Problem: ringbuffer_dequeue

Your task is to implement and verify the dequeue (pop) operation for a Ring Buffer data structure in Dafny. Because the ring buffer uses a fixed-size underlying array, the "front" of the queue is not fixed at the array's index 0 but is instead tracked by a moving head pointer. Verification: Verify that the operation returns the element currently at the "front" of the logical sequence (index 0). Structural Update: You must prove that after the element is returned, the new model sequence is shortened by one and contains the remaining elements in their original relative order. Difference from Standard Queue: Unlike a standard Vec-based queue where popping from the front requires shifting all subsequent elements (an $O(N)$ operation), verify that this operation achieves the same result by simply advancing the internal head pointer (an $O(1)$ operation), correctly wrapping around to the start of the array if the end is reached.

// Following is the block for necessary definitions
// <preamble>
class RingBuffer<T> {
    var data: seq<T>
    var head: int
    var len: int
    var capacity: int

    // View function: models the ring buffer as a linear sequence
    function view(): seq<T>
        reads this
        requires capacity > 0
        requires len >= 0
        // Explicitly require data length matches capacity for well-defined indexing
        requires |data| == capacity 
    {
        // Capture fields to local variables to satisfy lambda read requirements
        var d := data;
        var h := head;
        var c := capacity;
        
        seq(len, i => d[(h + i) % c])
    }

    predicate is_valid()
        reads this
    {
        capacity > 0 &&
        |data| == capacity &&
        0 <= len <= capacity &&
        0 <= head < capacity
    }

    constructor(cap: int, fill_value: T)
        requires cap > 0
        ensures is_valid()
        ensures |view()| == 0
        ensures capacity == cap
    {
        var d := [];
        var i := 0;
        while i < cap
            invariant |d| == i
            invariant i <= cap
        {
            d := d + [fill_value];
            i := i + 1;
        }
        data := d;
        head := 0;
        len := 0;
        capacity := cap;
    }
// </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 the oldest element from the buffer
    method dequeue() returns (val: T)
        requires is_valid()
        requires len > 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 ring buffer here.
    }
// </code>
}