The BinarySearch(L, x) function performs a binary search on list L for element x. List L is assumed to be sorted.  If a match is found, the position of the element is returned; otherwise, the value  is returned.

In this form of the calling sequence, x must be of type numeric or string and the list should have operands of the same type in ascending order.

If parameter f is specified in the calling sequence, it must be either a procedure or operator where  returns true if x precedes y, or a list of the form  such that  returns true if x precedes y.

If g is specified in the calling sequence, it must be either a procedure or operator where  returns true if x and y are equal, or a list of the form  such that  returns true if x and y are equal.

If g is not included, boolean equality is used to test if two objects are equal.