/**************************************************************************/
/*                                                                        */
/*  The Why platform for program certification                            */
/*                                                                        */
/*  Copyright (C) 2002-2014                                               */
/*                                                                        */
/*    Jean-Christophe FILLIATRE, CNRS & Univ. Paris-sud                   */
/*    Claude MARCHE, INRIA & Univ. Paris-sud                              */
/*    Yannick MOY, Univ. Paris-sud                                        */
/*    Romain BARDOU, Univ. Paris-sud                                      */
/*                                                                        */
/*  Secondary contributors:                                               */
/*                                                                        */
/*    Thierry HUBERT, Univ. Paris-sud  (former Caduceus front-end)        */
/*    Nicolas ROUSSET, Univ. Paris-sud (on Jessie & Krakatoa)             */
/*    Ali AYAD, CNRS & CEA Saclay      (floating-point support)           */
/*    Sylvie BOLDO, INRIA              (floating-point support)           */
/*    Jean-Francois COUCHOT, INRIA     (sort encodings, hyps pruning)     */
/*    Mehdi DOGGUY, Univ. Paris-sud    (Why GUI)                          */
/*                                                                        */
/*  This software is free software; you can redistribute it and/or        */
/*  modify it under the terms of the GNU Lesser General Public            */
/*  License version 2.1, with the special exception on linking            */
/*  described in file LICENSE.                                            */
/*                                                                        */
/*  This software is distributed in the hope that it will be useful,      */
/*  but WITHOUT ANY WARRANTY; without even the implied warranty of        */
/*  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.                  */
/*                                                                        */
/**************************************************************************/

// RUNCOQ: will ask regtests to check Coq proofs of this program

// int model: unbounded mathematical integers
//@+ CheckArithOverflow = no

/*@ inductive isfib(integer x, integer r) {
  @  case isfib0: isfib(0,0);
  @  case isfib1: isfib(1,1);
  @  case isfibn: 
  @   \forall integer n r p; 
  @     n >= 2 && isfib(n-2,r) && isfib(n-1,p) ==> isfib(n,p+r);
  @ }
  @*/ 

//@ lemma isfib_2_1 : isfib(2,1);
//@ lemma isfib_6_8 : isfib(6,8);

// provable only if def is inductive (least fix point)
//@ lemma not_isfib_2_2 : ! isfib(2,2);

public class Fibonacci {

    /*@ requires n >= 0;
      @ decreases n;
      @ ensures isfib(n, \result); 
      @*/
    public static long Fib(int n) {
	long y=0, x=1, aux;

	/*@ loop_invariant 0 <= i <= n && isfib(i+1,x) && isfib(i,y);
	  @ loop_variant n-i;
	  @*/
	for(int i=0; i < n; i++) {
	    aux = y;
	    y = x;
	    x = x + aux;
	}
	return y;
    }
}