The operations in [alg.sorting] defined directly in namespace std
have two versions:
one that takes a function object of type Compare and
one that uses an operator<.

Compare is a function object type ([function.objects])
that meets the requirements for a template parameter
named BinaryPredicate ([algorithms.requirements]).

The return value of the function call operation
applied to an object of type Compare,
when converted to bool,
yields true
if the first argument of the call is less than the second, and
false otherwise.

Compare comp is used throughout
for algorithms assuming an ordering relation.

For algorithms other than those described in [alg.binary.search],
comp shall induce a strict weak ordering on the values.

The term *strict* refers to the requirement
of an irreflexive relation (!comp(x, x) for all x),
and the term *weak* to requirements
that are not as strong as those for a total ordering,
but stronger than those for a partial ordering.

If we define equiv(a, b) as !comp(a, b) && !comp(b, a),
then the requirements are that comp and equiv
both be transitive relations:

- comp(a, b) && comp(b, c) implies comp(a, c)
- equiv(a, b) && equiv(b, c) implies equiv(a, c)

A sequence is *sorted with respect to a comp and proj*
for a comparator and projection comp and proj
if for every iterator i pointing to the sequence and
every non-negative integer n
such that i + n is a valid iterator
pointing to an element of the sequence,
bool(invoke(comp, invoke(proj, *(i + n)), invoke(proj, *i)))
is false.

A sequence is *sorted with respect to a comparator comp*
for a comparator comp
if it is sorted with respect to
comp and identity{} (the identity projection).

A sequence [start, finish) is
*partitioned with respect to an expression* f(e)
if there exists an integer n
such that for all 0 <= i < (finish - start),
f(*(start + i)) is true if and only if i < n.