The call heap[new](f) returns an empty heap where f is a Boolean-valued function which specifies a total ordering for the elements to be inserted into the heap.

The call heap[new](f, x1, ..., xn) returns a heap with the values x1, ..., xn initially inserted into the heap.

The call heap[insert](x, h) inserts the element x into the heap h while heap[extract](h) returns (and removes) the maximum element from the heap (according to the ordering defined by f).

The call heap[empty](h) returns true if the heap h is empty, and false if it is not empty.

Additionally, heap[max](h) returns the maximum element in the heap (but does not remove it) and heap[size](h) returns the number of elements in the heap.

$h≔\mathrm{heap}\left[\mathrm{new}\right]\left(\mathrm{lexorder}\,\mathrm{greg}\,\mathrm{tony}\,\mathrm{bruno}\,\mathrm{michael}\right)\:$

$\mathrm{heap}\left[\mathrm{insert}\right]\left(\mathrm{stefan}\,h\right)$

$\mathrm{stefan}$

$\mathrm{heap}\left[\mathrm{size}\right]\left(h\right)$

$5$

$\mathrm{heap}\left[\max \right]\left(h\right)$

$\mathrm{tony}$

$$\begin{gathered} \mathbf{while}\mathbf{not}\mathrm{heap}\left[\mathrm{empty}\right]\left(h\right)\mathbf{do} \\ \mathrm{heap}\left[\mathrm{extract}\right]\left(h\right) \\ \mathbf{end}\mathbf{do} \end{gathered}$$

$\mathrm{tony}$

$\mathrm{stefan}$

$\mathrm{michael}$

$\mathrm{greg}$

$\mathrm{bruno}$