Brace expansion tree

Here’s a crazy bash one-liner I found via an article by Peter Krumins:

echo {w,t,}h{e{n{,ce{,forth}},re{,in,fore,with{,al}}},ither,at}

This prints 30 English words:

when, whence, whenceforth, where, wherein, wherefore, wherewith, wherewithal, whither, what, then, thence, thenceforth, there, therein, therefore, therewith, therewithal, thither, that, hen, hence, henceforth, here, herein, herefore, herewith, herewithal, hither, hat

This post will explain how the one-liner works.

Bash brace expansion iterates through all possibilities listed within curly braces, with possibilities separated by a comma. Note that the comma is a separator and not a terminator. And so, for example, the expression `{w,t,}` is effectively `{w,t,""}`.

When bash sees two brace expressions, these expand to the cartesian product of the two expressions. For example,

echo {A,B}{1,2,3}

produces

A1 A2 A3 B1 B2 B3

In the expression above we have

{w,t,}h{e…,ither,at}

So the expansion will enumerate all possibilities of `{w,h,}` multiplied by all possibilities of `{e…,ither,at}` where `e…` is itself a brace expression.

A diagram will help a lot.

The brace expansion does a depth-first traversal of this tree.