evaluation of logical expression chain in /bin/sh - sh

Question

I have trouble understanding how this posix shell code works.
my_dir=/tmp/foo_dir
[ -d $my_dir ] || mkdir -p $my_dir || echo "Error creating '$my_dir'!"
Consider the case where the directory does not exist.
-d returns zero if directory doesn't exist, so then the "mkdir" is evaluated.
mkdir returns zero upon success, that should lead to "echo" being evaluated as well. Yet this code works (echo is only printed if directory creation fails by changing my_dir to /ttmp/foo_dir")

Answer 1

In a posix shell, 0 means success and other values means failure. When we use a command in a logical expression, we are testing it's exit status. We can use $? to check the last exit status.
Experimenting:
$ true
$ echo $?
0
$ false
$ echo $?
1
$ [ -d tmpdir ]
$ echo $?
1
$ mkdir tmpdir
$ echo $?
0
$ mkdir tmpdir
mkdir: tmpdir: File exists
$ echo $?
1
$ mkdir -p tmpdir
$ echo $?
0
$ [ -d tmpdir ]
$ echo $?
0
As you can see, -d returns 0 (success) when the directory is present and 1 otherwise. Similarly, mkdir returns 0 when it successfully creates a directory and 1 if it doesn't, but mkdir -p does not consider the file already existing as an error.
The thing is that || is a short-circuiting operator. Only what's needed gets executed. So, for example, in true || echo Hello, echo Hello never gets executed because the left side of || is always true. && is also a short-circuiting operator and false && echo Hello would never execute echo Hello because the left side of the operator is always false.
Keeping all that in mind, it's easy to see how it works:
If the directory exists, -d returns 0 (success) and the rest of the operands doesn't need to be evaluated (due to the short-circuiting behaviour)
If the directory doesn't exist, -d return 1 (failure) and mkdir -p is executed:
If the directory is successfully created (remember that mkdir -p does not return an error if the directory already exists), mkdir -p returns 0 (success) and echo msg doesn't get executed (due to short-circuiting behaviour)
If the directory isn't successfully created, mkdir -p returns 1 (failure) and echo msg is evaluated. Its exit status is the "value" of the whole expression.