Lazy lists

[bearophile]

A task from the RosettaCode site asks to generate a Sierpinski carpet like this, on given order:


###########################
# ## ## ## ## ## ## ## ## #
###########################
###   ######   ######   ###
# #   # ## #   # ## #   # #
###   ######   ######   ###
###########################
# ## ## ## ## ## ## ## ## #
###########################
#########         #########
# ## ## #         # ## ## #
#########         #########
###   ###         ###   ###
# #   # #         # #   # #
###   ###         ###   ###
#########         #########
# ## ## #         # ## ## #
#########         #########
###########################
# ## ## ## ## ## ## ## ## #
###########################
###   ######   ######   ###
# #   # ## #   # ## #   # #
###   ######   ######   ###
###########################
# ## ## ## ## ## ## ## ## #
###########################


This is a Scala implementation of a function that prints the carpet:


def nextCarpet(carpet: List[String]): List[String] = (
  carpet.map(x => x + x + x) :::
  carpet.map(x => x + x.replace('#', ' ') + x) :::
  carpet.map(x => x + x + x))
 
def sierpinskiCarpets(n: Int) = (Iterator.iterate(List("#"))(nextCarpet) drop n next) foreach println



A D version that uses arrays:

import std.stdio, std.string, std.algorithm, std.array, std.range;
 
string[] nextCarpet(string[] c) {
    auto b = array(map!q{a ~ a ~ a}(c));
    return b ~ array(map!q{a ~ a.replace("#"," ") ~ a}(c)) ~ b;
}
 
void main() {
    auto c = recurrence!((a, n){ return nextCarpet(a[n-1]); })(["#"]);
    writeln(array(take(c, 4)).back.join("\n"));
}


Few notes:
- I don't know how to take just the 4th item of a lazy sequence. array(take(c, 4)).back is not good.

- recurrence() is a bit overkill. A function like iterate() simplifies the code:
auto c = iterate!nextCarpet(["#"], 4);

- I don't see a simple way to create a lazy nextCarpet(), without those array(). The seed (["#"]) can't be an array, but even wrapping it with a lazy map!q{a}(["#"]) solves nothing. chain(map(chain...))) are all different types, so I think it can't work. The types in that Scala code are sound because it uses a lazy list type, that supports the ::: operator for concatenation, and List("#") to create the correctly typed seed. That carpet.map() returns a List[String]. So both the input and output of the Scala nextCarpet() are of the same type, List[String]. So such lazy list type template becomes really useful if you want to program in a lazy functional style.

Bye,
bearophile