Some lazy code to D
bearophile
bearophileHUGS at lycos.com
Tue Aug 28 15:53:40 PDT 2012
Once in a while I show some comparisons of code translated in
different languages.
A challenge from Reddit-Dailyprogrammer:
http://www.reddit.com/r/dailyprogrammer/comments/ywm28/8272012_challenge_92_difficult_bags_and_balls/
The purpose of this post of mine is to compare a nice looking
Haskell solution of this problem to its Python/D translation.
This means this post is about language design matters and it's
not about problem solving :-)
(I have used a little program from that Reddit because this
allows to show in this post complete runnable programs. Usually
you can't do this with real-world code. But I can attest that the
lazyness and other things shown in this program and this post are
present and used/useful in much larger programs too.)
------------------------------
The little problem:
Compute all the permutations of placing 9 balls into 4 bags such
that each bag contains an odd number of balls. Ball count is
transient when placing bags within one another. For example, a
bag containing 3 balls is placed inside a bag containing 2 balls.
The inner bag contains 3 balls and the outer bag contains 5
balls. Some example permutations:
((((9))))
(8(((1))))
(1)(1)((7))
------------------------------
The Haskell solution written by Ledrug, a little reformatted:
bags :: Int -> Int -> Int -> Int -> [String]
bags 0 _ 0 _ = [""]
bags b c n m
| b <= 0 || n <= 0 || c <= 0 || m <= 0 = []
| otherwise = [l ++ r |
n1 <- [1 .. m],
b1 <- if n1 == m then [1 .. c] else [1 .. b],
l <- bag b1 n1,
r <- bags (b - b1) b1 (n - n1) n1]
bag :: Int -> Int -> [String]
bag 0 0 = [""]
bag b n
| b <= 0 || n <= 0 = []
| even n = []
| otherwise = ["(" ++ replicate n1 '*' ++ chain ++ ")" |
n1 <- [0 .. n],
chain <- bags (b - 1) (b - 1) (n - n1) (n -
n1)]
pick :: Int -> Int -> [String]
pick b n = bags b b n n
main = do
mapM_ putStrLn $ (pick 4 9)
------------------------------
A direct translation to Python2 of the Haskell code comes very
similar, it's quite lazy, and it's short enough:
def pick(nbags, nballs):
def bag(b, n):
if b == 0 and n == 0:
return [""]
if b <= 0 or n <= 0 or n % 2 == 0:
return []
return ("(" + '*' * n1 + chain + ")"
for n1 in xrange(n + 1)
for chain in bags(b - 1, b - 1, n - n1, n - n1))
def bags(b, c, n, m):
if b == 0 and n == 0:
return [""]
if b <= 0 or n <= 0 or c <= 0 or m <= 0:
return []
return (l + r
for n1 in xrange(1, m + 1)
for b1 in (xrange(1, c+1) if n1 == m else
xrange(1, b+1))
for l in bag(b1, n1)
for r in bags(b - b1, b1, n - n1, n1))
return bags(nbags, nbags, nballs, nballs)
def main():
for sol in pick(4, 9):
print sol
main()
I have used inner functions because here they keep the global
namespace more clean. The user needs to see just the pick()
function.
------------------------------
This is a direct translation of the Python2 code to D (but uses
eager arrays, that currently are more idiomatic in D):
import std.stdio, std.array, std.range;
string[] pick(in int nbags, in int nballs) /*pure nothrow*/ {
static struct Namespace {
static string[] bag(in int b, in int n) /*pure nothrow*/ {
if (b == 0 && n == 0)
return [""];
if (b <= 0 || n <= 0 || n % 2 == 0)
return [];
typeof(return) result;
foreach (n1; 0 .. n + 1)
foreach (chain; bags(b - 1, b - 1, n - n1, n -
n1))
result ~= "(" ~ std.array.replicate("*", n1)
~ chain ~ ")";
return result;
}
static string[] bags(in int b, in int c, in int n, in int
m) /*pure nothrow*/ {
if (b == 0 && n == 0)
return [""];
if (b <= 0 || n <= 0 || c <= 0 || m <= 0)
return [];
typeof(return) result;
foreach (n1; 1 .. m + 1)
// iota is not pure, nor nothrow
foreach (b1; (n1 == m) ? iota(1, c+1) : iota(1, b
+ 1))
foreach (l; bag(b1, n1))
foreach (r; bags(b - b1, b1, n - n1, n1))
result ~= l ~ r;
return result;
}
}
return Namespace.bags(nbags, nbags, nballs, nballs);
}
void main() {
writefln("%-(%s\n%)", pick(4, 9));
}
In this D code there are few temporary problems:
- Iota is not pure nor nothrow, so none of the functions can be
pure nothrow. This Phobos problem will be fixed.
- I have had to fully qualify the path of std.array.replicate, to
avoid a name clash. Maybe this little problem will be solved.
There are some small problems:
- I have used a static inner struct Namespace (Don's idea), to
allow nested mutual recursion. It's not very nice, but for me
it's acceptable, also because mutual recursion among inner
functions is not so common.
- "*".replicate(n1) is less nice and less short than the Python
syntax "*" * n1, but it's not a big problem.
- The "%-(%s\n%)" formatting string is complex, this syntax isn't
so easy to remember, on the other hand here it has a voided one
foreach. So I think it's acceptable.
- Currently the DMD front-end doesn't contain logic that
specifically optimimizes better std.range.iota. Maybe in some
years this will improve. In the meantime this is not a big
problem.
A problem with inner functions is that in both D and Python they
become hard(er) to unittest. In D I'd like this to be valid code:
void main() {
int foo() { return 1; }
unittest { assert(foo() == 1; }
}
There is a significant problem:
- This program generates a small sequence of solutions, so
lazyness is not important. But sometimes the algoritms have to
generate tons of things, and lazyness becomes useful. This D
program is not lazy, unlike the Haskell and Python programs.
Writing this program with lazyness is not too much hard, but the
code becomes uglier, longer and more bug prone. I think C#
designers did the right thing adding yield to their language,
because it's a construct very often useful.
------------------------------
This is a lazy translation in D, using opApply:
import std.stdio, std.array, std.range;
auto pick(in int nbags, in int nballs) /*pure nothrow*/ {
static struct Namespace {
static struct Bag {
int b, n;
int opApply(int delegate(ref string) dg) {
int result;
string aux;
if (b == 0 && n == 0) {
aux = "";
result = dg(aux);
if (result) goto END;
}
if (b <= 0 || n <= 0 || n % 2 == 0)
goto END;
foreach (n1; 0 .. n + 1)
foreach (chain; Bags(b - 1, b - 1, n - n1, n
- n1)) {
aux = "(" ~ std.array.replicate("*", n1)
~ chain ~ ")";
result = dg(aux);
if (result) goto END;
}
END: return result;
}
}
static struct Bags {
int b, c, n, m;
int opApply(int delegate(ref string) dg) {
int result;
string aux;
if (b == 0 && n == 0) {
aux = "";
result = dg(aux);
if (result) goto END;
}
if (b <= 0 || n <= 0 || c <= 0 || m <= 0)
goto END;
foreach (n1; 1 .. m + 1)
foreach (b1; (n1 == m) ? iota(1, c+1) :
iota(1, b + 1))
foreach (l; Bag(b1, n1))
foreach (r; Bags(b - b1, b1, n - n1,
n1)) {
aux = l ~ r;
result = dg(aux);
if (result) goto END;
}
END: return result;
}
}
}
return Namespace.Bags(nbags, nbags, nballs, nballs);
}
void main() {
foreach (sol; pick(4, 9))
writeln(sol);
}
In main() I have had to use a foreach because currently writeln()
is not able to print all the items of an iterable implemented
with opApply. I hope this will be fixed
(http://d.puremagic.com/issues/show_bug.cgi?id=4264 ).
Both Walter and Andrei don't like opApply a lot, and I understand
why they do (for uniformity, language simplicity, for the higher
flexibility of ranges). On the other hand if you try to translate
the Haskell code to D using Ranges it becomes long.
------------------------------
Your can object that this is not idiomatic D code, because I was
translating (beautiful, short, readable, safe) Haskell/Python
code. My answer is that this kind of lazy code is so commonly
useful that I'd like it to be better supported in D :-)
Bye,
bearophile
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