- xoa: the definitions file now includes the notations file

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / lib / list.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_2/lib/list.ma b/matita/matita/contribs/lambdadelta/ground_2/lib/list.ma
new file mode 100644 (file)
index 0000000..d21e1b5
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/ground_2/lib/list.ma
@@ -0,0 +1,60 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "ground_2/notation/constructors/nil_1.ma".
+include "ground_2/notation/constructors/nil_2.ma".
+include "ground_2/notation/constructors/cons_3.ma".
+include "ground_2/notation/constructors/cons_5.ma".
+include "ground_2/notation/functions/append_2.ma".
+include "ground_2/lib/arith.ma".
+
+(* LISTS ********************************************************************)
+
+inductive list (A:Type[0]) : Type[0] :=
+  | nil : list A
+  | cons: A → list A → list A.
+
+interpretation "nil (list)" 'Nil A = (nil A).
+
+interpretation "cons (list)" 'Cons A hd tl = (cons A hd tl).
+
+let rec all A (R:predicate A) (l:list A) on l ≝
+  match l with
+  [ nil        ⇒ ⊤
+  | cons hd tl ⇒ R hd ∧ all A R tl
+  ].
+
+inductive list2 (A1,A2:Type[0]) : Type[0] :=
+  | nil2 : list2 A1 A2
+  | cons2: A1 → A2 → list2 A1 A2 → list2 A1 A2.
+
+interpretation "nil (list of pairs)" 'Nil A1 A2 = (nil2 A1 A2).
+
+interpretation "cons (list of pairs)" 'Cons A1 A2 hd1 hd2 tl = (cons2 A1 A2 hd1 hd2 tl).
+
+let rec append2 (A1,A2:Type[0]) (l1,l2:list2 A1 A2) on l1 ≝ match l1 with
+[ nil2           ⇒ l2
+| cons2 a1 a2 tl ⇒ {a1, a2} @ append2 A1 A2 tl l2
+].
+
+interpretation "append (list of pairs)"
+   'Append l1 l2 = (append2 ? ? l1 l2).
+
+let rec length2 (A1,A2:Type[0]) (l:list2 A1 A2) on l ≝ match l with
+[ nil2        ⇒ 0
+| cons2 _ _ l ⇒ length2 A1 A2 l + 1
+].
+
+interpretation "length (list of pairs)"
+   'card l = (length2 ? ? l).