I have a list like {{a,x},{b,y},{c,x},{d,z},{e,y}} and would like to produce from it a list formed by collecting all top-level elements whose second components are the same into a single list. For the list above, the desired output would be { {{a,c},x}, {{b,e},y}, {d, z}}. Here x, y, and z could also be lists, if that matters. This seems like an application of Reap and Sow. But the on-line documentation of these functions is pretty poor, and the examples don't add much. Shifrin's book keeps referring to a discussion of Reap and Sow in Part II, but I can't actually find a part II. Is there a resource somewhere that I can look at to understand the ins and outs of these functions, and see some real examples of how to use them?

The simple Reap[Map[Sow[#, #[[2]]] &, r]], where r is the list above, produces almost what I want, but instead of {{a,c},x} above, it produces {{a,x},{c,x}}.

(I'm sure that someone will post a solution to my programming problem; for that I would be grateful. But I really would like to understand these functions better.)

EDIT: The code Reap[Map[Sow[#[[1]], #[[2]]] &, r], _, {#2, #1} &] // Rest does the trick. Perhaps there's a better way. In any case, my question about documentation still stands.

  • 2
    $\begingroup$ Probably GatherBy is the way to go here. What in the docs is unclear/missing in your opinion? There are several answers using Reap/Sow around, a search may be useful. $\endgroup$
    – Yves Klett
    Commented Mar 16, 2014 at 13:38
  • $\begingroup$ @YvesKlett My major whine was that there seemed to be no way to see exactly what Sow was doing, but looking at more examples, I realized that providing an undefined function name as the third argument of Reap will show me exactly what my Sow produced. I'm much happier now. And GatherBy with a little postprocessing worked as well, so now I have two possible solutions. $\endgroup$
    – rogerl
    Commented Mar 16, 2014 at 14:02

1 Answer 1


This question may be deemed a duplicate, as the specific operation has been addressed before (actually quite a few times as I recall). Nevertheless I shall attempt to provide a useful answer regarding Sow and Reap. First, I there are many examples of the use of these functions on this site, and I encourage you to search for them, as they will provide a broader application than is practical in a single answer.

For your given example you could write:

data = {{a, x}, {b, y}, {c, x}, {d, z}, {e, y}};

Reap[Sow @@@ data, _, {#2, #} &][[2]]
{{{a, c}, x}, {{b, e}, y}, {{d}, z}}

This doesn't quite match your desired output but it is a more consistent format.

However, you mention: "Here x, y, and z could also be lists, if that matters." Yes, it does matter, because if the second argument of Sow is a list it is not treated as a single tag but a list of tags. Therefore you need to wrap the list itself in {} to have it treated as a single tag. First an example of the failure:

x = {1, 2, 3};

Reap[Sow @@@ data, _, {#2, #} &][[2]]
{{{a, c}, 1}, {{a, c}, 2}, {{a, c}, 3}, {{b, e}, y}, {{d}, z}}

And then the correction:

Reap[Sow[#, {#2}] & @@@ data, _, {#2, #} &][[2]]
{{{a, c}, {1, 2, 3}}, {{b, e}, y}, {{d}, z}}

A few posts you should read:

Perhaps also of interest:

Version 10 update: although specifically Reap and Sow were requested I think it is worth noting that this can be done with Associations as well, e.g.:

{#2, #} & @@@ Normal @ GroupBy[data, Last -> First]
{{{a, c}, x}, {{b, e}, y}, {{d}, z}}

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.