New Post: Dafny code for multiply an array

well you are absolutely right! i tried to say something about the division ofthe array but maybe it is unnecessary ,
after thinking again i got this :

method product(a: array<int>, key: int) returns (p: int)
    requires a != null
    ensures p == RecursivePositiveProduct(a, 0)
{

// Introduce local variable (6.1)
    var i : nat;
    assert  RecursivePositiveProduct(a,a.Length)==1 ;
    p, i := 1,a.Length;
    assert  p == RecursivePositiveProduct(a,i) ; 

// iteration (5.5)
    while (i > 0)
        invariant i <= a.Length && p == RecursivePositiveProduct(a,i)
        invariant p>=0;
        decreases i;
    {
        p, i := Product1(p, a, i);
    }
// Strengthen post condition (1.1)
    assert  i ==0 && p == RecursivePositiveProduct(a,i) ;
}


method Product1(p0 : nat, a: array<int>, i0 : nat) returns (p : nat, i : nat)
  requires a!=null;
    requires  0 <i0 <=a.Length && p0 == RecursivePositiveProduct(a,i0) ;
    ensures i ==i0-1 && p == RecursivePositiveProduct(a,i) ;
{
    p, i := p0, i0;

  assert a[i] <= 0 ==> p0 == RecursivePositiveProduct(a,i) ;
  assert a[i] > 0 ==> a[i]*p0 == RecursivePositiveProduct(a,i) ;


    if {
        case(a[i] > 0) =>
            p := p0 * a[i];
        case (a[i] <= 0) => 
            // Skip command (3.2)               
    }
       i := i0 - 1;
}

still complicating with the product 1 proove :/

http://rise4fun.com/Dafny/JmTK