize; autobatch ]
 qed.
 
+definition isnot_empty_list ≝
+λT:Type.λl:list T.match l with [ nil ⇒ False | cons _ _ ⇒ True ].
+
+definition isnotb_empty_list ≝
+λT:Type.λl:list T.match l with [ nil ⇒ false | cons _ _ ⇒ true ].
+
+lemma isnotbemptylist_to_isnotemptylist : ∀T,l.isnotb_empty_list T l = true → isnot_empty_list T l.
+ unfold isnotb_empty_list;
+ unfold isnot_empty_list;
+ intros;
+ elim l;
+ [ normalize; autobatch |
+   normalize; autobatch ]
+qed.
+
+lemma isempty_to_eq : ∀T,l.isb_empty_list T l = true → l = [].
+ do 2 intro;
+ elim l 0;
+ [ 1: intro; reflexivity
+ | 2: intros; normalize in H1:(%); destruct H1
+ ].
+qed.
+
+lemma eq_to_isempty : ∀T,l.l = [] → isb_empty_list T l = true.
+ do 2 intro;
+ elim l 0;
+ [ 1: intro; reflexivity
+ | 2: intros; destruct H1
+ ]
+qed. 
+
 (* ******** *)
 (* naturali *)
 (* ******** *)