Handy mapping with n-adic functions

[dlangBugzillaToGithub]

bearophile_hugs reported this on 2011-05-18T18:20:16Z

Transfered from https://issues.dlang.org/show_bug.cgi?id=6034

CC List

• andrei (@andralex)

Description

A very common operation is to map a n-adic function (like a triadic one) on n iterables. To do it in Haskell you use zipWith, example:

Prelude> let arr1 = [1, 2, 3]
Prelude> let arr2 = [10, 20, 30]
Prelude> let arr3 = [100, 200, 300]
Prelude> let foo x y z = x + y * z
Prelude> zipWith3 foo arr1 arr2 arr3
[1001,4002,9003]


In Python2.6 the normal map function is enough, it optionally accepts more than one iterable (in Python3 map does the same, but it's lazy):


def foo(x, y, z):
    return x + y * z

arr1 = [1, 2, 3]
arr2 = [10, 20, 30]
arr3 = [100, 200, 300]
print map(foo, arr1, arr2, arr3)


But in D2+Phobos you need to write awkward code:

import std.stdio, std.algorithm, std.range;

int foo(int x, int y, int z) {
    return x + y * z;
}

void main() {
    auto arr1 = [1, 2, 3];
    auto arr2 = [10, 20, 30];
    auto arr3 = [100, 200, 300];
    auto r = map!((t){ return foo(t.tupleof); })(zip(arr1, arr2, arr3));
    writeln(r);
}

Output:
[1001, 4002, 9003]


Unlike Python currently std.algorithm.map() is designed to optionally accept more than one function, and return a tuple. It's sometimes useful to do this, but in my experience the semantics of the Python map is useful more often. So I'd like the semantics of D map to become similar to the semantics of the Python3 map. In this case the D code becomes something like:

auto r = map!foo(arr1, arr2, arr3);

If this is not possible, or not desired (or it leads to too much complex Phobos code), then I suggest to introduce a new function in std.algorithm (or even in std.range) that acts like the Haskell zipWith. In this case the D code becomes something like:

auto r = zipWith!foo(arr1, arr2, arr3);

[dlangBugzillaToGithub]

bearophile_hugs commented on 2011-05-18T18:32:21Z

An example usage for triadic map/zipWith (this is Euler problem 18, http://projecteuler.net/index.php?section=problems&id=18 ):


import std.stdio, std.algorithm, std.range, std.array;

auto reversed(R)(R range) {
    auto result = array(range);
    result.reverse;
    return result;
}

int f(int x, int y, int z) { return x + max(y, z); }

int[] g(int[] xs, int[] ys) {
    return array(map!((t){ return f(t.tupleof); })(zip(ys, xs[0..$-1], xs[1..$])));
}

void main() {
    auto tri = [[75],
                [95,64],
                [17,47,82],
                [18,35,87,10],
                [20, 4,82,47,65],
                [19, 1,23,75, 3,34],
                [88, 2,77,73, 7,63,67],
                [99,65, 4,28, 6,16,70,92],
                [41,41,26,56,83,40,80,70,33],
                [41,48,72,33,47,32,37,16,94,29],
                [53,71,44,65,25,43,91,52,97,51,14],
                [70,11,33,28,77,73,17,78,39,68,17,57],
                [91,71,52,38,17,14,91,43,58,50,27,29,48],
                [63,66, 4,68,89,53,67,30,73,16,69,87,40,31],
                [ 4,62,98,27,23, 9,70,98,73,93,38,53,60, 4,23]];

    writeln(reduce!g(reversed(tri))[0]);
}


In Haskell it becomes:


problem_18 = head $ foldr1 g tri
  where
    f x y z = x + max y z
    g xs ys = zipWith3 f xs ys $ tail ys
    tri = [...]



In Python2.6 (this is not pythonic code):

f = lambda x, y, z: x + max(y, z)
g = lambda xs, ys: map(f, ys, xs[:-1], xs[1:])
print reduce(g, reversed(tri))[0]


With a n-way map the function g() becomes (this uses the array version of map):

int[] g(int[] xs, int[] ys) {
    return amap!f(ys, xs[0..$-1], xs[1..$]);
}


With a zipWith the function g() becomes:

int[] g(int[] xs, int[] ys) {
    return array(zipWith!f(ys, xs[0..$-1], xs[1..$]));
}