The map function seems eager, e.g.
map(x->x+1, 1:3) gives one [2,3,4].
I want to find a lazy and iterative version of map so that the values are not generated all at once, so I can just get values one by one from the result of the map?
You can use Base.Generator for this, e.g. in your case:
julia> g = (x + 1 for x in 1:3)
Base.Generator{UnitRange{Int64},getfield(Main, Symbol("##5#6"))}(getfield(Main, Symbol("##5#6"))(), 1:3)
julia> collect(g)
3-element Array{Int64,1}:
2
3
4