passing predicates to lowerBound, or alternatively, how lazy is map?

[Andrew Brown via Digitalmars-d-learn]

Hi there,

The problem this question is about is now solved, by writing my 
own binary search algorithm, but I'd like to ask it anyway as I 
think I could learn a lot from the answers.

The problem was, given an array of numbers, double[] numbers, and 
an ordering from makeIndex size_t[] order, I want to count how 
many numbers are less than a number N. The obvious way would be 
to use lowerBound from std.range, but I can't work out how to 
pass it a predicate like "numbers[a] < b". Could someone explain 
the template:

(SearchPolicy sp = SearchPolicy.binarySearch, V)(V value) if 
(isTwoWayCompatible!(predFun, ElementType!Range, V));

The alternative way I thought to do it was to combine map with 
lowerBound, i.e.:

map!(a => numbers[a])(order).assumeSorted
                            .lowerBound(N)
                            .length

My question about this is how lazy is map? Will it work on every 
value of order and then pass it to lowerBound, or could it work 
to evaluate only those values asked by lowerBound? I guess 
probably not, but could a function be composed that worked in 
this way?

Thank you very much

Andrew