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Here's one of the shortest ways to describe the Oil language:
A Unix shell that's familiar to people who know Python, JavaScript, or Ruby.
This document gives you a feel for that, with brief examples. It's not a comprehensive or precise guide. Roughly speaking, Oil code has more punctuation than those 3 languages, but less than shell and Perl.
If you're totally unfamiliar with the language, read The Simplest Explanation of Oil first.
Recall that expression mode is like Python and appears to the right of =:
var x = 42 + array[i]
And command mode is like shell:
echo $x 
The examples below aren't organized along those lines, but they use var and
echo to remind you of the context.  Some constructs are valid in both modes.
(I use echo $x for familiarity, even though write -- $x is more correct.)
Sigils are punctuation characters that precede a name, e.g. the $ in
$mystr.
Unlike Perl and PHP, Oil doesn't use sigils on the LHS of assignments, or in expression mode. The syntactic concepts doc explains this difference.
The $ and @ sigils mean roughly what they do in shell, Perl, and
PowerShell.
$ means string / scalar.  These shell constructs are idiomatic in Oil:
$mvar   ${myvar}
$(hostname)
And these Oil language extensions also use $:
echo $[42 + a[i]]            # string interpolation of expression
echo $len(x)                 # string interpolation of function call
grep $/ digit+ /             # inline eggex (not implemented yet)
@ means array / splice an array:
echo "$@"                    # Legacy syntax; prefer @ARGV
Oil:
echo @strs                   # splice array
echo @split(x) @glob(x)      # splice function that returns array
for i in @(seq 3) {          # split command sub
  echo $i
}   
proc p(first, @rest) {       # named varargs in proc signatures
  write -- $first            # (procs are shell-like functions)
  write -- @rest
}
Oil doesn't need sigils for hashes, so % isn't used the way it's used in
Perl.  Instead, % means "unquoted word" in these two cases:
var mysymbol = %key             # not implemented yet
var myarray = %(one two three)
These sigils are parsed, but not entirely implemented:
& for Ruby-like blocks in expression mode: means "out param" / "nameref", or "lazily evaluated"The {} [] and () characters have several different meanings, but we try
our best to make them consistent.  They're subject to legacy constraints from
Bourne shell, Korn shell, and bash.
The {} characters are used for blocks of code and dict literals (aka hash
tables, associative arrays), which makes Oil look like JavaScript in many
circumstances:
var d = {name: 'Bob', age: 10}
while (x > 0) {
  setvar x -= 1
}
Oil also has Ruby-like blocks:
cd /tmp {
  echo $PWD
}
Which can be used for "declarative" configuration:
server www.example.com {
  port = 80
  root = '/home/www'
  section bar {
    ...
  }
}
Parens are used in expressions:
var x = (42 + a[i]) * myfunc(42, 'foo')
if (x > 0) {         # compare with if test -d /tmp
  echo 'positive'
}
And signatures:
proc p(x, y) {
  echo $x $y
}
In Eggex, they mean grouping and not capture, which is consistent with arithmetic:
var p = / digit+ ('seconds' | 'minutes' | 'hours' ) /
The "sigil pairs" with parens enclose commands:
echo $(ls | wc -l)             # command sub
echo @(seq 3)                  # split command usb
var myblock = &(echo $PWD)     # block literal in expression mode
diff <(sort left.txt) <(sort right.txt)  # bash syntax
And shell words:
var mylist = %(one two three)  # equivalent to ['one', 'two', 'three']
Unlike brackets and braces, the () characters can't appear in shell commands,
which makes them useful as delimiters.
In expression mode, [] means sequence:
var mylist = ['one', 'two', 'three']
or subscript:
var item = mylist[1]
var item = mydict['foo']
In command mode, it means "expression":
echo $[1 + 2]
kebab-case is for procs and filenames:
gc-test   opt-stats   gen-mypy-asdl
test/spec-runner.oil   spec/data-enum.tea
snake_case is for local variables:
proc foo {
  var deploy_dest = 'bar@example.com'
  echo $deploy_dest
}
CAPS are used for global variables built into the shell:
PATH  IFS  UID  HOSTNAME
External programs also accept environment variables in CAPS:
PYTHONPATH  LD_LIBRARY_PATH
(In progress) Global variables that are silently mutated by the
interpreter start with _:
_argv   _status   _pipe_status   _line
As do functions to access such mutable vars:
_match()  _start()   _end()  _field()
Here are other usages of the punctuation discussed:
echo *.[ch]                    # glob char and char classes
echo {alice,bob}@example.com   # brace expansion
Eggex:
/ [a-f A-F 0-9] /         # char classes use []
/ digit+ ('ms' | 'us') /  # non-capturing group
                          # Consistent with arithmetric expressions!
< digit+ >                # capturing group
< digit+ : hour >         # named capture
dot{3,4} a{+ N}           # repetition
The ~ character is used in operators that mean "pattern" or "approximate":
if (s ~ /d+/) {
  echo 'number'
}   
if (s ~~ '*.py') {
  echo 'Python'
}
if (mystr ~== myint) {
  echo 'string equals number'
}
Extended globs are discouraged in Oil because they're a weird way of writing regular expressions. But they also use "sigil pairs" with parens:
,(*.py|*.sh)   # preferred synonym for @(*.py|*.sh)
+(...)         # bash/ksh-compatible
*(...)
?(...)
!(...)
Shell arithmetic is also discouraged in favor of Oil arithmetic:
echo $((1 + 2))  # shell: confusing coercions, dynamically parsed
echo $[1 + 2]    # Oil: types, statically parsed
This table is mainly for Oil language designers. Many constructs aren't implemented, but we reserve space for them. The Oil Help is a better reference for users.
Example      Description        What's Inside  Where Valid  Notes
${x %2d}     Var Sub            Formatting     cmd,expr     not implemented
$(hostname)  Command Sub        Command        cmd,expr
@(seq 3)     Split Command Sub  Command        cmd,expr
^(echo hi)   Block Literal      Command        expr
{ echo hi }  Block Literal      Command        cmd          shell requires ;
>(sort -n)   Process Sub        Command        cmd          rare
<(echo hi)   Process Sub        Command        cmd          rare
%(array lit) Array Literal      Words          expr
${.echo hi}  Builtin Sub        Words          cmd,expr     not implemented
@{.echo hi}  Builtin Sub        Words          cmd,expr     not implemented
$[42 + a[i]] Stringify Expr     Expression     cmd
^[42 + a[i]] Lazy Expression    Expression     expr         not implemented
json (x)     Typed Arg List     Argument       cmd
                                Expressions
$/d+/        Inline Eggex       Eggex Expr     cmd          not implemented
r''          Raw String         String         expr         cmd when shopt
             Literal                                        parse_raw_string
$''          C-escaped String   String         cmd,expr
             Literal
#'a'         Char Literal       UTF-8 char     expr
Discouraged / Deprecated
${x%%pre}    Shell Var Sub      Shell          cmd,expr     mostly deprecated
$((1+2))     Shell Arith Sub    Shell Arith    cmd          deprecated
@(*.py|*.sh) Extended Glob      Glob Words     cmd          deprecated
+(...)
*(...)
?(...)
!(...)
,(*.py|*.sh) Extended Glob      Glob Words     cmd          break conflict
                                                            with split command
                                                            sub
Key to "where valid" column:
cmd means lex_mode_e.ShCommandexpr means lex_mode_e.ExprSome unused sigil pairs:
~()   -()   =()   /()   _()   .()