Using Comparator in Set

[Rajesh1978]

I have the piece of code

#include<iostream>
#include<set>

using namespace std;

class Test
{
        public:
                int val;
};

class comp
{
        bool operator()(Test a, Test b)
        {
                return a.val < b.val;
        }
};

bool cmp(Test a, Test b)
{
        return a.val<b.val;
}
int main()
{
        set<Test,comp>s;
        return 0;
}

It comiles fine

but 

int main()
{
        set<Test,cmp>s;
        return 0;
}
gives following error

setTest.cpp: In function ‘int main()’:
setTest.cpp:26: error: type/value mismatch at argument 2 in template parameter list for ‘template<class _Key, class _Compare, class _Alloc> class std::set’
setTest.cpp:26: error:   expected a type, got ‘cmp’
setTest.cpp:26: error: invalid type in declaration before ‘;’ token

My doubt is why we can only use functor and not predicate function.

because in algorithms we can use both functor and predicate.

help me understanding it..