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[helm.git] / matita / library / datatypes / constructors.ma

diff --git a/matita/library/datatypes/constructors.ma b/matita/library/datatypes/constructors.ma
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+(**************************************************************************)
+(*       ___                                                               *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||       A.Asperti, C.Sacerdoti Coen,                          *)
+(*      ||A||       E.Tassi, S.Zacchiroli                                 *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU Lesser General Public License Version 2.1         *)
+(*                                                                        *)
+(**************************************************************************)
+
+set "baseuri" "cic:/matita/datatypes/constructors/".
+include "logic/equality.ma".
+
+inductive void : Set \def.
+
+inductive unit : Set ≝ something: unit.
+
+inductive Prod (A,B:Type) : Type \def
+pair : A \to B \to Prod A B.
+
+interpretation "Pair construction" 'pair x y =
+ (cic:/matita/datatypes/constructors/Prod.ind#xpointer(1/1/1) _ _ x y).
+
+notation "hvbox(\langle x break , y \rangle )" with precedence 89
+for @{ 'pair $x $y}.
+
+interpretation "Product" 'product x y =
+ (cic:/matita/datatypes/constructors/Prod.ind#xpointer(1/1) x y).
+
+notation "hvbox(x break \times y)" with precedence 89
+for @{ 'product $x $y}.
+
+definition fst \def \lambda A,B:Type.\lambda p: Prod A B.
+match p with
+[(pair a b) \Rightarrow a]. 
+
+definition snd \def \lambda A,B:Type.\lambda p: Prod A B.
+match p with
+[(pair a b) \Rightarrow b].
+
+interpretation "First projection" 'fst x =
+ (cic:/matita/datatypes/constructors/fst.con _ _ x).
+
+notation "\fst x" with precedence 89
+for @{ 'fst $x}.
+
+interpretation "Second projection" 'snd x =
+ (cic:/matita/datatypes/constructors/snd.con _ _ x).
+
+notation "\snd x" with precedence 89
+for @{ 'snd $x}.
+
+theorem eq_pair_fst_snd: \forall A,B:Type.\forall p:Prod A B.
+p = 〈 (\fst p), (\snd p) 〉.
+intros.elim p.simplify.reflexivity.
+qed.
+
+inductive Sum (A,B:Type) : Type \def
+  inl : A \to Sum A B
+| inr : B \to Sum A B.
+
+interpretation "Disjoint union" 'plus A B =
+ (cic:/matita/datatypes/constructors/Sum.ind#xpointer(1/1) A B).
+
+inductive option (A:Type) : Type ≝
+   None : option A
+ | Some : A → option A.
\ No newline at end of file