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.

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

$\mathrm{heap}:-\mathrm{insert}\left(\mathrm{stefan}\,h\right)$

$\mathrm{stefan}$

$\mathrm{heap}:-\mathrm{size}\left(h\right)$

$5$

$\mathrm{heap}:-\max \left(h\right)$

$\mathrm{tony}$

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

$\mathrm{tony}$

$\mathrm{stefan}$

$\mathrm{michael}$

$\mathrm{greg}$

$\mathrm{bruno}$