On 02/23/2011 03:28 AM, bearophile wrote:
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.

Maybe we should reverse the point of view and start with Range. A base type for anything 'sequential' (iterable) is Range of E (element type). Then, an array E[] is a Range of E that just happens to have its elements pre-stored. Ditto for any other collection. And a slice, or any other kind of 'view' into a collection, is a Range of E that just happens to have direct access to its elements (in memory, via pointer; or via cursor, or whatever).

Denis
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