(* *)
(**************************************************************************)
-include "ground_2/notation/constructors/nil_0.ma".
-include "ground_2/notation/constructors/cons_2.ma".
-include "ground_2/notation/constructors/cons_3.ma".
-include "ground_2/notation/functions/append_2.ma".
-include "ground_2/lib/arith.ma".
+include "ground_2/notation/functions/circledE_1.ma".
+include "ground_2/notation/functions/oplusright_3.ma".
+include "ground_2/lib/relations.ma".
(* LISTS ********************************************************************)
| nil : list A
| cons: A → list A → list A.
-interpretation "nil (list)" 'Nil = (nil ?).
+interpretation "nil (list)" 'CircledE A = (nil A).
-interpretation "cons (list)" 'Cons hd tl = (cons ? hd tl).
+interpretation "cons (list)" 'OPlusRight A hd tl = (cons A hd tl).
-let rec length (A:Type[0]) (l:list A) on l ≝ match l with
-[ nil ⇒ 0
-| cons _ l ⇒ length A l + 1
-].
-
-interpretation "length (list)"
- 'card l = (length ? l).
-
-let rec all A (R:predicate A) (l:list A) on l ≝
+rec definition all A (R:predicate A) (l:list A) on l ≝
match l with
[ nil ⇒ ⊤
- | cons hd tl ⇒ R hd ∧ all A R tl
+ | 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 = (nil2 ? ?).
-
-interpretation "cons (list of pairs)" 'Cons hd1 hd2 tl = (cons2 ? ? 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).