Seeing "Broken pipe" in this situation is rare, but normal.
When you run
type rvm | head -1, bash executes
type rvm in one process,
head -1 in another.1 The stdout of
type is connected to the "write" end of a pipe, the stdin of
head to the "read" end. Both processes run at the same time.
head -1 process reads data from stdin (usually in chunks of 8 kB), prints out a single line (according to the
-1 option), and exits, causing the "read" end of the pipe to be closed. Since the
rvm function is quite long (around 11 kB after being parsed and reconstructed by bash), this means that
head exits while
type still has a few kB of data to write out.
At this point, since
type is trying to write to a pipe whose other end has been closed – a broken pipe – the write() function it caled will return an EPIPE error, translated as "Broken pipe". In addition to this error, the kernel also sends the SIGPIPE signal to
type, which by default kills the process immediately.
(The signal is very useful in interactive shells, since most users do not want the first process to keep running and trying to write to nowhere. Meanwhile, non-interactive services ignore SIGPIPE – it would not be good for a long-running daemon to die on such a simple error – so they find the error code very useful.)
However, signal delivery is not 100% immediate, and there may be cases where write() returns EPIPE and the process continues to run for a short while before receiving the signal. In this case,
type gets enough time to notice the failed write, translate the error code and even print an error message to stderr before being killed by SIGPIPE. (The error message says "-bash: type:" since
type is a built-in command of bash itself.)
This seems to be more common on multi-CPU systems, since the
type process and the kernel's signal delivery code can run on different cores, literally at the same time.
It would be possible to remove this message by patching the
type builtin (in bash's source code) to immediately exit when it receives an EPIPE from the write() function.
However, it's nothing to be concerned about, and it is not related to your
rvm installation in any way.