INVOCATION
  A login shell is one whose first character of argument zero is a -, or
  one started with the --login option.
  An interactive shell is one started without non-option arguments and
  without the -c option whose standard input and error are both connected
  to terminals (as determined by isatty(3)), or one started with the -i
  option. PS1 is set and $- includes i if bash is interactive, allowing
  a shell script or a startup file to test this state.
  The following paragraphs describe how bash executes its startup files.
  If any of the files exist but cannot be read, bash reports an error.
  Tildes are expanded in filenames as described below under Tilde Expan‐
  sion in the EXPANSION section.
  When bash is invoked as an interactive login shell, or as a non-inter‐
  active shell with the --login option, it first reads and executes com‐
  mands from the file /etc/profile, if that file exists. After reading
  that file, it looks for ~/.bash_profile, ~/.bash_login, and ~/.profile,
  in that order, and reads and executes commands from the first one that
  exists and is readable. The --noprofile option may be used when the
  shell is started to inhibit this behavior.
  When a login shell exits, bash reads and executes commands from the
  file ~/.bash_logout, if it exists.
  When an interactive shell that is not a login shell is started, bash
  reads and executes commands from /etc/bash.bashrc and ~/.bashrc, if
  these files exist. This may be inhibited by using the --norc option.
  The --rcfile file option will force bash to read and execute commands
  from file instead of /etc/bash.bashrc and ~/.bashrc.
  When bash is started non-interactively, to run a shell script, for
  example, it looks for the variable BASH_ENV in the environment, expands
  its value if it appears there, and uses the expanded value as the name
  of a file to read and execute. Bash behaves as if the following com‐
  mand were executed:
    if [ -n "$BASH_ENV" ]; then . "$BASH_ENV"; fi
  but the value of the PATH variable is not used to search for the file‐
  name.

bash-4.3$