(also know as lexicographic comparison)
If you are familiar with perl and the relationship between its comparison operators and that of shell scripts, you would probably write the test as follows:
$ test bar '<' foo
$ test foo '>' bar
And yes, that would work, but not with all shells. I'm afraid to tell you that the < and > comparison operators are not required by the POSIX:2001 specification and are, therefore, bashisms.
What does this have to do with perl? well, the shell way is the inverse of the perl way.
What? In Perl you test the equality of two numbers with '==', in shell you use '-eq'; in perl the equality of strings is 'eq', in shell it is '='. In shell scripts you can compare two numbers with -gt (test 1 -gt 0) while in perl the equivalent comparison is with > (1 > 0).
So in this case the perl way is "bar lt foo" and based on the above the shell way should be "bar < foo". However, care must be taken when using such operators in shell scripts. Since < and > are used for redirections in shell scripts, one must quote them even when using bash. An alternative is to use the [[ special test function of bash which alters the shell syntax.
This time I didn't write a function to portably (or "somewhat portably") replace such comparisons. Feel free to share your solution in the comments, with bonus points if you come up with a solution without using external commands.