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Bash-2.01 contained only a few new features:

new `GROUPS' builtin array variable containing the user's group list
new bindable readline commands: history-and-alias-expand-line and
	alias-expand-line

Bash-2.0 contained extensive changes and new features from bash-1.14.7.
Here's a short list:

new `time' reserved word to time pipelines, shell builtins, and
	shell functions
one-dimensional arrays with a new compound assignment statement,
        appropriate expansion constructs and modifications to some
	of the builtins (read, declare, etc.) to use them
new quoting syntaxes for ANSI-C string expansion and locale-specific
	string translation
new expansions to do substring extraction, pattern replacement, and
	indirect variable expansion
new builtins: `disown' and `shopt'
new variables: HISTIGNORE, SHELLOPTS, PIPESTATUS, DIRSTACK, GLOBIGNORE,
	       MACHTYPE, BASH_VERSINFO
special handling of many unused or redundant variables removed
	(e.g., $notify, $glob_dot_filenames, $no_exit_on_failed_exec)
dynamic loading of new builtin commands; many loadable examples provided
new prompt expansions: \a, \e, \n, \H, \T, \@, \v, \V
history and aliases available in shell scripts
new readline variables: enable-keypad, mark-directories, input-meta,
	visible-stats, disable-completion, comment-begin
new readline commands to manipulate the mark and operate on the region
new readline emacs mode commands and bindings for ksh-88 compatibility
updated and extended builtins
new DEBUG trap
expanded (and now documented) restricted shell mode

implementation stuff:	
autoconf-based configuration
nearly all of the bugs reported since version 1.14 have been fixed
most builtins converted to use builtin `getopt' for consistency
most builtins use -p option to display output in a reusable form
	(for consistency)
grammar tighter and smaller (66 reduce-reduce conflicts gone)
lots of code now smaller and faster
test suite greatly expanded

B2) Are there any user-visible incompatibilities between bash-4.2 and
    previous bash versions?

There are a few incompatibilities between version 4.2 and previous
versions.  They are detailed in the file COMPAT in the bash distribution.
That file is not meant to be all-encompassing; send mail to
[e-mail] (or [e-mail] if you would like
community discussion) if you find something that's not mentioned there.

Section C:  Differences from other Unix shells

C1) How does bash differ from sh, the Bourne shell?

This is a non-comprehensive list of features that differentiate bash
from the SVR4.2 shell.  The bash manual page explains these more
completely.

Things bash has that sh does not:
	long invocation options
	[+-]O invocation option
	-l invocation option
	`!' reserved word to invert pipeline return value
	`time' reserved word to time pipelines and shell builtins
	the `function' reserved word
	the `select' compound command and reserved word
	arithmetic for command: for ((expr1 ; expr2; expr3 )); do list; done
	new $'...' and $"..." quoting
	the $(...) form of command substitution
	the $(<filename) form of command substitution, equivalent to
		$(cat filename)
	the ${#param} parameter value length operator
	the ${!param} indirect parameter expansion operator
	the ${!param*} prefix expansion operator
	the ${param:offset[:length]} parameter substring operator
	the ${param/pat[/string]} parameter pattern substitution operator
	expansions to perform substring removal (${p%[%]w}, ${p#[#]w})
	expansion of positional parameters beyond $9 with ${num}
	variables: BASH, BASHPID, BASH_VERSION, BASH_VERSINFO, UID, EUID, REPLY,
		   TIMEFORMAT, PPID, PWD, OLDPWD, SHLVL, RANDOM, SECONDS,
		   LINENO, HISTCMD, HOSTTYPE, OSTYPE, MACHTYPE, HOSTNAME,
		   ENV, PS3, PS4, DIRSTACK, PIPESTATUS, HISTSIZE, HISTFILE,
		   HISTFILESIZE, HISTCONTROL, HISTIGNORE, GLOBIGNORE, GROUPS,
		   PROMPT_COMMAND, FCEDIT, FIGNORE, IGNOREEOF, INPUTRC,
		   SHELLOPTS, OPTERR, HOSTFILE, TMOUT, FUNCNAME, histchars,
		   auto_resume, PROMPT_DIRTRIM, BASHOPTS, BASH_XTRACEFD
	DEBUG trap
	ERR trap
	variable arrays with new compound assignment syntax
	redirections: <>, &>, >|, <<<, [n]<&word-, [n]>&word-, >>&
	prompt string special char translation and variable expansion
	auto-export of variables in initial environment
	command search finds functions before builtins
	bash return builtin will exit a file sourced with `.'
	builtins: cd -/-L/-P, exec -l/-c/-a, echo -e/-E, hash -d/-l/-p/-t.
		  export -n/-f/-p/name=value, pwd -L/-P,
		  read -e/-p/-a/-t/-n/-d/-s/-u/-i/-N,
		  readonly -a/-f/name=value, trap -l, set +o,
		  set -b/-m/-o option/-h/-p/-B/-C/-H/-P,
		  unset -f/-v, ulimit -i/-m/-p/-q/-u/-x,
		  type -a/-p/-t/-f/-P, suspend -f, kill -n,
		  test -o optname/s1 == s2/s1 < s2/s1 > s2/-nt/-ot/-ef/-O/-G/-S
	bash reads ~/.bashrc for interactive shells, $ENV for non-interactive
	bash restricted shell mode is more extensive
	bash allows functions and variables with the same name
	brace expansion
	tilde expansion
	arithmetic expansion with $((...)) and `let' builtin
	the `[[...]]' extended conditional command
	process substitution
	aliases and alias/unalias builtins
	local variables in functions and `local' builtin
	readline and command-line editing with programmable completion
	command history and history/fc builtins
	csh-like history expansion
	other new bash builtins: bind, command, compgen, complete, builtin,
				 declare/typeset, dirs, enable, fc, help,
				 history, logout, popd, pushd, disown, shopt,
				 printf, compopt, mapfile
	exported functions
	filename generation when using output redirection (command >a*)
	POSIX.2-style globbing character classes
	POSIX.2-style globbing equivalence classes
	POSIX.2-style globbing collating symbols
	egrep-like extended pattern matching operators
	case-insensitive pattern matching and globbing
	variable assignments preceding commands affect only that command,
		even for builtins and functions
	posix mode and strict posix conformance
	redirection to /dev/fd/N, /dev/stdin, /dev/stdout, /dev/stderr,
		/dev/tcp/host/port, /dev/udp/host/port
	debugger support, including `caller' builtin and new variables
	RETURN trap
	the `+=' assignment operator
	autocd shell option and behavior
	command-not-found hook with command_not_found_handle shell function
	globstar shell option and `**' globbing behavior
	|& synonym for `2>&1 |'
	;& and ;;& case action list terminators
	case-modifying word expansions and variable attributes
	associative arrays
	coprocesses using the `coproc' reserved word and variables
	shell assignment of a file descriptor used in a redirection to a variable

Things sh has that bash does not:
	uses variable SHACCT to do shell accounting
	includes `stop' builtin (bash can use alias stop='kill -s STOP')
	`newgrp' builtin
	turns on job control if called as `jsh'
	$TIMEOUT (like bash $TMOUT)
	`^' is a synonym for `|'
	new SVR4.2 sh builtins: mldmode, priv

Implementation differences:
	redirection to/from compound commands causes sh to create a subshell
	bash does not allow unbalanced quotes; sh silently inserts them at EOF
	bash does not mess with signal 11
	sh sets (euid, egid) to (uid, gid) if -p not supplied and uid < 100
	bash splits only the results of expansions on IFS, using POSIX.2
		field splitting rules; sh splits all words on IFS
	sh does not allow MAILCHECK to be unset (?)
	sh does not allow traps on SIGALRM or SIGCHLD
	bash allows multiple option arguments when invoked (e.g. -x -v);
		sh allows only a single option argument (`sh -x -v' attempts
		to open a file named `-v', and, on SunOS 4.1.4, dumps core.
		On Solaris 2.4 and earlier versions, sh goes into an infinite
		loop.)
	sh exits a script if any builtin fails; bash exits only if one of
		the POSIX.2 `special' builtins fails

C2)  How does bash differ from the Korn shell, version ksh88?

Things bash has or uses that ksh88 does not:
	long invocation options
	[-+]O invocation option
	-l invocation option
	`!' reserved word
	arithmetic for command: for ((expr1 ; expr2; expr3 )); do list; done
	arithmetic in largest machine-supported size (intmax_t)
	posix mode and posix conformance
	command hashing
	tilde expansion for assignment statements that look like $PATH
	process substitution with named pipes if /dev/fd is not available
	the ${!param} indirect parameter expansion operator
	the ${!param*} prefix expansion operator
	the ${param:offset[:length]} parameter substring operator
	the ${param/pat[/string]} parameter pattern substitution operator
	variables: BASH, BASH_VERSION, BASH_VERSINFO, BASHPID, UID, EUID, SHLVL,
		   TIMEFORMAT, HISTCMD, HOSTTYPE, OSTYPE, MACHTYPE,
		   HISTFILESIZE, HISTIGNORE, HISTCONTROL, PROMPT_COMMAND,
		   IGNOREEOF, FIGNORE, INPUTRC, HOSTFILE, DIRSTACK,
		   PIPESTATUS, HOSTNAME, OPTERR, SHELLOPTS, GLOBIGNORE,
		   GROUPS, FUNCNAME, histchars, auto_resume, PROMPT_DIRTRIM
	prompt expansion with backslash escapes and command substitution
	redirection: &> (stdout and stderr), <<<, [n]<&word-, [n]>&word-, >>&
	more extensive and extensible editing and programmable completion
	builtins: bind, builtin, command, declare, dirs, echo -e/-E, enable,
		  exec -l/-c/-a, fc -s, export -n/-f/-p, hash, help, history,
		  jobs -x/-r/-s, kill -s/-n/-l, local, logout, popd, pushd,
		  read -e/-p/-a/-t/-n/-d/-s/-N, readonly -a/-n/-f/-p,
		  set -o braceexpand/-o histexpand/-o interactive-comments/
		  -o notify/-o physical/-o posix/-o hashall/-o onecmd/
		  -h/-B/-C/-b/-H/-P, set +o, suspend, trap -l, type,
		  typeset -a/-F/-p, ulimit -i/-q/-u/-x, umask -S, alias -p,
		  shopt, disown, printf, complete, compgen, compopt, mapfile
	`!' csh-style history expansion
	POSIX.2-style globbing character classes
	POSIX.2-style globbing equivalence classes
	POSIX.2-style globbing collating symbols
	egrep-like extended pattern matching operators
	case-insensitive pattern matching and globbing
	`**' arithmetic operator to do exponentiation
	redirection to /dev/fd/N, /dev/stdin, /dev/stdout, /dev/stderr
	arrays of unlimited size
	TMOUT is default timeout for `read' and `select'
	debugger support, including the `caller' builtin
	RETURN trap
	Timestamps in history entries
	{x..y} brace expansion
	The `+=' assignment operator
	autocd shell option and behavior
	command-not-found hook with command_not_found_handle shell function
	globstar shell option and `**' globbing behavior
	|& synonym for `2>&1 |'
	;& and ;;& case action list terminators
	case-modifying word expansions and variable attributes
	associative arrays
	coprocesses using the `coproc' reserved word and variables
	shell assignment of a file descriptor used in a redirection to a variable

Things ksh88 has or uses that bash does not:
	tracked aliases (alias -t)
	variables: ERRNO, FPATH, EDITOR, VISUAL
	co-processes (bash uses different syntax)
	weirdly-scoped functions
	typeset +f to list all function names without definitions
	text of command history kept in a file, not memory
	builtins: alias -x, cd old new, newgrp, print,
		  read -p/-s/var?prompt, set -A/-o gmacs/
		  -o bgnice/-o markdirs/-o trackall/-o viraw/-s,
		  typeset -H/-L/-R/-Z/-A/-ft/-fu/-fx/-t, whence
	using environment to pass attributes of exported variables
	arithmetic evaluation done on arguments to some builtins
	reads .profile from $PWD when invoked as login shell

Implementation differences:
	ksh runs last command of a pipeline in parent shell context
	bash has brace expansion by default (ksh88 compile-time option)
	bash has fixed startup file for all interactive shells; ksh reads $ENV
	bash has exported functions
	bash command search finds functions before builtins
	bash waits for all commands in pipeline to exit before returning status
	emacs-mode editing has some slightly different key bindings

C3)  Which new features in ksh-93 are not in bash, and which are?

This list is current through ksh93t+ (05/05/2009)

New things in ksh-93 not in bash-4.2:
	floating point arithmetic and variables
	math library functions
	${!name[sub]} name of subscript for associative array
	`.' is allowed in variable names to create a hierarchical namespace
	more extensive compound assignment syntax
	discipline functions
	KEYBD trap
	variables: .sh.edchar, .sh.edmode, .sh.edcol, .sh.edtext, .sh.version,
		   .sh.name, .sh.subscript, .sh.value, .sh.match, HISTEDIT
	backreferences in pattern matching (\N)
	`&' operator in pattern lists for matching (match all instead of any)
	exit statuses between 0 and 255
	FPATH and PATH mixing
	lexical scoping for local variables in `ksh' functions
	no scoping for local variables in `POSIX' functions
	$''  \C[.collating-element.] escape sequence
	-C/-I invocation options
	print -f (bash uses printf)
	`fc' has been renamed to `hist'
	`.' can execute shell functions
	getopts -a
	printf %B, %H, %P, %R, %Z modifiers, output base for %d, `=' flag
	read -n/-N differ/-v
	set -o showme/-o multiline (bash default)
	`sleep' and `getconf' builtins (bash has loadable versions)
	typeset -n and `nameref' variables
	[[ -R name ]] (checks whether or not name is a nameref)
	typeset -C/-S/-T/-X/-h/-s
	experimental `type' definitions (a la typedef) using typeset
	array expansions ${array[sub1..sub2]} and ${!array[sub1..sub2]}
	associative array assignments using `;' as element separator
	command substitution $(n<#) expands to current byte offset for fd N
	new '${ ' form of command substitution, executed in current shell
	new >;/<>;/<#pat/<##pat/<#/># redirections
	brace expansion printf-like formats 

New things in ksh-93 present in bash-4.2:
	associative arrays
	[n]<&word- and [n]>&word- redirections (combination dup and close)
        for (( expr1; expr2; expr3 )) ; do list; done - arithmetic for command
        ?:, ++, --, `expr1 , expr2' arithmetic operators
	expansions: ${!param}, ${param:offset[:len]}, ${param/pat[/str]},
		    ${!param*}
	compound array assignment
	negative subscripts for indexed array variables
	the `!' reserved word
	loadable builtins -- but ksh uses `builtin' while bash uses `enable'