Problem: queue_dequeue

Your task is to implement a Queue and verify its First-In, First-Out correctness in Dafny. The queue is modeled as a sequence where elements enter at the "back" and exit from the "front." Now you should implement and verify the dequeue (pop) operation. Dequeue (Pop): Verify that the operation returns the first element (index 0) of the sequence and that the new model sequence contains all remaining elements in their original relative order.

// Following is the block for necessary definitions
// <preamble>
class VerifiableQueue<T> {
    var data: seq<T>

    function view(): seq<T>
        reads this
    {
        data
    }

    predicate is_valid()
        reads this
    {
        true
    }

    constructor()
        ensures is_valid()
        ensures |view()| == 0
    {
        data := [];
    }

    method len() returns (l: int)
        requires is_valid()
        ensures l == |view()|
        ensures l >= 0
    {
        l := |data|;
    }
// </preamble>

// Following is the block for potential helper specifications
// <helpers>

// </helpers>

// Following is the block for proofs of lemmas
// <proofs>

// </proofs>

// Following is the block for the main specification
// <spec>
    // Pop from the front of the queue
    method dequeue() returns (val: T)
        requires is_valid()
        requires |view()| > 0
        modifies this
        ensures is_valid()
        // The value returned is the first element of the old sequence
        ensures val == old(view())[0]
        // The new sequence is the old sequence minus the first element
        ensures view() == old(view())[1..]
// </spec>
// <code>
    {
        // Implement and verify the dequeue operation for the queue here.
    }
// </code>
}