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+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+(* Standard functions and combinators.
+ * Proofs about them require functional extensionality and can be found in [Combinators].
+ *
+ * Author: Matthieu Sozeau
+ * Institution: LRI, CNRS UMR 8623 - UniversitÃcopyright Paris Sud
+ *              91405 Orsay, France *)
+
+(* $Id: Basics.v 11046 2008-06-03 22:48:06Z msozeau $ *)
+
+(** The polymorphic identity function. *)
+
+Definition id {A} := fun x : A => x.
+
+(** Function composition. *)
+
+Definition compose {A B C} (g : B -> C) (f : A -> B) := 
+  fun x : A => g (f x).
+
+Hint Unfold compose.
+
+Notation " g ∘ f " := (compose g f)  
+  (at level 40, left associativity) : program_scope.
+
+Open Local Scope program_scope.
+
+(** The non-dependent function space between [A] and [B]. *)
+
+Definition arrow (A B : Type) := A -> B.
+
+(** Logical implication. *)
+
+Definition impl (A B : Prop) : Prop := A -> B.
+
+(** The constant function [const a] always returns [a]. *)
+
+Definition const {A B} (a : A) := fun _ : B => a.
+
+(** The [flip] combinator reverses the first two arguments of a function. *)
+
+Definition flip {A B C} (f : A -> B -> C) x y := f y x.
+
+(** Application as a combinator. *)
+
+Definition apply {A B} (f : A -> B) (x : A) := f x.
+
+(** Curryfication of [prod] is defined in [Logic.Datatypes]. *)
+
+Implicit Arguments prod_curry [[A] [B] [C]].
+Implicit Arguments prod_uncurry [[A] [B] [C]].