S03-operators.pod

=encoding utf8

=head1 TITLE

Synopsis 3: Perl 6 Operators

=head1 AUTHORS

    Luke Palmer <luke@luqui.org>
    Larry Wall <larry@wall.org>
    Darren Duncan <darren@darrenduncan.net>

=head1 VERSION

    Created: 8 Mar 2004

    Last Modified: 11 August 2012
    Version: 256

=head1 Overview

For a summary of the changes from Perl 5, see L</Changes to Perl 5 operators>.

=head1 Operator precedence

Perl 6 has about the same number of precedence levels as Perl 5,
but they're differently arranged in spots.  Here we list the
levels from "tightest" to "loosest", along with a few examples of
each level:

    A  Level             Examples
    =  =====             ========
    N  Terms             42 3.14 "eek" qq["foo"] $x :!verbose @$array
    L  Method postfix    .meth .+ .? .* .() .[] .{} .<> .«» .:: .= .^ .:
    N  Autoincrement     ++ --
    R  Exponentiation    **
    L  Symbolic unary    ! + - ~ ? | || +^ ~^ ?^ ^
    L  Multiplicative    * / % %% +& +< +> ~& ~< ~> ?& div mod gcd lcm
    L  Additive          + - +| +^ ~| ~^ ?| ?^
    L  Replication       x xx
    X  Concatenation     ~
    X  Junctive and      &
    X  Junctive or       | ^
    L  Named unary       temp let
    N  Structural infix  but does <=> leg cmp .. ..^ ^.. ^..^
    C  Chaining infix    != == < <= > >= eq ne lt le gt ge ~~ === eqv !eqv
    X  Tight and         &&
    X  Tight or          || ^^ // min max
    R  Conditional       ?? !! ff fff
    R  Item assignment   = => += -= **= xx= .=
    L  Loose unary       so not
    X  Comma operator    , :
    X  List infix        Z minmax X X~ X* Xeqv ...
    R  List prefix       print push say die map substr ... [+] [*] any Z=
    X  Loose and         and andthen
    X  Loose or          or xor orelse
    X  Sequencer         <==, ==>, <<==, ==>>
    N  Terminator        ; {...}, unless, extra ), ], }

Using two C<!> symbols below generically to represent any pair of operators
that have the same precedence, the associativities specified above
for binary operators are interpreted as follows:

        Assoc     Meaning of $a ! $b ! $c
        =====     =========================
    L   left      ($a ! $b) ! $c
    R   right     $a ! ($b ! $c)
    N   non       ILLEGAL
    C   chain     ($a ! $b) and ($b ! $c)
    X   list      infix:<!>($a; $b; $c)

For unaries this is interpreted as:

        Assoc     Meaning of !$a!
        =====     =========================
    L   left      (!$a)!
    R   right     !($a!)
    N   non       ILLEGAL

(In standard Perl there are no unaries that can take advantage of
associativity, since at each precedence level the standard operators
are either consistently prefix or postfix.)

Note that list associativity (X) only works between identical operators.
If two different list-associative operators have the same precedence,
they are assumed to be non-associative with respect to each other,
and parentheses must be used to disambiguate.

For example, the C<X> cross operator and the C<Z> zip operator both
have a precedence of "list infix", but:

    @a X @b Z @c

is illegal and must be written as either of:

    (@a X @b) Z @c
    @a X (@b Z @c)

If the only implementation of a list-associative operator
is binary, it will be treated as right associative.

The standard precedence levels attempt to be consistent in their
associativity, but user-defined operators and precedence levels may mix
right and left associative operators at the same precedence level.
If two conflicting operators are used ambiguously in the same
expression, the operators will be considered non-associative with
respect to each other, and parentheses must be used to disambiguate.

If you don't see your favorite operator above, the following
sections cover all the operators in precedence order.  Basic operator
descriptions are here; special topics are covered afterwards.

=head2 Term precedence

This isn't really a precedence level, but it's in here because no operator
can have tighter precedence than a term.  See L<S02> for longer descriptions of
various terms.  Here are some examples.

=over

=item *

C<Int> literal

    42

=item *

C<Num> literal

    3.14

=item *

Non-interpolating C<Str> literal

    '$100'

=item *

Interpolating C<Str> literal

    "Answer = $answer\n"

=item *

Generalized C<Str> literal

    q["$100"]
    qq["$answer"]

=item *

Heredoc

    qq:to/END/
        Dear $recipient:
        Thanks!
        Sincerely,
        $me
        END

=item *

Array composer

    [1,2,3]

Provides list context inside.  (Technically, it really provides a
"semilist" context, which is a semicolon-separated list of statements,
each of which is interpreted in list context and then concatenated
into the final list.)

=item *

Hash composer

    { }
    { a => 42 }

Inside must be either empty, or a single list starting with a pair or a hash,
otherwise you must use C<hash()> or C<%()> instead.

=item *

Closure

    { ... }

When found where a statement is expected, executes immediately.  Otherwise
always defers evaluation of the inside scope.

=item *

Capture composer

    \(@a,$b,%c)

An abstraction representing an argument list that doesn't yet know its context.

=item *

Sigiled variables

    $x
    @y
    %z
    $^a
    $?FILE
    &func
    &div:(Int, Int --> Int)

=item *

Sigils as contextualizer functions

    $()
    @()
    %()
    &()

=item *

Regexes in quote-like notation

    /abc/
    rx:i[abc]
    s/foo/bar/

=item *

Transliterations

    tr/a..z/A..Z/

Note ranges use C<..> rather than C<->.

=item *

Type names

    Num
    ::Some::Package

=item *

Subexpressions circumfixed by parentheses

    (1+2)

Parentheses are parsed on the inside as a semicolon-separated list
of statements, which (unlike the statements in a block) returns the results
of all the statements concatenated together as a C<List> of C<Parcel>.
How that is subsequently treated depends on its eventual binding.

=item *

Function call with parens:

    a(1)

In term position, any identifier followed immediately by a
parenthesized expression is always parsed as a term representing
a function call even if that identifier also has a prefix meaning,
so you never have to worry about precedence in that case.  Hence:

    not($x) + 1         # means (not $x) + 1

=item *

Pair composers

    :limit(5)
    :!verbose

=item *

Signature literal

    :(Dog $self:)

=item *

Method call with implicit invocant

    .meth       # call on $_
    .=meth      # modify $_

Note that this may occur only where a term is expected.  Where a
postfix is expected, it is a postfix.  If only an infix is expected
(that is, after a term with intervening whitespace), C<.meth> is a
syntax error.  (The C<.=meth> form is allowed there only because there
is a special C<.=> infix assignment operator that is equivalent in
semantics to the method call form but that allows whitespace between
the C<=> and the method name.)

=item *

Listop (leftward)

    4,3, sort 2,1       # 4,3,1,2

As in Perl 5, a list operator looks like a term to the expression on
its left, so it binds tighter than comma on the left but looser than
comma on the right--see List prefix precedence below.

=back

=head2 Method postfix precedence

All method postfixes start with a dot, though the dot is optional
for subscripts.  Since these are the tightest standard operator,
you can often think of a series of method calls as a single term that
merely expresses a complicated name.

See L<S12> for more discussion of single dispatch method calls.

=over

=item *

Standard single-dispatch method calls

    $obj.meth

=item *

Variants of standard single-dispatch method call

    $obj.+meth
    $obj.?meth
    $obj.*meth

In addition to the ordinary C<.> method invocation, there are variants
C<.*>, C<.?>, and C<.+> to control how multiple related methods of
the same name are handled.

=item *

Class-qualified method call

    $obj.::Class::meth
    $obj.Class::meth    # same thing, assuming Class is predeclared

As in Perl 5, tells the dispatcher which class to start searching from,
not the exact method to call.

=item *

Mutating method call

    $obj.=meth

The C<.=> operator does inplace modification of the object on the left.

=item *

Meta-method call

    $obj.^meth

The C<.^> operator calls a class metamethod;
C<foo.^bar> is short for C<foo.HOW.bar>.

=item *

Method-like postcircumfixes

    $routine.()
    $array.[]
    $hash.{}
    $hash.<>
    $hash.«»

The dotless forms of these have exactly the same precedences.

=item *

Dotted form of any other postfix operator

    $x.++         # postfix:<++>($x)

=item *

Dotted postfix form of any other prefix operator

    $x.:<++>       # prefix:<++>($x)

=item *

There is specifically no C<< infix:<.> >> operator, so

    $foo . $bar

will always result in a compile-time error indicating the user should
use C<< infix:<~> >> instead.  This is to catch an error likely to
be made by Perl 5 programmers learning Perl 6.

=back

=head2 Autoincrement precedence

As in C, these operators increment or decrement the object in question
either before or after the value is taken from the object, depending on
whether it is put before or after.  Also as in C, multiple references
to a single mutating object in the same expression may result in undefined
behavior unless some explicit sequencing operator is interposed.
See L</Sequence points>.

As with all postfix operators in Perl 6, no space is allowed between
a term and its postfix.  See L<S02> for why, and for how to work around the
restriction with an "unspace".

As mutating methods, all these operators dispatch to the type of
the operand and return a result of the same type, but they are legal
on value types only if the (immutable) value is stored in a mutable
container.  However, a bare undefined value (in a suitable C<Scalar>
container) is allowed to mutate itself into an C<Int> in order to
support the common idiom:

    say $x unless %seen{$x}++;

Increment of a C<Str> (in a suitable container) works similarly to
Perl 5, but is generalized slightly.
A scan is made for the final alphanumeric sequence in
the string that is not preceded by a '.' character.  Unlike in Perl 5, this
alphanumeric sequence need not be anchored to the beginning of the
string, nor does it need to begin with an alphabetic character;
the final sequence in the string matching C<< <!after '.'> <rangechar>+ >>
is incremented regardless of what comes before it.

The C<< <rangechar> >> character class is defined as that subset of
characters that Perl knows how to increment within a range, as defined
below.

The additional matching behaviors provide two useful benefits:
for its typical use of incrementing a filename, you don't have to
worry about the path name or the extension:

    $file = "/tmp/pix000.jpg";
    $file++;            # /tmp/pix001.jpg, not /tmp/pix000.jph

Perhaps more to the point, if you happen to increment a string that ends
with a decimal number, it's likely to do the right thing:

    $num = "123.456";
    $num++;             # 124.456, not 123.457

Character positions are incremented within their natural range for
any Unicode range that is deemed to represent the digits 0..9 or
that is deemed to be a complete cyclical alphabet for (one case
of) a (Unicode) script.  Only scripts that represent their alphabet
in codepoints that form a cycle independent of other alphabets may
be so used.  (This specification defers to the users of such a script
for determining the proper cycle of letters.)  We arbitrarily define
the ASCII alphabet not to intersect with other scripts that make use
of characters in that range, but alphabets that intersperse ASCII letters are
not allowed.

If the current character in a string position is the final character
in such a range, it wraps to the first character of the range and
sends a "carry" to the position left of it, and that position is
then incremented in its own range.  If and only if the leftmost
position is exhausted in its range, an additional character of the
same range is inserted to hold the carry in the same fashion as Perl 5,
so incrementing '(zz99)' turns into '(aaa00)' and incrementing
'(99zz)' turns into '(100aa)'.

The following Unicode ranges are some of the possible rangechar ranges.
For alphabets we might have ranges like:

    A..Z        # ASCII uc
    a..z        # ASCII lc
    Α..Ω        # Greek uc
    α..ω        # Greek lc (presumably skipping C<U+03C2>, final sigma)
    א..ת        # Hebrew
      etc.      # (XXX out of my depth here)

For digits we have ranges like:

    0..9        # ASCII
    ٠..٩        # Arabic-Indic
    ०..९        # Devangari
    ০..৯        # Bengali
    ੦..੯        # Gurmukhi
    ૦..૯        # Gujarati
    ୦..୯        # Oriya
      etc.

Other non-script 0..9 ranges may also be incremented, such as

    ⁰..⁹        # superscripts (note, cycle includes latin-1 chars)
    ₀..₉        # subscripts
    ０..９      # fullwidth digits

Conjecturally, any common sequence may be treated as a cycle even if it does
not represent 0..9:

    Ⅰ..Ⅻ        # clock roman numerals uc
    ⅰ..ⅻ        # clock roman numerals lc
    ①..⑳        # circled digits 1..20
    ⒜..⒵        # parenthesize lc
    ⚀..⚅        # die faces 1..6
    ❶..❿        # dingbat negative circled 1..10
      etc.

While it doesn't really make sense to "carry" such numbers when they
reach the end of their cycle, treating such values as incrementable may
be convenient for writing outlines and similar numbered bullet items.
(Note that we can't just increment unrecognized characters, because
we have to locate the string's final sequence of rangechars before knowing
which portion of the string to increment.  Note also that all character
increments can be handled by lookup in a single table of successors
since we've defined our ranges not to include overlapping cycles.)

Perl 6 also supports C<Str> decrement with similar semantics, simply by
running the cycles the other direction.  However, leftmost characters
are never removed, and the decrement fails when you reach a string like
"aaa" or "000".

Increment and decrement on non-C<Str> types are defined in terms of the
C<.succ> and C<.pred> methods on the type of object in the C<Scalar>
container.  More specifically,

    ++$var
    --$var

are equivalent to

    $var.=succ
    $var.=pred

If the type does not support these methods, the corresponding increment
or decrement operation will fail.  (The optimizer is allowed to assume
that the ordinary increment and decrement operations on integers will
not be overridden.)

Increment of a C<Bool> (in a suitable container) turns it true.
Decrement turns it false regardless of how many times it was
previously incremented.  This is useful if your C<%seen> hash is
actually a C<KeySet>, in which case decrement actually deletes it
from the C<KeySet>.

Increment/decrement of an undefined C<Numeric>, C<Cool>, or C<Any> variable
sets the variable to 0 and then performs the increment/decrement.  Hence a
postincrement returns 0 the first time:

    my $x; say $x++;    # 0, not Any

=over

=item *

Autoincrement C<< prefix:<++> >> or C<< postfix:<++> >> operator

    $x++
    ++$x;

=item *

Autodecrement C<< prefix:<--> >> or C<< postfix:<--> >> operator

    $x--
    --$x

=back

=head2 Exponentiation precedence

=over

=item *

C<< infix:<**> >> exponentiation operator

    $x ** 2

Unless the right argument is a non-negative integer the result is likely to
be an approximation.  If the right argument is of an integer type,
exponentiation is at least as accurate as repeated multiplication on
the left side's type.  (From which it can be deduced that C<Int**UInt>
is always exact, since C<Int> supports arbitrary precision.
C<Rat**UInt> is accurate to the precision of C<Rat>.)  If the
right argument is an integer represented in a non-integer type, the
accuracy is left to implementation provided by that type; there is
no requirement to recognize an integer to give it special treatment.
(Coercion of an integer C<Str> via C<Cool> is likely to do the right thing, however.)

=back

=head2 Symbolic unary precedence

=over

=item *

C<< prefix:<?> >>, boolean context

    ?$x

Evaluates the expression as a boolean and returns C<True> if expression
is true or C<False> otherwise.
See "so" below for a low-precedence alternative.

=item *

C<< prefix:<!> >>, boolean negation

    !$x

Returns the opposite of what C<?> would.
See "not" below for a low-precedence alternative.

=item *

C<< prefix:<+> >>, numeric context

    +$x

Unlike in Perl 5, where C<+> is a no-op, this operator coerces to
numeric context in Perl 6.  (It coerces only the value, not the
original variable.)  For values that do not already do the
C<Numeric> role, the narrowest appropriate type of C<Int>, C<Rat>, C<Num>, or
C<Complex> will be returned; however, string containing two integers
separated by a C</> will be returned as a C<Rat> (or a C<FatRat> if the
denominator overflows an C<int64>).  Exponential notation
and radix notations are recognized.

Only leading and trailing whitespace are allowed as extra characters;
any other unrecognized character results in the return of a failure.

=item *

C<< prefix:<-> >>, numeric negation

    -$x

Coerces to numeric and returns the arithmetic negation of the resulting number.

=item *

C<< prefix:<~> >>, string context

    ~$x

Coerces the value to a string, if it does not already do the C<Stringy>
role.  (It only coerces the value, not the original variable.)  As with
numerics, it is guaranteed only to coerce to something C<Stringy>,
not necessarily C<Str>.

=item *

C<< prefix:<|> >>, flatten object into arglist

    | $capture

Interpolates the contents of the C<Capture> (or C<Capture>-like) value
into the current argument list as if they had been specified literally.
If the first argument of the capture is marked as an invocant but is used
in a context not expecting one, it is treated as an ordinary positional
argument.

=item *

C<< prefix:<||> >>, flatten object into semicolon list

    || $parcel

Interpolates the elements of the C<Parcel> (or any other ordered value)
into the current argument list as if they had been specified literally,
separated by semicolons, that is, at the multi-dimensional level.
It is an error to use this operator outside of a lol context; in
other words it must be bound into a C<**> (slice) parameter rather
than a C<*> (slurpy) parameter.

=item *

C<< prefix:<+^> >>, numeric bitwise negation

    +^$x

Coerces to C<Int> and then does bitwise negation on the number, returning an C<Int>.
(In order not to have to represent an infinitude of 1's, it represents
that value as some negative in 2's complement form.)

=item *

C<< prefix:<~^> >>, string bitwise negation

    ~^$x

Coerces NFG strings to non-variable-encoding string buffer type (such as buf8,
buf16, or buf32) and then does negation (complement) on each
bit of each integer element, returning a buffer of the same size as the input.

The use of coercion probably indicates a design error, however.  This operator
is distinguished from numeric bitwise negation in order to provide bit vectors
that extend on the right rather than the left (and always do unsigned extension).

=item *

C<< prefix:<?^> >>, boolean negation

    ?^$x

Coerces to boolean and then flips the bit.  (Same as C<!>.)

=item *

C<< prefix:<^> >>, upto operator

    ^$limit

Constructs a range of C<0 ..^ +$limit>.  See L</Range and RangeIter semantics>.

=back

=head2 Multiplicative precedence

=over

=item *

C<< infix:<*> >>

    $x*$y

Multiplication, resulting in the wider type of the two.

=item *

C<< infix:</> >>

    $numerator / $denominator

Performs division of real or complex numbers, returning a real or complex
number of appropriate type.

If both operands are of integer or rational type, the operator returns the
corresponding C<Rat> value (except when the result does not fit into a
C<Rat>, as detailed in L<S02>).

Otherwise, if either operand is of C<Complex> type, converts both
operands to C<Complex> and does division returning C<Complex>.

Otherwise, if either operand is of C<Num> type, converts both operands to C<Num>
and does division returning C<Num>.  If the denominator is zero,
returns an object representing either C<+Inf>, C<NaN>, or C<-Inf>
as the numerator is positive, zero, or negative.  (This is construed
as the best default in light of the operator's possible use within
hyperoperators and junctions.  Note however that these are not
actually the native IEEE non-numbers; they are undefined values of the
"unthrown exception" type that happen to represent the corresponding
IEEE concepts, and if you subsequently try to use one of these values
in a non-parallel computation, it will likely throw an exception at
that point.)

=item *

C<< infix:<div> >>, integer division

    $numerator div $denominator

Dispatches to the C<< infix:<div> >> multi most appropriate to the
operand types, returning a value of the same type.
Not coercive, so fails on differing types.

Policy on what to do about division by zero is up to the type,
but for the sake of hyperoperators and junctions those types that
can represent overflow (or that can contain an unthrown exception)
should try to do so rather than simply throwing an exception.  (And in
general, other operators that might fail should also consider their
use in hyperops and junctions, and whether they can profitably benefit
from a lazy exception model.)

In general, C<div> should give the same result as

    $x div $y == floor($x/$y)

but the return value should be the same type as $x.

This identity stops holding when C<$x/$y> degrades to a C<Num> and runs
into precision limits.  A C<div> operation on two C<Int> objects must always
be done precisely.

=item *

C<< infix:<%> >>, modulo

    $x % $y

If necessary, coerces non-numeric arguments to an appropriate C<Numeric> type,
then calculates the remainder, which is defined as:

    $x % $y == $x - floor($x / $y) * $y

=item *

C<< infix:<%%> >>, is divisible by

    $x %% $y

Performs a C<%> and then tests the result for 0, returning C<Bool::True> if
the C<$x> is evenly divisible by C<$y>, and C<Bool::False> otherwise.

You may use C<!%%> to mean "not divisible by", though C<%> itself generally
has the same effect.

=item *

C<< infix:<mod> >>, integer modulo

    $x mod $y

Dispatches to the C<< infix:<mod> >> multi most appropriate to
the operand types, returning a value of the same type.
Not coercive, so fails on differing types.

This should preserve the identity

    $x mod $y == $x - ($x div $y) * $y

=item *

C<< infix:['+&'] >>, numeric bitwise and

    $x +& $y

Converts both arguments to C<Int> and does a boolean AND between
corresponding bits of each integer, returning an C<Int> result.

=item *

C<< infix:['+<'] >>, numeric shift left

    $integer +< $bits

=item *

C<< infix:['+>'] >>, numeric shift right

    $integer +> $bits

By default, signed types do sign extension, while unsigned types do not, but
this may be enabled or disabled with a C<:signed> or C<:!signed> adverb.

=item *

C<< infix:<~&> >>, buffer bitwise and

    $x ~& $y

Coerces NFG strings to non-variable-encoding string buffer type (such as buf8,
buf16, or buf32) and then does numeric bitwise AND on corresponding integers
of the two buffers, logically padding the shorter buffer with 0 values.
returning a buffer sufficiently large to contain all non-zero integer results
(which for AND is at most the size of the shorter of the two buffers).

The use of coercion probably indicates a design error, however.  This operator
is distinguished from numeric bitwise AND in order to provide bit vectors
that extend on the right rather than the left (and always do unsigned extension).

=item *

C<< infix:['~<'] >>, buffer bitwise shift left

    $buf ~< $bits

=item *

C<< infix:['~>'] >>, buffer bitwise shift right

    $buf ~> $bits

Sign extension is not done by default but may be enabled with a C<:signed>
adverb.

=item *

C<< infix:<?&> >>, boolean and

    $x ?& $y

Converts both arguments to type C<Bool> and then ANDs those, returning the
resulting C<Bool>.

=item *

C<< infix:<gcd> >>, greatest common divisor

    $x gcd $y

Converts both arguments to an integral type and then finds the largest integer
that both arguments are evenly divisible by, and returns that integer.

=item *

C<< infix:<lcm> >>, least common multiple

    $x lcm $y

Converts both arguments to an integral type and then finds the smallest integer
that is evenly divisible by both arguments, and returns that integer.

=back

Any bit shift operator may be turned into a rotate operator with the
C<:rotate> adverb.  If C<:rotate> is specified, the concept of
sign extension is meaningless, and you may not specify a C<:signed> adverb.

=head2 Additive precedence

=over

=item *

C<< infix:<+> >>, numeric addition

    $x + $y

Microeditorial: As with most of these operators, any coercion or type
mismatch is actually handled by multiple dispatch.  The intent is that
all such variants preserve the notion of numeric addition to produce a
numeric result, presumably stored in a numeric type suitably "large" to
hold the result.  Do not overload the C<+> operator for other purposes,
such as concatenation.  (And please do not overload the bitshift
operators to do I/O.)  In general we feel it is much better for you
to make up a different operator than overload an existing operator for
"off topic" uses.  All of Unicode is available for this purpose.

=item *

C<< infix:<-> >>, numeric subtraction

    $x - $y

=item *

C<< infix:<+|> >>, numeric bitwise inclusive or

    $x +| $y

Converts both arguments to C<Int> and does a boolean OR between
corresponding bits of each integer, returning an C<Int> result.

=item *

C<< infix:<+^> >> numeric bitwise exclusive or

    $x +^ $y

Converts both arguments to C<Int> and does a boolean XOR between
corresponding bits of each integer, returning an C<Int> result.

=item *

C<< infix:<~|> >>, buffer bitwise inclusive or

    $x ~| $y

Coerces NFG strings to non-variable-encoding string buffer type (such as buf8,
buf16, or buf32) and then does numeric bitwise OR on corresponding integers
of the two buffers, logically padding the shorter buffer with 0 values, and
returning a buffer sufficiently large to contain all non-zero integer results
(which for OR is at most the size of the longer of the two buffers).

The use of coercion probably indicates a design error, however.  This operator
is distinguished from numeric bitwise OR in order to provide bit vectors
that extend on the right rather than the left (and always do unsigned extension).

=item *

C<< infix:<~^> >> buffer bitwise exclusive or

    $x ~^ $y

Coerces NFG strings to non-variable-encoding string buffer type (such as buf8,
buf16, or buf32) and then does numeric bitwise XOR on corresponding integers
of the two buffers, logically padding the shorter buffer with 0 values.
returning a buffer sufficiently large to contain all non-zero integer results
(which for XOR is at most the size of the longer of the two buffers).

The use of coercion probably indicates a design error, however.  This operator
is distinguished from numeric bitwise XOR in order to provide bit vectors
that extend on the right rather than the left (and always do unsigned extension).

=item *

C<< infix:<?|> >>, boolean inclusive or

    $x ?| $y

Converts both arguments to type C<Bool> and then ORs those, returning the
resulting C<Bool>.

=item *

C<< infix:<?^> >> boolean exclusive or

    $x ?^ $y

Converts both arguments to type C<Bool> and then XORs those, returning the
resulting C<Bool>.

=back

=head2 Replication

=over

=item *

C<< infix:<x> >>, string/buffer replication

    $string x $count

Evaluates the left argument in string context, replicates the resulting
string value the number of times specified by the right argument, and
returns the result as a single concatenated string regardless of context.

If the count is less than 1, returns the null string.
The count may not be C<*> because Perl 6 does not support
infinite strings.  (At least, not yet...)  Note, however, that an
infinite string may someday be emulated with C<cat($string xx *)>,
in which case C<$string x *> may be a shorthand for that.

=item *

C<< infix:<xx> >>, expression repetition operator

    @list xx $count

Evaluates the left argument the number of times specified by the right
argument.  Each evaluation is in list context, and returns a C<Parcel>.
The result of all these evaluations is returned as a list of C<Parcels>
(which will behave differently depending on whether it's bound into
a flat context or a lol context).

If the count is less than 1, returns the empty list, C<()>.
If the count is C<*>, returns an infinite list (lazily, since lists
are lazy by default).

Since the expression on the left is treated as a thunk that is re-evaluated
each time, expressions that rely on this behavior are possible:

    rand xx *;                # infinite supply of random numbers
    [ 0 xx $cols ] xx $rows   # distinct arrays, not the same row replicated

Of course, the optimizer can notice when the left side is a constant and avoid
re-evaluation.  When this is not possible, you can subvert the re-evaluation
by use of a temporary.

=back

=head2 Concatenation

=over

=item *

C<< infix:<~> >>, string/buffer concatenation

    $x ~ $y

=back

=head2 Junctive and (all) precedence

=over

=item *

C<< infix:<&> >>, all() operator

    $a & $b & $c ...

By default junctions are allowed to reorder the comparisons in any
order that makes sense to the optimizer.  To suppress this, use
the C<S> metaoperator for force sequential evaluation, which will
construct a list of ANDed patterns with the same semantics as C<<
infix:<&> >>, but with left-to-right evaluation guaranteed, for use
in guarded patterns:

    $target ~~ MyType S& *.mytest1 S& *.mytest2

This is useful when later tests might throw exceptions if earlier
tests don't pass.  This cannot be guaranteed by:

    $target ~~ MyType & *.mytest1 & *.mytest2

=back

=head2 Junctive or (any) precedence

=over

=item *

C<< infix:<|> >>, any() operator

    $a | $b | $c ...

=item *

By default junctions are allowed to reorder the comparisons in
any order that makes sense to the optimizer.  To suppress this,
use the C<S> metaoperator for force sequential evaluation, which
will construct a list of ORed patterns with the same semantics as
C<< infix:<|> >>, but with left-to-right evaluation guaranteed, for
use in guarded patterns where the left argument is much more easily
falsifiable than the right:

    $target ~~ *.mycheaptest S| *.myexpensivetest

This is also useful when you want to perform tests in order
of safety:

    $target ~~ MyType S| *.mysafetest S| *.mydangeroustest

=item *

C<< infix:<^> >>, one() operator

    $a ^ $b ^ $c ...

The C<S^> variant guarantees left-to-right evaluation, and in boolean
context short-circuits to false if it sees a second match.

=back

=head2 Named unary precedence

Operators of one argument

    let
    temp

Note that, unlike in Perl 5, you must use the C<.meth> forms to default
to C<$_> in Perl 6.

There is no unary C<rand> prefix in Perl 6, though there is a C<.rand>
method call and an argumentless C<rand> term.   There is no unary C<int>
prefix either; you must use a typecast to a type such as C<Int> or C<int>.
(Typecasts require parentheses and may not be used as prefix operators.)
In other words:

    my $i = int $x;   # ILLEGAL

is a syntax error (two terms in a row), because C<int> is a type name now.

=head2 Nonchaining binary precedence

=over

=item *

C<< infix:<but> >>

    $value but Mixin

=item *

C<< infix:<does> >>

    $object does Mixin

=item *

Sort comparisons

    $num1 <=> $num2
    $str1 leg $str2
    $obj1 cmp $obj2

These operators compare their operands using numeric, string,
or C<eqv> semantics respectively, and depending on the order return
one of C<Order::Increase>, C<Order::Same>, or C<Order::Decrease>
(which numerify to -1, 0, or +1).  See L</Comparison semantics>.

=item *

Range object constructor

    $min .. $max
    $min ^.. $max
    $min ..^ $max
    $min ^..^ $max

Constructs C<Range> objects, optionally excluding one or both endpoints.
See L</Range and RangeIter semantics>.

=back

=head2 Chaining binary precedence

All operators on this precedence level may be I<chained>; see
L</Chained comparisons>.  They all return a boolean value.

=over

=item *

C<< infix:<==> >> etc.

    == != < <= > >=

As in Perl 5, converts to C<Num> before comparison.  C<!=> is short for C<!==>.

=item *

C<< infix:<eq> >> etc.

    eq ne lt le gt ge

As in Perl 5, converts to C<Str> before comparison. C<ne> is short for C<!eq>.

=item *

Generic ordering

    $a before $b
    $a after $b

=item *

Smart match

    $obj ~~ $pattern

Perl 5's C<=~> becomes the "smart match" operator C<~~>, with an
extended set of semantics.  See L</Smart matching> for details.

To catch "brainos", the Perl 6 parser defines an C<< infix:<=~> >>
operator, which always fails at compile time with a message directing
the user to use C<~~> or C<~=> (string append) instead if they meant
it as a single operator, or to put a space between if they really
wanted to assign a stringified value as two separate operators.

A negated smart match is spelled C<!~~>.

=item *

Container identity

    VAR($a) =:= VAR($b)

See L</Comparison semantics>.

=item *

Value identity

    $x === $y

For objects that are not value types, their identities are their values.
(Identity is returned by the C<.WHICH> metamethod.)  The actual contents of
the objects are ignored.  These semantics are those used by hashes that
allow objects for keys.  See also L</Comparison semantics>.

Note that C<===> is defined with an C<(Any,Any)> signature, and therefore
autothreads over junctions; hence it I<cannot> be used to determine if two
objects are the same, if either or both of them are junctions.  However,
since C<.WHICH> is a macro that always returns a value and never autothreads,
you can easily work around this limitation by saying:

    $junk1.WHICH eqv $junk2.WHICH

[Conjecture: primitive identity is checked with C<< $junk1 \=== $junk2 >>.]

=item *

Canonical equivalence

    $obj1 eqv $obj2

Compares two objects for canonical equivalence.  For value types compares
the values.  For object types, compares current contents according to some
scheme of canonicalization.  These semantics are those used by hashes
that allow only values for keys (such as Perl 5 string-key hashes).
See also L</Comparison semantics>.

Note that C<eqv> autothreads over junctions, as do all other comparison
operators.  (Do not be confused by the fact that these return boolean values;
in general, only boolean I<context> forces junction collapse.)

[Conjecture: primitive equivalence is checked with C<< $junk1 \eqv $junk2 >>.]

=item *

Negated relational operators

    $num !== 42
    $str !eq "abc"
    "foo" !~~ /^ <ident> $/
    VAR($a) !=:= VAR($b)
    $a !=== $b
    $a !eqv $b

See L</Negated relational operators>.

=back

=head2 Tight and precedence

=over

=item *

C<< infix:<&&> >>, short-circuit and

    $a && $b && $c ...

Returns the first argument that evaluates to false, otherwise
returns the result of the last argument.  In list context forces
a false return to mean C<()>.  See C<and> below for low-precedence
version.

=back

=head2 Tight or precedence

=over

=item *

C<< infix:<||> >>, short-circuit inclusive-or

    $a || $b || $c ...

Returns the first argument that evaluates to a true value, otherwise
returns the result of the last argument.  It is specifically allowed
to use a list or array both as a boolean and as a list value produced
if the boolean is true:

    @a = @b || @c;              # broken in Perl 5; works in Perl 6

In list context this operator forces a false return to mean C<()>.
See C<or> below for low-precedence version.

=item *

C<< infix:<^^> >>, short-circuit exclusive-or

    $a ^^ $b ^^ $c ...

Returns the true argument if there is one (and only one).  Returns the
last argument if all arguments are false.  Returns C<Bool::False>
otherwise (when more than one argument is true).  In list context
forces a false return to mean C<()>.  See C<xor> below for
low-precedence version.

This operator short-circuits in the sense that it does not evaluate
any arguments after a 2nd true result.  Closely related is the reduce
operator:

    [^^] a(), b(), c() ...

but note that reduce operators are not macros but ordinary list
operators, so c() is always called before the reduce is done.


=item *

C<< infix:<//> >>, short-circuit default operator

    $a // $b // $c ...

Returns the first argument that evaluates to a defined value, otherwise
returns the result of the last argument.  In list context forces a
false return to mean C<()>.  See C<orelse> below for a similar but
not identical low-precedence version.

=item *

Minimum and maximum

    $a min $b min $c ...
    $a max $b max $c ...

These return the minimum or maximum value.  See also the
C<minmax> listop.

Not all types can support the concept of infinity.  Therefore any
value of any type may be compared with C<+Inf> or C<-Inf> values,
in which case the infinite value stands for "larger/smaller than any
possible value of the type."  That is,

    "foo" min +Inf              # "foo"
    "foo" min -Inf              # -Inf
    "foo" max +Inf              # +Inf
    "foo" max -Inf              # "foo"

All orderable object types must support C<+Inf> and C<-Inf> values
as special forms of the undefined value.  It's an error, however,
to attempt to store an infinite value into a native type that cannot
support it:

    my int $max;
    $max max= -Inf;     # ERROR

=back

=head2 Conditional operator precedence

=over

=item *

Conditional operator

    say "My answer is: ", $maybe ?? "yes" !! "no";

Also known as the "ternary" or "trinary" operator, but we prefer
"conditional" just to stop people from fighting over the terms.  The
operator syntactically separates the expression into three subexpressions.
It first evaluates the left part in boolean context, then based on that
selects one of the other two parts to evaluate. (It never evaluates
both of them.)  If the conditional is true it evaluates and returns
the middle part; if false, the right part.  The above is therefore
equivalent to:

    say "My answer is: ", do {
        if $maybe {
            "yes";
        }
        else {
            "no";
        }
    };

It is a syntax error to use an operator in the middle part that binds
looser in precedence, such as C<=>.

    my $x;
    hmm() ?? $x = 1 !! $x = 2;        # ERROR
    hmm() ?? ($x = 1) !! ($x = 2);    # works

Note that both sides have to be parenthesized.  A partial fix is
even wronger:

    hmm() ?? ($x = 1) !! $x = 2;      # parses, but WRONG

That actually parses as:

    (
        hmm() ?? ($x = 1) !! $x
    ) = 2;

and always assigns C<2> to C<$x> (because C<($x = 1)> is a valid lvalue).

And in any case, repeating the C<$x> forces you to declare it earlier.
The best don't-repeat-yourself solution is simply:

    my $x = hmm() ?? 1 !! 2;          # much better

=item *

C<< infix:<?> >>

To catch likely errors by people familiar with C-derived languages
(including Perl 5), a bare question mark in infix position will
produce an error suggesting that the user use C<?? !!> instead.

=item *

Flipflop ranges

    start() ff end()
    start() ^ff end()
    start() ff^ end()
    start() ^ff^ end()

=item *

Flipflop ranges (sed style)

    start() fff end()
    start() ^fff end()
    start() fff^ end()
    start() ^fff^ end()

=back

=head1 Adverbs

Operator adverbs are special-cased in the grammar, but give
the appearance of being parsed as trailing unary operators at a
pseudo-precedence level slightly tighter than item assignment.
(They're not officially "postfix" operators
because those require the absence of whitespace, and these allow whitespace.
These adverbs insert themselves in the spot where the parser is
expecting an infix operator, but the parser continues to look for
an infix after parsing the adverb and applying it to the previous
term.)  Thus,

    $a < 1 and $b == 2 :carefully

does the C<==> carefully, while

    $a < 1 && $b == 2 :carefully

does the C<&&> carefully because C<&&> is of
tighter precedence than "comma".  Use

    $a < 1 && ($b == 2 :carefully)

to apply the adverb to the C<==> operator instead.  We say that
C<==> is the "topmost" operator in the sense that it is at the
top of the parse tree that the adverb could possibly apply to.
(It could not apply outside the parens.)  If you are unsure
what the topmost operator is, just ask yourself which operator
would be applied last.  For instance, in

    +%hash{$key} :foo

the subscript happens first and the C<+> operator happens last,
so C<:foo> would apply to that.  Use

    +(%hash{$key} :foo)

to apply C<:foo> to the subscripting operator instead.

Adverbs will generally attach the way you want when you say things like

    1 op $x+2 :mod($x)

The proposed internal testing syntax makes use of these precedence rules:

    $x eqv $y+2  :ok<$x is equivalent to $y+2>;

Here the adverb is considered to be modifying the C<eqv> operator.

=head2 Item assignment precedence

=over

=item *

C<< infix:<=> >>

    $x = 1, $y = 2;

With simple lvalues, C<=> has this precedence, which is tighter than comma.
(List assignments have listop precedence below.)

=item *

C<< infix:['=>'] >>, Pair constructor

    foo => 1, bar => "baz"

Binary C<< => >> is no longer just a "fancy comma".  It now constructs
a C<Pair> object that can, among other things, be used to pass named
arguments to functions.  It provides item context to both sides.
It does not actually do an assignment except in a notional sense;
however its precedence is now equivalent to assignment, and it is
also right associative.  Note that, unlike in Perl 5, C<< => >>
binds more tightly than comma.

=item *

Assignment operators

    += -= **= xx= .= etc.

See L</Assignment operators>.

=back

=head2 Loose unary precedence

=over

=item *

C<< prefix:<not> >>

    not any(@args) eq '-v' | '-V'

Returns a C<Bool> value representing the logical negation of an expression.

=item *

C<< prefix:<so> >>

    so any(@args) eq '-v' | '-V'

Returns a C<Bool> value representing the logical non-negation of an expression.
Mostly useful as documentation in parallel to a C<not> when C<else> isn't
appropriate:

    if not $x { print "LOL"; }
    mumble();
    if so $x { print "SRSLY!" }

=back

=head2 Comma operator precedence

=over

=item *

C<< infix:<,> >>, the argument separator

    1, 2, 3, @many

Unlike in Perl 5, comma operator never returns the last value.  (In item
context it returns a list instead.)

=item *

C<< infix:<:> >>, the invocant marker

    say $*OUT: "howdy, world"
    say($*OUT: "howdy, world")
    push @array: 1,2,3
    push(@array: 1,2,3)
    \($object: 1,2,3, :foo, :!bar)

The colon operator parses just like a comma, but marks the argument to its left as an
invocant, which has the effect of turning what would otherwise be a function
call into a method call.  It may only be used on the first argument of
an argument list or capture, and will fail to parse if used in any other position.
When used within a capture, it is not yet known what signature the capture will
be bound to; if bound to a non-method's signature, the invocant merely turns
into the first positional argument, as if the colon had been a comma.

To avoid confusion with other colon forms, the colon infix operator
must be followed by whitespace or a terminator.  It may optionally
have whitespace in front of it.

Note: distinguish this infix operator from the colon in

    @array.push: 1,2,3
    @array.push(1,2,3): 4,5,6
    push(@array, 1,2,3): 4,5,6

which is a special form that turns an ordinary function or method
call into a list operator.  The special form is recognized only after
a dotty method call, or after the right parenthesis of a method or
function call.  The special form does not allow intervening whitespace,
but requires whitespace before the next argument.  In all other
cases a colon will be parsed as the start of an adverb if possible,
or otherwise the invocant marker (the infix described above).

Another way to think of it is that the special colon is allowed to
add listop arguments to a parenthesized argument list only after
the right parenthesis of that argument list, with the proviso that
you're allowed to shorten C<.foo(): 1,2,3> down to C<.foo: 1,2,3>.
(But only for method calls, since ordinary functions don't need the
colon in the first place to turn into a listop, just whitespace.
If you try to extend a function name with a colon, it's likely
to be taken as a label.)

    foo $obj.bar: 1,2,3     # special, means foo($obj.bar(1,2,3))
    foo $obj.bar(): 1,2,3   # special, means foo($obj.bar(1,2,3))
    foo $obj.bar(1): 2,3    # special, means foo($obj.bar(1,2,3))
    foo $obj.bar(1,2): 3    # special, means foo($obj.bar(1,2,3))
    foo($obj.bar): 1,2,3    # special, means foo($obj.bar, 1,2,3)
    foo($obj.bar, 1): 2,3   # special, means foo($obj.bar, 1,2,3)
    foo($obj.bar, 1,2): 3   # special, means foo($obj.bar, 1,2,3)
    foo $obj.bar : 1,2,3    # infix:<:>, means $obj.bar.foo(1,2,3)
    foo ($obj.bar): 1,2,3   # infix:<:>, means $obj.bar.foo(1,2,3)
    foo $obj.bar:1,2,3      # syntax error
    foo $obj.bar :1,2,3     # syntax error
    foo $obj.bar :baz       # adverb, means foo($obj.bar(:baz))
    foo ($obj.bar) :baz     # adverb, means foo($obj.bar, :baz)
    foo $obj.bar:baz        # extended identifier, foo( $obj.'bar:baz' )
    foo $obj.infix:<+>      # extended identifier, foo( $obj.'infix:<+>' )
    foo: 1,2,3              # label at statement start, else infix

The moral of the story is: if you don't know how the colon is
going to bind, use whitespace or parentheses to make it clear.

=back

=head2 List infix precedence

List infixes all have list associativity, which means that identical
infix operators work together in parallel rather than one after
the other.  Non-identical operators are considered non-associative
and must be parenthesized for clarity.

=over

=item *

C<< infix:<Z> >>, the zip operator

    1,2 Z 3,4   # (1,3),(2,4)

The C<Z> operator is actually a degenerate case of the C<Z> zipwith
metaoperator (see L<Zip operators> below).

=item *

C<< infix:<minmax> >>, the minmax operator

    @a minmax @b

Returns a C<Range> from the minimum element of C<@a> and C<@b> to the maximum
element. C<Range> elements in the input are treated as if their
minimum and maximum values were passed individually, except that if the
corresponding C<excludes> flag is set in Range, the excludes flag is also set
in the returned C<Range>.

=item *

C<< infix:<X> >>, the cross operator

    1,2 X 3,4          # (1,3), (1,4), (2,3), (2,4)

In contrast to the zip operator, the C<X> operator returns all possible
lists formed by taking one element from each of its list arguments.  The
returned lists are ordered such that the rightmost elements vary most rapidly.
If there are just two lists, for instance, it forms all pairs
where one element is from the first list and the other one from
the second, with the second element varying most rapidly.  Hence you may say:

    <a b> X <1 2>

and you end up with

    ('a', '1'), ('a', '2'), ('b', '1'), ('b', '2')

This becomes a flat list in flat context and a C<LoL> in lol context:

    say flat(<a b> X <1 2>).perl
    'a', '1', 'a', '2', 'b', '1', 'b', '2'
    say lol(<a b> X <1 2>).perl
    LoL.new( ('a', '1'), ('a', '2'), ('b', '1'), ('b', '2') )

The operator is list associative, so

    1,2 X 3,4 X 5,6

produces

    (1,3,5),(1,3,6),(1,4,5),(1,4,6),(2,3,5),(2,3,6),(2,4,5),(2,4,6)

On the other hand, if any of the lists is empty, you will end up with
a null list.

While either side's list may be infinite, use of an infinite list on
the right may produce unexpected results.  For instance

    <a b> X 0..*

would produce

    ('a',0), ('a',1), ('a',2), ('a',3), ('a',4), ('a',5), ...

and you'd never get to 'b'.  If your left list consists of only
a single element, though, this may be useful, especially if C<X> is used as
a metaoperator.  See below.

=item *

Cross metaoperators

    @files X~ '.' X~ @extensions
    1..10 X* 1..10
    @x Xeqv @y
    etc.

A common idiom is to have a list with a single element on one side or the other:

    @vector X* 2;               # multiply each element by 2
    $prefix X~ @infinitelist;   # prefix each element of an infinite list

In this last case it's okay to have an infinite list on the right.

See L</Cross operators>.


=item *

C<< infix:<...> >>, the sequence operator.

As a list infix operator, C<...> takes a list on both its left and
right and evaluates them as lazily as possible to produce the desired
sequence of values.  The lists are evaluated as flat lists.  As with
all list infix operators, this operator is looser in precedence than
comma, so you do not need to parenthesize comma lists on either side
of it.

The operator starts by getting the first value of the righthand list.
This is the only value of the right list that the C<...> operator is
actually interested in; any additional list elements are treasured
up lazily to be returned after the C<...> is done.

The righthand first value is considered to be the endpoint or limit of the
sequence that is to be generated from the lefthand side by the C<...>
operator itself.

Once we know the limit of the sequence, the left list is evaluated item
by item, and ordinary numeric or string values are passed through
unchanged (to the extent allowed by the limit on the right).
If any value in the sequence smartmatches the limit value,
the sequence terminates, including that final limit value.  To omit
the final value, use the C<...^> form instead.

Internally, these two forms are checking to see if an anonymous loop
is going to terminate, where the loop is what is returning the values
of the sequence.  Assuming the next candidate value is in C<$x> and the
first element of the right side is in C<$limit>, the two operators
are implemented respectively as:

    ...     last($x) if $x ~~ $limit;
    ...^    last     if $x ~~ $limit;

Since this uses smartmatching via the C<~~> operator (see L<Smart
matching> below), the usual smartmatching rules apply.  If the
limit is C<*>, the sequence has no limit.  If the limit is a closure,
it will be evaluated for boolean truth on the current candidate,
and the sequence will continue as long as the closure returns false.
It's quite possible for a sequence to return fewer values than are
listed if the very first value matches the end test:

    my $lim = 0;
    1,2,3 ...^ * > $lim      # returns Nil, since 1 > 0

This operator would be fairly useless if it could only return the
literal values on the left.  The power comes from generating 
new values from the old ones.  You may, for instance, use an existing
generator that happens to produce an infinite list:

    1..* ... * >= $lim
    @fib ... * >= $lim

More typically, if the next item in the left-hand 
list is a closure, it is not returned; rather it is called
on the tail of the existing list to produce a new value.  The
arity of the closure determines how many preceding values to
use as input in generating the next value in the sequence.  For
instance, counting by twos only requires a single argument:

    2, { $^a + 2 } ... *      # 2,4,6,8,10,12,14,16...

Generating the Fibonacci sequence takes two arguments at a time:

    1, 1, { $^a + $^b } ... * # 1,1,2,3,5,8,13,21...

Any means of specifying a function will do, as long as you arrange
it as a list value rather than calling it:

    1, 1, &infix:<+> ... *    # 1,1,2,3,5,8...
    1, 1, &[+] ... *          # same thing
    1, 1, *+* ... *           # same thing

More typically the function is unary, in which case any extra values
in the lefthand list may be construed as human-readable documentation:

    0,2,4, { $_ + 2 } ... 42   # all the evens up to 42
    0,2,4, *+2 ... 42          # same thing
    <a b c>, { .succ } ... *   # same as 'a'..*

The function need not be monotonic:

    1, -* ... *                # 1, -1, 1, -1, 1, -1...
    False, &prefix:<!> ... *   # False, True, False...

The function can be 0-ary as well, in which case it's okay for the
closure to be the first thing:

    { rand } ... *             # list of random numbers

The function may also be slurpy (n-ary), in which case C<all> the
preceding values are passed in (which means they must all be cached
by the operator, so performance may suffer, and you may find yourself
with a "space leak").

The arity of the function need not match the number of return values, but
if they do match you may interleave unrelated sequences:

    1,1,{ $^a + 1, $^b * 2 }...*   # 1,1,2,2,3,4,4,8,5,16,6,32...

Note in this case that the any limit test is applied to the entire parcel
returned from the function, which contains two values.

A sequence operator generated from an explicit function places no type
constraints on the sequence other than those constraints implied by
the signature of the function.  If the signature of the function does
not match the existing values, the sequence terminates.

If no generating closure is provided, and the sequence is numeric,
and is obviously arithmetic or geometric (from examining its I<last>
3 values), the appropriate function is deduced:

    1, 3, 5 ... *   # odd numbers
    1, 2, 4 ... *   # powers of 2
    10,9,8 ... 0    # countdown

That is, supposing we call the last three numbers C<$a>, C<$b>, and
C<$c>, and then define:

    $ab = $b - $a;
    $bc = $c - $b;

If C<$ab == $bc> and C<$ab> is not zero, then we deduce an arithmetic
progression determined by the function C<*+$ab>.  If C<$ab> is zero,
and the three values look like numbers, then the function is C<*+0>.
If they do not look like numbers, then the function selected is either
C<*.succ> or C<*.pred> depending on whether C<$b cmp $c> appears to be
Increasing or Decreasing.  If C<cmp> returns Same then an identity
function is assumed.

If C<$ab != $bc> and C<none($a,$b,$c) == 0>, then a similar calculation
is done using division rather than subtraction to determine whether
a geometric progression is warranted.  Define:

    $ab = $b / $a;
    $bc = $c / $b;

If the two quotients are equal (and finite), then a geometric
function of C<{$_ * $bc}> is deduced.

If there are only two values in the list so far, C<$a> and C<$b>, and the difference C<$ab>
is non-zero, we assume an arithmetic progression of C<*+$ab>.  If C<$ab>
is zero, then again whether we use C<*+0> or C<*.succ>/C<*.pred> depends on
whether the two values look like numbers.

If there is only one value, we always assume incrementation via
C<.succ>.  (This may be forced to C<.pred> by examination of a limit,
as specified below.)  Hence these come out the same:

    1 .. *
    1 ... *
    1,2 ... *
    1,2,3 ... *
    <1 2 3> ... *

Likewise, if the given value or values are not numeric, C<.succ> is assumed,
so these come out the same:

    'a' .. *
    'a' ... *
    'a','b' ... *
    'a','b','c' ... *
    <a b c> ... *

If the list on the left is C<()>, we use the function C<{()}> to generate an
infinite supply of nothing.

If a limit is given, it must smartmatch exactly.  If it does not,
an infinite list results.  For instance, since "asymptotically
approaching" is not the same as "equals", both of the following are
infinite lists, as if you'd specified C<*> for the limit rather than 0:

    1,1/2,1/4 ... 0    # like 1,1/2,1/4 ... *
    1,-1/2,1/4 ... 0   # like 1,-1/2,1/4 ... *

Likewise, this is all of the even numbers:

    my $end = 7;
    0,2,4 ... $end

To catch such a situation, it is advised to write an inequality instead:

    0,2,4 ...^ { $_ > $end }

When an explicit limit function is used, it
may choose to terminate its list by returning any true value.
Since this operator is list associative, an inner function may be
followed by a C<...> and another function to continue the list,
and so on.  Hence,

    1,   *+1   ... { $_ ==   9 },
    10,  *+10  ... { $_ ==  90 },
    100, *+100 ... { $_ == 900 }

produces

    1,2,3,4,5,6,7,8,9,
    10,20,30,40,50,60,70,80,90,
    100,200,300,400,500,600,700,800,900

Given the normal matching rules when there's no closure,
we can write that more simply as:

    1, 2, 3 ... 9,
    10, 20, 30 ... 90,
    100, 200, 300 ... 900

or even just:

    1, 2, 3 ...
    10, 20, 30 ...
    100, 200, 300 ... 900

since an exactly matching limit is returned as part of the
sequence, provided it is a value of the appropriate type, and
not a closure.

For functions deduced when there is only one value on the left,
the final value is used to determine whether C<*.succ> or C<*.pred> is
more appropriate.  The two values are compared with C<cmp> to determine
the direction of the progression.

Hence the sequence operator is "auto-reversing", unlike a range operator.

    'z' .. 'a'   # represents a null range
    'z' ... 'a'  # z y x ... a

As with numeric values, a string match must be exact, or an infinite sequence
is produced.  Use a different smartmatch such as a regular expression or
a closure to do fancier tests.

Note that the sequence

    1.0, *+0.2 ... 2.0

is calculated in C<Rat> arithmetic, not C<Num>, so the C<2.0> matches
exactly and terminates the sequence.

Note: the yada operator is recognized only where a term is expected.
This operator may only be used where an infix is expected.  If you
put a comma before the C<...> it will be taken as a yada list operator
expressing the desire to fail when the list reaches that point:

    1..20, ... "I only know up to 20 so far mister"

A special exception is made for any sequence whose endpoints are strings that
happen to represent single codepoints, since the user will typically be thinking
of such strings as characters rather than strings.  If you say something like:

    'A' ... 'z'
    "\xff" ... "\0"

it is assumed that you aren't interested in carrying within alphabetic
ranges, so instead of using the ordinary C<.succ>/C<.pred> for
strings, it uses a monotonic function that increments or decrements
the underlying codepoint number like

    'A', { $^prev.ord.succ.chr } ... 'z';
    "\xff", { $^prev.ord.pred.chr } ... "\0";

You will note that this alternate definition doesn't change the meaning of
any sequence that falls within a conventional rangechar range:

    'a'...'z'
    '9'...'0'

If the start and stop strings are the same length, this is applied at every position, with carry.

    'aa' ... 'zz'   # same as 'a' .. 'z' X~ 'a' .. 'z'

Hence, to produce all octal numbers that fit in 16 bits, you can say:

    '000000' ... '177777'

If the start string is shorter than the stop string, the strings are
assumed to be right justified, and the leftmost start character is
duplicated when there is a carry:

    '0' ... '177777'    # same octal sequence, without leading 0's

Going the other way, digits are dropped when they go to the first existing
digit until the current value is as short as the final value, then the digits
are left there.  Which is a fancy way of saying that

    '177777' ... '000000' 

and

    '177777' ... '0' 

both do exactly what the forward sequences do above, only in reverse.

As an extra special rule, that works in either direction: if the bottom
character is a '0' and the top character is alphanumeric, it is assumed
to be representing a number in some base up to base 36, where digits above ten 
are represented by letters.  Hence the same sequences of 16-bit numbers, only in
hexadecimal, may be produced with:

    '0000' ... 'ffff'
    '0' ... 'ffff'
    'ffff' ... '0000' 
    'ffff' ... '0' 

And as a limiting case, this applies to single characters also:

    '0' .. 'F'    # 0..9, 'A'..'F'

Note that case is intuited from the top character of the range.

There are many different possible semantics for string increment.
If this isn't the semantics you want, you can always write your own
successor function.  Sometimes the stupid codepoint counting is what you want.
For instance, you can get away with ranges of capital Greek letters:

    'ΑΑΑ' ... 'ΩΩΩ'

However, if you try it with the lowercase letters, you'll get both
forms of lowercase sigma, which you probably don't want.  If there's
only one or two letters you don't want, you can grep out those entries,
but in the general case, you need an incrementer that knows what sequence
you're interested in.  Perhaps there can be a generic method,

    'ααα', *.succ-in(@greek) ... 'ωωω'

that will take any given sequence and use it as the universe of incrementation
for any matching characters in the string.

To preserve Perl 5 length limiting semantics of a range like
C<'A'..'zzz'>, you'd need something like:

    'A', *.succ ... { last if .chars > 3; $_ eq 'zzz' }

(That's not an exact match to what Perl 5 does, since C<Str.succ> is
a bit fancier in Perl 6, but starting with 'A' it'll work the same.
You can always supply your own increment function.)

Note that the C<last> call above returns no argument, so even though
the internal test calls C<last($x)>, this call to C<last> bypasses that
as if the sequence had been specified with C<...^> instead.  Going the
other way, a C<...^> maybe be forced to have a final value by passing
an argument to an explicit C<last($my-last-value)>.  In the same way,
that will bypass the argumentless internal C<last>.

In a similar way, the sequence may be terminated by calling C<last>
from the generator function:

    10,9,8, { $_ - 1 || last } ... *   # same as 10 ... 1

For purposes of deciding when to terminate the eager part of a 'mostly
eager' list, any sequence that terminates with an exact value (or
that starts another sequence with exact values) is considered finite,
as is any sequence that has an explicit ending closure.
However, any sequence that ends C<*> is considered to be of unknowable
length.  However, by the definition of "mostly eager" in L<S07>,
the implementation may be able to determine that such a sequence is
finite by conjectural evaluation; such workahead cannot, of course, always
prove that a sequence is infinite without running a Very Long Time.
Note also that, by using the form that specifies both a closure and
a final value, it is possible to write a sequence that appears to be
finite but that never actually reaches its final value before resources
are exhausted; such a sequence will be treated as finite, but eventually
will come to grief:

    @a = 1, *+0.00000000000000000000000000000000000001 ... 2;  # heat death

For any such sequence or list that the user knows to be infinite, but
the computer can't easily know it, it is allowed to mark the end of
the list with a C<*>, which indicates that it is to be treated as an
infinite list in contexts that care.  Similarly, any list ending
with an operator that interprets C<*> as infinity may be taken the
same way, such as C<$n xx *>, or C<1..*>.

On the other hand, it's possible to write a sequence that appears to be
infinite, but is terminated by a C<last> from the iterator closure.  An
implementation is required to trap such a loop termination and change the
status of the list from 'infinite' to 'finite, such that C<.elems> reports
the actual produced length, not C<Inf>.


=back

Many of these operators return a list of C<Parcel>s, which depending on
context may or may not flatten them all out into one flat list.  The
default is to flatten, but see the contextualizers below.

=head2 List prefix precedence

=over

=item *

C<< infix:<=> >>, list assignment

    @array = 1,2,3;

With compound targets, performs list assignment.  The right side
is looser than list infix.  You might be wondering why we've classified
this as a prefix operator when its token name is C<< infix:<=> >>.
That's because you can view the left side as a special syntax for a
prefix listop, much as if you'd said:

    @array.assign: 1,2,3

However, the tokener classifies it as infix because it sees it when
it's expecting an infix operator.  Assignments in general are treated
more like retroactive macros, since their meanings depend greatly on
what is on the left, especially if what is on the left is a declarator
of some sort.  We even call some of them pseudo-assignments, but they're
all a bit pseudo insofar as we have to figure out whether the left side
is a list or a scalar destination.

In any case, list assignment is defined to be arbitrarily lazy,
insofar as it basically does the obvious copying as long as there
are scalar destinations on the left or already-computed values on
the right.  However, many list lvalues end with an array destination
(where assignment directly to an array can be considered a degenerate
case).  When copying into an array destination, the list assignment is
"mostly eager"; it requests the list to evaluate its leading iterators
(and values) to the extent that they are known to be finite, and
then suspend, returning the known values.  The assignment then copies
the known values into the array.  (These two steps might actually be
interleaved depending on how the iterator API ends up being defined.)
It then sets up the array to be self-extending by using the remainder
of the list as the "specs" for the array's remaining values, to be
reified on demand.  Hence it is legal to say:

    @natural = 0..*;

(Note that when we say that an iterator in list context suspends,
it is not required to suspend immediately.  When the scheduler is
running an iterator, it may choose to precompute values in batches if
it thinks that approach will increase throughput.  This is likely to
be the case on single-core architectures with heavy context switching,
and may very well be the case even on manycore CPU architectures when
there are more iterators than cores, such that cores may still have
to do context switching.  In any case, this is all more-or-less
transparent to the user because in the abstract the list is all
there, even if it hasn't been entirely computed yet.)

Though elements may be reified into an array on demand, they act
like ordinary array elements both before and after reification, as
far as the user is concerned. These elements may be written to if
the underlying container type supports it:

    @unnatural = 0..*;
    @unnatural[42] = "Life, the Universe, and Everything";

Note that, unlike assignment, binding replaces the container,
so the following fails because a range object cannot be subscripted:

    @natural := 0..*;     # bind a Range object
    @natural[42] = "Life, the Universe, and Everything";  # FAILS

but this succeeds:

    @unnatural := [0..*]; # bind an Array object
    @unnatural[42] = "Life, the Universe, and Everything"; # ok

It is erroneous to make use of any side effects of reification, such
as movement of a file pointer, since different implementations may
have different batch semantics, and in any case the unreified part
of the list already "belongs" to the array.

When a self-extending array is asked for its count of elements, it
is allowed to return C<+Inf> without blowing up if it can determine
by inspection that its unreified parts contain any infinite lists.
If it cannot determine this, it is allowed to use all your
memory, and then some.  C<:)>

Assignment to a hash is not lazy (probably).

=item *

C<< infix:<:=> >>, run-time binding

    $signature := $capture

A new form of assignment is present in Perl 6, called I<binding>, used in
place of typeglob assignment.  It is performed with the C<:=> operator.
Instead of replacing the value in a container like normal assignment, it
replaces the container itself.  For instance:

    my $x = 'Just Another';
    my $y := $x;
    $y = 'Perl Hacker';

After this, both C<$x> and C<$y> contain the string C<"Perl Hacker">,
since they are really just two different names for the same variable.

There is also an identity test, C<=:=>, which tests whether two names
are bound to the same underlying variable.  C<$x =:= $y> would return
true in the above example.

The binding fails if the type of the variable being bound is sufficiently
inconsistent with the type of the current declaration.  Strictly speaking,
any variation on

    my Any $x;
    $x := [1,2,3];

should fail because the type being bound is not consistent with
C<Scalar of Any>, but since the C<Any> type is not a real instantiable
type but a generic (non)constraint, and C<Scalar of Any> is sort of
a double non-constraint similar to C<Any>, we treat this situation
specially as the equivalent of binding to a typeless variable.

The binding operator parses as a list assignment, so it is reasonable to
generate a list on the right without parens:

    @list := 1 ... *;

=item *

C<< infix:<::=> >>, bind and make readonly

    $signature ::= $capture

This does the same as C<:=>, then marks any destination parameters as
readonly (unless the individual parameter overrides this with either
the C<rw> trait or the C<copy> trait).  It's particularly useful
for establishing readonly dynamic variables for a dynamic scope:

    {
        my $*OUT ::= open($file, :w) || die $!;
        doit();     # runs with redirected stdout
    }
    doit();     # runs with original stdout

If C<doit> wants to change C<$*OUT>, it must declare its own
dynamic variable.  It may not simply assign to C<$*OUT>.

Note that the semantics of C<::=> are virtually identical to
the normal binding of arguments to formal subroutine parameters
(which also default to readonly).

This operator parses as a list assignment.

=item *

Normal listops

    print push say join split substr open etc.

=item *

Listop forms of junctional operators

    any all one none

=item *

Exception generators

    fail "Division by zero"
    die System::Error(ENOSPC,"Drive $d seems to be full");
    warn "Can't open file: $!"

=item *

Stubby exception generators

    ...
    !!! "fill this in later, Dave"
    ??? "oops in $?CLASS"

The C<...> operator is the "yada, yada, yada" list operator, which
among other things is used as the body in function prototypes.
It complains bitterly (by calling C<fail>) if it is ever executed.
Variant C<???> calls C<warn>, and C<!!!> calls C<die>.  The argument
is optional, but if provided, is passed onto the C<fail>, C<warn>,
or C<die>.  Otherwise the system will make up a message for you based
on the context, indicating that you tried to execute something that
is stubbed out.  (This message differs from what C<fail>, C<warn>, and
C<die> would say by default, since the latter operators typically point
out bad data or programming rather than just an incomplete design.)

=item *

Reduce operators

    [+] [*] [<] [\+] [\*] etc.

See L<Reduction operators> below.

=item *

Sigils as coercions to roles

    Sigil       Alpha variant
    -----       -------------
    $           Scalar
    @           Positional (or Iterable?)
    %           Associative
    &           Callable

Note that, since these are coercions to roles, they are allowed
to return any actual type that does the role in question.

Unless applied directly to a scalar variable, as in C<@$a>, these
may only be applied with explicit parens around an argument that
is processed as a bare C<Parcel> object, not a flattening list:

     $(1,2 Z 3,4)      # Scalar((1,3),(2,4))
     @(1,2 Z 3,4)      # ((1,3),(2,4))
     %(1,2 Z 3,4)      # PairSeq(1 => 3, 2 => 4)

     $(1,2 X 3,4)      # Scalar((1,3),(1,4),(2,3),(2,4))
     @(1,2 X 3,4)      # ((1,3),(1,4),(2,3),(2,4))

(Note, internal parens indicate nested C<Parcel> structure here,
since there is no flattening.)

Since a C<Parcel> with one argument is transparent, there can be no
difference between the meaning of C<@($a)> and C<@$a>.

=item *

The C<item> contextualizer

    item foo()

The new name for Perl 5's C<scalar> contextualizer.  Equivalent to C<$(...)>
(except that empty C<$()> means C<$<?> // Str($/)>, while empty C<item()> yields C<Failure>).
We still call the values scalars, and talk about "scalar operators", but
scalar operators are those that put their arguments into item context.

If given a list, this function makes a C<Seq> object from it.  The function
is agnostic about any C<Parcel> embedded in such a sequence, and any contextual
decisions will be deferred until subsequent use of the contents.

Note that this parses as a list operator, not a unary prefix operator,
since you'd generally want it for converting a list to a sequence object.
(Single items don't need to be converted to items.)  Note, however, that
it does no flattening of its list items:

    @x = lol(item (1,2),(3,4))  # @x eqv LoL( (1,2), (3,4) )

=item *

The C<list> contextualizer

    list foo()

Forces the subsequent expression to be evaluated in list context.
Any flattening happens lazily.

=item *

The C<flat> contextualizer

    flat foo()

Forces the subsequent expression to be evaluated in a flattening
list context.  The result will be recursively flattened, i.e.,
contain no embedded C<Parcel> objects.

=item *

The C<lol> contextualizer

    lol foo()

Forces the subsequent expression to be evaluated in list-of-lists
context.  This is typically used to form a multidimensional slice.
A parcel potentially containing subparcels will be transformed into
a list of lists, specifically of type C<LoL>.

=item *

The C<hash> contextualizer

    hash foo()

Forces the subsequent expression to be evaluated in hash context.
The expression is evaluated in list context (flattening any C<Parcel>s),
then a hash will be created from the list, taken as a list of C<Pair>s.
(Any element in the list that is not a C<Pair> will pretend to be a key
and grab the next value in the list as its value.)  Equivalent to
C<%(...)> (except that empty C<%()> means C<%($/)>, while
empty C<hash()> means an empty hash).

=back

=head2 Loose and precedence

=over

=item *

C<< infix:<and> >>, short-circuit and

    $a and $b and $c ...

Returns the first argument that evaluates to false, otherwise
returns the result of the last argument.  In list context forces
a false return to mean C<()>.  See C<&&> above for high-precedence
version.

=item *

C<< infix:<andthen> >>, proceed on success

    test1() andthen test2() andthen test3() ...

Returns the first argument whose evaluation indicates failure
(that is, if the result is undefined).  Otherwise it
evaluates and returns the right argument.

If the right side is a block or pointy block, the result of the left
side is bound to any arguments of the block.  If the right side is
not a block, a block scope is assumed around the right side, and the
result of the left side is implicitly bound to C<$_> for the scope
of the right side.  That is,

    test1() andthen test2()

is equivalent to

    test1() andthen -> $_ { test2() }

There is no corresponding high-precedence version.

=back

=head2 Loose or precedence

=over

=item *

C<< infix:<or> >>, short-circuit inclusive or

    $a or $b or $c ...

Returns the first argument that evaluates to true, otherwise returns
the result of the last argument.  In list context forces a false return
to mean C<()>, or C<Nil>.  See C<||> above for high-precedence version.

=item *

C<< infix:<xor> >>, exclusive or

    $a xor $b xor $c ...

Returns the true argument if there is one (and only one).  Returns the
last argument if all arguments are false.  Returns C<Bool::False>
otherwise (when more than one argument is true).  In list context
forces a false return to mean C<()>. See C<^^> above for
high-precedence version.

=item *

C<< infix:<orelse> >>, proceed on failure

    test1() orelse test2() orelse test3() ...

Returns the first argument that evaluates successfully (that is,
if the result is defined).  Otherwise returns the result of the
right argument.

If the right side is a block or pointy block, the result of the left
side is bound to any arguments of the block.  If the right side is
not a block, a block scope is assumed around the right side, and the
result of the left side is implicitly bound to C<$!> for the scope
of the right side.  That is,

    test1() orelse test2()

is equivalent to

    test1() orelse -> $! { test2() }

(The high-precedence C<//> operator is similar, but does not set C<$!> or
treat blocks specially.)

=back

=head2 Terminator precedence

As with terms, terminators are not really a precedence level, but
looser than the loosest precedence level.  They all have the effect of
terminating any operator precedence parsing and returning a complete
expression to the main parser.  They don't care what state the operator
precedence parser is in.  If the parser is currently expecting a term
and the final operator in the expression can't deal with a nullterm,
then it's a syntax error.  (Notably, the comma operator and many prefix
list operators can handle a nullterm.)

=over

=item *

Semicolon: ;

    $x = 1; $y = 2;

The context determines how the expressions terminated by semicolon
are interpreted.  At statement level they are statements.  Within a
bracketing construct they are interpreted as lists of C<Parcel>s,
which in lol context will be treated as the multiple dimensions of a
multidimensional slice.  (Other contexts may have other interpretations
or disallow semicolons entirely.)

=item *

Feed operators: <==, ==>, <<==, ==>>

    source() ==> filter() ==> sink()

The forms with the double angle append rather than clobber the sink's
todo list.  The C<<< ==>> >>> form always looks ahead for an appropriate
target to append to, either the final sink in the chain, or the next
filter stage with an explicit C<@(*)> or C<@(**)> target.  This means
you can stack multiple feeds onto one filter command:

    source1() ==>>
    source2() ==>>
    source3() ==>>
    filter(@(*)) ==> sink()

Similar semantics apply to C<<< <<== >>> except it looks backward for
an appropriate target to append to.

=item *

Control block: <ws>{...}

When a block occurs after whitespace where an infix is expected, it is
interpreated as a control block for a statement control construct.
(If there is no whitespace, it is a subscript, and if it is where a
term is expected, it's just a bare closure.)  If there is no statement
looking for such a block currently, it is a syntax error.

=item *

Statement modifiers: if, unless, while, until, for

Statement modifiers terminate one expression and start another.

=item *

Any unexpected ), ], } at this level.

Calls into the operator precedence parser may be parameterized
to recognize additional terminators, but right brackets of any
sort (except angles) are automatically included in the set of
terminators as tokens of length one.  (An infix of longer length
could conceivably start with one of these characters, and would be
recognized under the longest-token rule and continue the expression,
but this practice is discouraged.  It would be better to use Unicode
for your weird operator.)  Angle brackets are exempted so that they
can form hyperoperators (see L</Hyper operators>).

=item *

A block-final } at the end of the line terminates the current expression.
A block within an argument list terminates the argument list unless
followed by the comma operator.

=back

=head1 Changes to Perl 5 operators

Several operators have been given new names to increase clarity and better
Huffman-code the language, while others have changed precedence.

=over

=item *

Perl 5's C<${...}>, C<@{...}>, C<%{...}>, etc. dereferencing
forms are now C<$(...)>, C<@(...)>, C<%(...)>, etc. instead.
(Use of the Perl 5 curly forms will result in an error message
pointing the user to the new forms.)
As in Perl 5, the parens may be dropped when dereferencing
a scalar variable.

=item *

C<< -> >> becomes C<.>, like the rest of the world uses.  There is
a pseudo C<< postfix:['->'] >> operator that produces a compile-time
error reminding Perl 5 users to use dot instead.  (The "pointy block"
use of C<< -> >> in Perl 6 requires preceding whitespace when the arrow
could be confused with a postfix, that is, when an infix is expected.
Preceding whitespace is not required in term position.)

=item *

The string concatenation C<.> becomes C<~>.  Think of it as
"stitching" the two ends of its arguments together.  String append
is likewise C<~=>.

=item *

The filetest operators are gone.  We now use a C<Pair> as a
pattern that calls an object's method:

    if $filename.IO ~~ :e { say "exists" }

is the same as

    if so $filename.IO.e { say "exists" }

Likewise

    if $filename.IO ~~ :!e { say "doesn't exist" }

is the same as

    if not $filename.IO.e { say "doesn't exist" }

The 1st form actually translates to the latter form, so the object's
class decides how to dispatch methods.  It just so happens that the
C<IO> role defaults to the expected filetest semantics, but C<$regex.i> might
tell you whether the regex is case insensitive, for instance.  Likewise,
you can test anything for definedness or undefinedness:

    $obj ~~ :defined
    $obj ~~ :!defined

Using the pattern form, multiple tests may be combined via junctions:

    given $handle {
        when :r & :w & :x {...}
        when :!w | :!x    {...}
        when *            {...}
    }

When adverbial pairs are stacked into one term, it is assumed they are
ANDed together, so

    when :r :w :x

is equivalent to either of:

    when :r & :w & :x
    when all(:r,:w,:x)

The pair forms are useful only for boolean tests because the method's
value is evaluated as a Bool, so the
method form must be used for any numeric-based tests:

    if stat($filename).s > 1024 {...}

However, these still work:

    given $fh {
        when :s  {...} # file has size > 0
        when :!s {...} # file size == 0
    }

One advantage of the method form is that it can be used in places that
require tighter precedence than C<~~> provides:

    sort { $^a.M <=> $^b.M }, @files».IO

though that's a silly example since you could just write:

    sort { .M }, @files».IO

But that demonstrates the other advantage of the method form, which is
that it allows the "unary dot" syntax to test the current topic.

Unlike in earlier versions of Perl 6, these filetest methods do not return
stat buffers, but simple scalars of type C<Bool>, C<Int>, or C<Num>.

In general, the user need not worry about caching the stat buffer
when a filename is queried.  The stat buffer will automatically be
reused if the same object has recently been queried, where "recently"
is defined as less than a second or so.  If this is a concern, an
explicit stat() or lstat() may be used to return an explicit C<IO>
object that will not be subject to timeout, and may be tested
repeatedly just as a filename or handle can.  An C<IO> object has
a C<.file> method that can be queried for its filename (if known).

(Inadvertent use of the Perl 5 forms will normally result in treatment
as a negated postdeclared subroutine, which is likely to produce an
error message at the end of compilation.)

=item *

All postfix operators that do not start with a dot also have
an alternate form that does.  (The converse does not hold--just because
you can write C<x().foo> doesn't mean you can write C<x()foo>.  Likewise
the ability to say C<$x.'foo'> does not imply that C<$x'foo'> will work.)

The postfix interpretation of an operator may be overridden by
use of a quoted method call, which calls the prefix form instead.
So C<x().!> is always the postfix operator, but C<x().'!'> will always
call C<!x()>.  In particular, you can say things like C<$array.'@'>.
This also includes any operator that would look like something
with a special meaning if used after the method-calling dot.  For example,
if you defined a C<< prefix:<=> >>, and you wanted to write it using
the method-call syntax instead of C<=$object>, the parser would take
C<$object.=> as the mutation syntax (see L<S12>, "Mutating methods").
Writing C<$object.'='> will call your prefix operator.

=item *

Unary C<~> now imposes a string (C<Stringy>) context on its
argument, and C<+> imposes a numeric (C<Numeric>) context (as opposed
to being a no-op in Perl 5).  Along the same lines, C<?> imposes
a boolean (C<Bool>) context, and the C<|> unary operator imposes
a function-arguments (C<Parcel> or C<Capture>) context on its argument.
Unary sigils are allowed when followed by a C<$> sigil on a scalar variable;
they impose the container context implied by their sigil.
As with Perl 5, however, C<$$foo[bar]> parses as C<( $($foo) )[bar]>,
so you need C<$($foo[bar])> to mean the other way.  In other
words, sigils are not really parsed as operators, and you must
use the parenthetical form for anything complicated.

=item *

Bitwise operators get a data type prefix: C<+>, C<~>, or C<?>.
For example, Perl 5's C<|> becomes either C<+|> or C<~|> or C<?|>,
depending on whether the operands are to be treated as numbers,
strings, or boolean values.  Perl 5's left shift C< << > becomes
C< +< >, and correspondingly with right shift. Perl 5's unary C<~>
(one's complement) becomes either C<+^> or C<~^> or C<?^>, since a
bitwise NOT is like an exclusive-or against solid ones.  Note that
C<?^> is functionally identical to C<!>, but conceptually coerces to
boolean first and then flips the bit.  Please use C<!> instead. As
explained in L</Assignment operators>, a bitwise operator can be turned
into its corresponding assignment operator by following it with C<=>.
For example Perl 5's C< <<= > becomes C< +<= >.

C<?|> is a logical OR but differs from C<||> in that C<?|> always
evaluates both sides and returns a standard boolean value.  That is,
it's equivalent to C<< ?$a + ?$b != 0 >>.  Another difference is that
it has the precedence of an additive operator.

C<?&> is a logical AND but differs from C<&&> in that C<?&> always
evaluates both sides and returns a standard boolean value.  That is,
it's equivalent to C<< ?$a * ?$b != 0 >>.  Another difference is that
it has the precedence of a multiplicative operator.

Bitwise string operators (those starting with C<~>) may only be
applied to C<buf> types or similar compact integer arrays, and treat
the entire chunk of memory as a single huge integer.  They differ from
the C<+> operators in that the C<+> operators would try to convert
the string to a number first on the assumption that the string was an
ASCII representation of a number.

=item *

C<x> splits into two operators: C<x> (which concatenates repetitions
of a string to produce a single string), and C<xx> (which creates a list of
repetitions of a list or item).  C<"foo" xx *> represents an arbitrary
number of copies, useful for initializing lists.  The left side of
an C<xx> is re-evaluated for each copy; use a temporary to force a single
evaluation.  (But note that this is not necessary when the optimizer will
do constant folding.)

=item *

The C<? :> conditional operator becomes C<?? !!>.  A pseudo operator,
C<< infix:<?> >>, catches migratory brainos at compile time.

=item *

C<qw{ ... }> gets a synonym: C<< < ... > >>, and an interpolating
variant, C<«...»>.
For those still living without the blessings of Unicode, that can also be
written: C<<< << ... >> >>>.

=item *

Comma C<,> now constructs a C<Parcel> object from its
operands.  In item context this turns into a C<Seq> object.  You have to use a C<[*-1]> subscript to get the last one.
(Note the C<*>.  Negative subscripts no longer implicitly count from
the end; in fact, the compiler may complain if you use C<[-1]> on an
object known at compile time not to have negative subscripts.)

=item *

The unary backslash operator is not really an operator, but a special noun form.
It "captures" its argument or arguments, and returns an
object representing those arguments.  You can I<dereference> this object
in several ways to retrieve different parts of the arguments; see the
definition of C<Capture> in L<S02> for details.  (No whitespace is allowed
after the backslash because that would instead start an "unspace", that is,
an escaped sequence of whitespace or comments.  See L<S02> for details.
However, oddly enough, because of that unspace rule, saying C<\\ $foo>
turns out to be equivalent to C<\$foo>.)

=item *

The old C<..> flipflop operator is now done with
C<ff> operator.  (C<..> now always produces a C<Range> object
even in item context.)  The C<ff> operator may take a caret on
either end to exclude either the beginning or ending.  There is
also a corresponding C<fff> operator with Perl 5's C<...> semantics.
You may say

    /foo/ ff *

to indicate a flipflop that never flops once flipped.

The state of a flipflop is kept in an anonymous state variable, so separate
closure clones get their own states.

=item *

All comparison operators are unified at the same precedence level.
See L</Chained comparisons> below.

=item *

The list assignment operator now parses on the right like
any other list operator, so you don't need parens on the right side of:

    @foo = 1, 2, 3;

You do still need them on the left for

    ($a, $b, $c) = 1, 2, 3;

since assignment operators are tighter than comma to their left.

"Don't care" positions may be indicated by assignment to the C<*> token.
A final C<*> throws away the rest of the list:

    ($a, *, $c) = 1, 2, 3;      # throw away the 2
    ($a, $b, $c, *) = 1..42;    # throw away 4..42

(Within signature syntax, a bare C<$> can ignore a single argument as well,
and a bare C<*@> can ignore the remaining arguments.)

List assignment offers the list on the right to each container on the
left in turn, and each container may take one or more elements from the
front of the list.  If there are any elements left over, a warning is
issued unless the list on the left ends with C<*> or the final iterator
on the right is defined in terms of C<*>.  Hence none of these warn:

    ($a, $b, $c, *) = 1..9999999;
    ($a, $b, $c) = 1..*;
    ($a, $b, $c) = 1 xx *;
    ($a, $b, $c) = 1, 2, *;

This, however, warns you of information loss:

    ($a, $b, $c) = 1, 2, 3, 4;

As in Perl 5, assignment to an array or hash slurps up all the
remaining values, and can never produce such a warning.  (It will,
however, leave any subsequent lvalue containers with no elements,
just as in Perl 5.)

The left side is evaluated completely for its sequence of containers before
any assignment is done.  Therefore this:

    my $a = 0; my @b;
    ($a, @b[$a]) = 1, 2;

assigns 2 to @b[0], not @b[1].

=item *

The item assignment operator expects a single expression with
precedence tighter than comma, so

    loop ($a = 1, $b = 2; ; $a++, $b++) {...}

works as a C programmer would expect.   The term on the right of the
C<=> is always evaluated in item context.

The syntactic distinction between item and list assignment is similar
to the way Perl 5 defines it, but has to be a little different because
we can no longer decide the nature of an inner subscript on the basis
of the outer sigil.  So instead, item assignment is restricted to
lvalues that are simple scalar variables, and assignment to anything
else is parsed as list assignment.  The following forms are parsed as
"simple lvalues", and imply item assignment to the scalar container:

    $a = 1          # scalar variable
    $foo::bar = 1   # scalar package variable
    $(ANY) = 1      # scalar dereference (including $$a)
    $::(ANY) = 1    # symbolic scalar dereference
    $foo::(ANY) = 1 # symbolic scalar dereference

Such a scalar variable lvalue may be decorated with declarators,
types, and traits, so these are also item assignments:

    my $fido = 1
    my Dog $fido = 1
    my Dog $fido is trained is vicious = 1

However, anything more complicated than that (including parentheses
and subscripted expressions) forces parsing as list assignment instead.
Assignment to anything that is not a simple scalar container also forces
parsing as list assignment.  List assignment expects an expression
that is looser than comma precedence.  The right side is always
evaluated in list context:

    ($x) = 1,2,3
    $x[1] = 1,2,3
    @$array = 1,2,3
    my ($x, $y) = 1,2,3
    our %map = :a<1>, :b<2>

The rules of list assignment apply, so all the assignments involving
C<$x> above produce warnings for discarded values.  A warning may be
issued at compile time if it is detected that a run-time warning is
inevitable.

The C<=> in a default declaration within a signature is not really
assignment, and is always parsed as item assignment.  (That is, to
assign a list as the default value you must use parentheses to hide
any commas in the list value.)

To assign a list to a scalar value, you cannot say:

    $a = 1, 2, 3;

because the 2 and 3 will be seen as being in a sink (void) context, as if
you'd said:

    ($a = 1), 2, 3;

Instead, you must do something to explicitly disable or subvert the
item assignment interpretation:

    $a = [1, 2, 3];             # force construction (probably best practice)
    $a = (1, 2, 3);             # force grouping as syntactic item
    $a = list 1, 2, 3;          # force grouping using listop precedence
    $a = @(1, 2, 3);            # same thing
    @$a = 1, 2, 3;              # force list assignment
    $a[] = 1, 2, 3;             # same thing

If a function is contextually sensitive and you wish to return a scalar
value, you must use C<item> (or C<$> or C<+> or C<~>) if you wish to
force item context for either the subscript or the right side:

    @a[foo()] = bar();           # foo() and bar() called in list context
    @a[item foo()] = item bar(); # foo() and bar() called in item context
    @a[$(foo())] = $(bar());     # same thing
    @a[+foo()] = +bar();         # foo() and bar() called in numeric context
    %a{~foo()} = ~bar();         # foo() and bar() called in string context

But note that the first form still works fine if C<foo()> and C<bar()>
are item-returning functions that are not context sensitive.

In general, this will all just do what the user expects most of the time.
The rest of the time item or list behavior can be forced with minimal
syntax.

=item *

List operators are all parsed consistently.  As in Perl 5,
to the left a list operator looks like a term, while to the right it looks like
an operator that is looser than comma.  Unlike in Perl 5, the difference
between the list operator form and the function form is consistently
indicated via whitespace between the list operator and the first
argument.  If there is whitespace, it is always a list operator,
and the next token will be taken as the first term of the list (or
if there are no terms, as the expression terminator).  Any infix operator
occurring where a term is expected will be misinterpreted as a term:

    say + 2;    # means say(+2);

If there is no whitespace, subsequent parsing depends on the
syntactic category of the next item.  Parentheses (with or without
a dot) turn the list operator into a function call instead, and
all the function's arguments must be passed inside the parentheses
(except for postfix adverbs, which may follow the parentheses provided they
would not attach to some other operator by the rules of precedence).

A postfix operator following a listop is parsed as working on
the return value of the listop.

    foo.[]      # same as foo()[]
    foo.()      # same as foo()()
    foo++       # legal (if foo() is rw)

If the next item after the list operator is an infix operator,
a syntax error is reported.

Examples:

    say foo + 1;                        say(foo(+1));
    say foo $x;                         say(foo($x));
    say foo$x;                          ILLEGAL, need space or parens
    say foo+1;                          ILLEGAL, need space or parens

    say foo($bar+1),$baz                say(foo($bar+1), $baz);
    say foo.($bar+1),$baz               say(foo().($bar+1), $baz);
    say foo ($bar+1),$baz               say(foo($bar+1, $baz));
    say foo .($bar+1),$baz              say(foo($_.($bar+1), $baz));

    say foo[$bar+1],$baz                say((foo()[$bar+1]), $baz);
    say foo.[$bar+1],$baz               say((foo()[$bar+1]), $baz);
    say foo [$bar+1],$baz               say(foo([$bar+1], $baz));
    say foo .[$bar+1],$baz              say(foo($_.[$bar+1], $baz));

    say foo{$bar+1},$baz                say((foo(){$bar+1}), $baz);
    say foo.{$bar+1},$baz               say((foo(){$bar+1}), $baz);
    say foo {$bar+1},$baz               say(foo({$bar+1}, $baz));
    say foo .{$bar+1},$baz              say(foo($_.{$bar+1}, $baz));

    say foo<$bar+1>,$baz                say(foo()<$bar+1>, $baz);
    say foo.<$bar+1>,$baz               say(foo()<$bar+1>, $baz);
    say foo <$bar+1>,$baz               say(foo(<$bar+1>, $baz));
    say foo .<$bar+1>,$baz              say(foo($_.<$bar+1>, $baz));

Note that Perl 6 is making a consistent three-way distinction between
term vs postfix vs infix, and will interpret an overloaded character
like C<< < >> accordingly:

    any <a b c>                 any('a','b','c')        # term
    any()<a b c>                (any).{'a','b','c'}     # postfix
    any() < $x                  (any) < $x              # infix
    any<a b c>                  ILLEGAL                 # stealth postfix

This will seem unfamiliar and "undwimmy" to Perl 5 programmers, who
are used to a grammar that sloppily hardwires a few postfix operators
at the price of extensibility.  Perl 6 chooses instead to mandate a
whitespace dependency in order to gain a completely extensible class
of postfix operators.

=item *

A list operator's arguments are also terminated by a closure
that is not followed by a comma or colon.  (And a semicolon is implied
if the closure is the final thing on a line.  Use an "unspace" to
suppress that.)  This final closure may be followed by a postfix,
in which case the postfix is applied to the result of the entire
list operator.

=item *

A function predeclared with an empty signature is considered 0-ary
at run time but is still parsed as a list prefix operator, and looks
for a following argument list, which it may reject at run time.

    my sub foo () {...}
    foo;          # okay
    foo();        # okay
    foo (),(),(); # okay
    foo 1;        # fails to dispatch

The compiler is allowed to complain about anything it knows cannot
succeed at run time.  Note that a multi may contain () as one
of its signatures, however:

    my multi foo () {...}
    my multi foo ($x) {...}
    foo;          # okay
    foo();        # okay
    foo (),(),(); # okay
    foo 1;        # okay

To declare an item that is parsed as a simple term, you must use the
form C<< term:<foo> >>, or some other form of constant declaration such
as an enum declaration.  Such a term never looks for its arguments,
is never considered a list prefix operator, and may not work with
subsequent parentheses because it will be parsed as a function call
instead of the intended term.  (The function in question may or
may not exist.)  For example, C<rand> is a simple term in Perl 6
and does not allow parens, because there is no C<rand()> function
(though there's a C<$n.rand> method).  Most constant values such as
C<e> and C<pi> are in the same category.  After parsing one of these
the parser expects to see a postfix or an infix operator, not a term.
Therefore any attempt to use a simple value as a list operator is
destined to fail with an error indicating the parser saw two terms
in a row.

For those values (such as types) that do respond to parentheses
(that is, that do the C<Callable> role), the parentheses (parsed as
a postfix operator) are required in order to invoke the object:

    my $i = Int.($x);   # okay
    my $i = Int($x);    # okay
    my $i = Int $x;     # ILLEGAL, two terms in a row

=item *

A non-multi sub predeclared with an arity of exactly 1 also still
parses as a list prefix operator expecting multiple arguments.  You must explicitly use the form
C<< prefix:<foo> >> to declare C<foo> as a named unary in precedence;
it must still take a single positional parameter (though any number of
named parameters are allowed, which can be bound to adverbs).
All other subs with arguments parse as list operators.

=back

=head1 Junctive operators

C<|>, C<&>, and C<^> are no longer bitwise operators (see
L</Changes to Perl 5 operators>) but now serve a much higher cause:
they are now the junction constructors.

A junction is a single value that is equivalent to multiple values. They
thread through operations, returning another junction representing the
result:

     (1|2|3) + 4;                            # 5|6|7
     (1|2) + (3&4);                          # (4|5) & (5|6)

As illustrated by the last example, when two junctions are applied
through a single operator, the result is a junction representing the
application of the operator to each possible combination of values.

Junctions come with the functional variants C<any>, C<all>, C<one>, and C<none>.

This opens doors for constructions like:

     if $roll == none(1..6) { print "Invalid roll" }

     if $roll == 1|2|3 { print "Low roll" }

Junctions work through subscripting:

    doit() if @foo[any(1,2,3)]

Junctions are specifically unordered.  So if you say

    foo() | bar() | baz() == 42

it indicates to the compiler that there is no coupling between
the junctional arguments.  They can be evaluated in any order or in
parallel.  They can short-circuit as soon as any of them return 42,
and not run the others at all.  Or if running in parallel, the first
successful thread may terminate the other threads abruptly.  In general
you probably want to avoid code with side effects in junctions.

Use of negative operators with junctions is potentially problematic if
autothreaded naively.  However, by defining C<!=> and C<ne> in terms
of the negation metaoperator, we automatically get the "not raising"
that is expected by an English speaker.  That is

    if $a != 1 | 2 | 3 {...}

really means

    if $a ![==] 1 | 2 | 3 {...}

which the metaoperator rewrites to a higher-order function resembling
something like:

    negate((* == *), $a, (1|2|3));

which ends up being equivalent to:

    if not $a == 1 | 2 | 3 {...}

which is the semantics an English speaker expects.  However, it may well
be better style to write the latter form yourself.

Junctive methods on arrays, lists, and sets work just like the
corresponding list operators.  However, junctive methods on a hash
make a junction of only the hash's keys.  Use the listop form (or an
explicit C<.pairs>) to make a junction of pairs.

=head1 Comparison semantics

=over

=item *

Perl 5's comparison operators are basically unchanged, except that they
can be chained because their precedence is unified.

=item *

Binary C<===> tests immutable type and value correspondence:
for two value types (that is, immutable types), tests whether
they are the same value (eg. C<1 === 1>); for two mutable types
(object types), checks whether they have the same identity value.
(For most such types the identity is simply the reference itself.)
It is not true that C<[1,2] === [1,2]> because those are different
C<Array> objects, but it is true that C<@a === @a> because those are
the same C<Array> object).

Any object type may pretend to be a value type by defining a C<.WHICH>
method which returns a value type that can be recursively compared
using C<===>, or in cases where that is impractical, by overloading
C<===> such that the comparison treats values consistently with their
"eternal" identity.  (Strings are defined as values this way despite
also being objects.)

Two values are never equivalent unless they are of exactly the same type.  By
contrast, C<eq> always coerces to string, while C<==> always coerces to
numeric.  In fact, C<$a eq $b> really means "C<~$a === ~$b>" and C<$a == $b>
means C<+$a === +$b>.

Note also that, while string-keyed hashes use C<eq> semantics by default,
object-keyed hashes use C<===> semantics, and general value-keyed hashes
use C<eqv> semantics.

=item *

Binary C<eqv> tests equality much like C<===> does, but does
so with "snapshot" semantics rather than "eternal" semantics.  For
top-level components of your value that are of immutable types, C<eqv>
is identical in behavior to C<===>.  For components of your value
that are mutable, however, rather than comparing object identity using
C<===>, the C<eqv> operator tests whether the canonical representation
of both subvalues would be identical if we took a snapshot of them
right now and compared those (now-immutable) snapshots using C<===>.

If that's not enough flexibility, there is also an C<eqv()> function
that can be passed additional information specifying how you want
canonical values to be generated before comparison.  This gives
C<eqv()> the same kind of expressive power as a sort signature.
(And indeed, the C<cmp> operator from Perl 5 also has a functional
analog, C<cmp()>, that takes additional instructions on how to
do 3-way comparisons of the kind that a sorting algorithm wants.)
In particular, a signature passed to C<eqv()> will be bound to the
two operands in question, and then the comparison will proceed
on the formal parameters according to the information contained
in the signature, so you can force numeric, string, natural, or
other comparisons with proper declarations of the parameter's type
and traits.  If the signature doesn't match the operands, C<eqv()>
reverts to standard C<eqv> comparison.  (Likewise for C<cmp()>.)

=item *

Binary C<cmp> is no longer the comparison operator that
forces stringification.  Use the C<leg> operator for the old Perl 5
C<cmp> semantics.  The C<cmp> is just like the C<eqv> above except that
instead of returning C<Bool::False> or C<Bool::True> values it always
returns C<Order::Increase>, C<Order::Same>, or C<Order::Decrease>
(which numerify to -1, 0, or +1).

=item *

The C<leg> operator (less than, equal to, or greater than) is defined
in terms of C<cmp>, so C<$a leg $b> is now defined as C<~$a cmp ~$b>.
The sort operator still defaults to C<cmp> rather than C<leg>.  The
C<< <=> >> operator's semantics are unchanged except that it returns
an C<Order> value as described above.  In other words, C<< $a <=> $b >>
is now equivalent to C<+$a cmp +$b>.

=item *

For boolean comparison operators with non-coercive C<cmp>
semantics, use the generic C<before> and C<after> infix operators.
As ordinary infix operators these may be negated (C<!before> and C<!after>)
as well as reduced (C<[before]> and C<[after]>).

=item *

Infix C<min> and C<max> may be used to select one or the other
of their arguments.  Reducing listop forms C<[min]> and C<[max]> are
also available, as are the C<min=> and C<max=> assignment operators.
By default C<min> and C<max> use C<cmp> semantics.  As with all C<cmp>-based
operators, this may be modified by an adverb specifying different semantics.

=item *

Note that, like most other operators, a comparison naturally returns
failure if either of its arguments is undefined, and the general
policy on unthrown exceptions is that the exception is thrown as soon
as you try to use the exception as a real value.  However, various
parallelizable contexts such as hyper (or other "mass production"
contexts such as sort) will pass through unthrown exceptions rather
than throwing them.

=back

=head1 Range and RangeIter semantics

The C<..> range operator has variants with C<^> on either end to
indicate exclusion of that endpoint from the range.  It always
produces a C<Range> object.  Range objects are immutable, and primarily
used for matching intervals.  C<1..2> is the interval from 1 to 2
inclusive of the endpoints, whereas 1^..^2 excludes the endpoints
but matches any real number in between.

For numeric arguments of differing type, ranges coerce to the wider type, so:

    1 .. 1.5

is taken to mean:

    1.0 .. 1.5

These coercions are defined by multi signatures.  (Other types may
have different coercion policies.)  It is specifically illegal to
use a C<Range> as an endpoint:

    0 ..^ 10  # 0 .. 9
    0 .. ^10  # ERROR

For ranges with other non-numeric types on the right, the right
argument is coerced to numeric and then used above.
Hence, C<Array> types in the second argument are assumed
to be intended as numeric if the left argument is numeric:

    0 ..^ @x    # okay
    0 ..^ +@x   # same thing

Likewise for strings:

    0 .. '1.5'  # okay
    0 .. +'1.5' # same thing

C<Whatever> types are also supported to represent -Inf/+Inf.  If
either endpoint is a C<WhateverCode>, the range is primed into
another C<WhateverCode>.

For other types, ranges may be composed for any two arguments
of the same type, if the type itself supports it.  That is,
in general, C<< infix:<..>:(::T Any $x, T $y) >> is defined such that,
if type C<T> defines generic comparison (that is, by defining
C<< infix:<cmp> >> or equivalent), a range is constructed in that type.
If C<T> also defines C<.succ>, then the range may be iterated.
(Otherwise the range may only be used as an interval, and will return
failure if asked for a C<RangeIter>.)  Note that it is not necessary
to define a range multimethod in type C<T>, since the generic
routine can usually auto-generate the range for you.

Range objects support C<.min> and C<.max> methods representing
their left and right arguments.  The C<.bounds> method returns both
values as a two-element list representing the interval.  Ranges are
not autoreversing: C<2..1> is always a null range.  (The sequence
operator C<...> can autoreverse, however.  See below.)

Range objects support C<.excludes_min> and C<.excludes_max> methods
representing the exclusion (has C<^>) or inclusion (no C<^>) of each
endpoint in the Range.

    Range      | .min | .max | .excludes_min | .excludes_max
    -----------+------+------+---------------+------------
    1..10      | 1    | 10   | Bool::False   | Bool::False
    2.7..^9.3  | 2.7  | 9.3  | Bool::False   | Bool::True
    'a'^..'z'  | 'a'  | 'z'  | Bool::True    | Bool::False
    1^..^10    | 1    | 10   | Bool::True    | Bool::True

If used in a list context, a C<Range> object returns an iterator that
produces a sequence of values starting at the min and ending at the max.
Either endpoint may be excluded using C<^>.  Hence C<1..2> produces
C<(1,2)> but C<1^..^2> is equivalent to C<2..1> and produces no values (Nil).
To specify a sequence that counts down, use a reverse:

    reverse 1..2
    reverse 'a'..'z'

Alternately, for numeric sequences, you can use the sequence operator instead
of the range operator:

    100,99,98 ... 0
    100, *-1 ... 0      # same thing

In other words, any C<Range> used as a list assumes C<.succ> semantics,
never C<.pred> semantics.  No other increment is allowed; if you wish
to increment a numeric sequence by some number other than 1, you must
use the C<...> sequence operator.  (The C<Range> operator's C<:by> adverb
is hereby deprecated.)

    0, *+0.1 ... 100    # 0, 0.1, 0.2, 0.3 ... 100

A C<Range> may be iterated only if the type in question supports the C<.succ> method.
If it does not, any attempt to iterate returns failure.

Smart matching against a C<Range> object does comparisons
(by coercion, if necessary) in the C<Real> domain
if either endpoint does C<Real>.  Otherwise comparison is in
the C<Stringy> domain if either argument does C<Stringy>.
Otherwise the min's type is used if it defines ordering, or if not,
the max's type.  If neither min nor max have an ordering, 
dispatch to .ACCEPTS fails.  It may also fail if the ordering
in question does not have any way to coerce the object
being smartmatched into an appropriate type implied by the
chosen domain of ordering.

In general, the domain of comparison should be a type that can
represent all the values in question, if possible.  Hence, since Int
is not such a type, it is promoted to a Real, so fractional numbers
are I<not> truncated before comparison to integer ranges.  Instead the
integers are assumed to represent points on the real number line:

    1.5 ~~ 1^..^2  # true, equivalent to 1 < 1.5 < 2
    2.1 ~~ 1..2    # false, equivalent to 1 <= 2.1 <= 2

If a C<*> (see the "Whatever" type in L<S02>) occurs on the right side
of a range, it is taken to mean "positive infinity" in whatever
typespace the range is operating, as inferred from the left operand.
A C<*> on the left means "negative infinity" for types that support
negative values, and the first value in the typespace otherwise as
inferred from the right operand.  (A star on both sides is not allowed.)

    0..*        # 0 .. +Inf
    'a'..*      # 'a' le $_
    *..0        # -Inf .. 0
    *..*        # Illegal
    v1.2.3 .. * # Any version higher than 1.2.3.
    May .. *    # May through December

An empty range cannot be iterated; it returns a C<Nil> instead.  An empty
range still has a defined C<.min> and C<.max>, but one of the following is
true:  1. The C<.min> is greater than the C<.max>.  2. The C<.min> is equal
to the C<.max> I<and> at least one of C<.excludes_min> or C<.excludes_max> is true.
3. Both C<.excludes_min> and C<.excludes_max> are true I<and> C<.min> and C<.max>
are consecutive values in a discrete type that cannot create new
values between those two consecutive values.  For this purpose,
interval representations in C<Real> (including integers) are
considered infinitely divisible even though there is a practical
limit depending on the actual representation, so #3 does not apply.
(Nor does it apply to strings, versions, instants, or durations.
#3 does apply to enums, however, so C<< Tue ^..^ Wed >> is considered
empty because the enum in question does not define "Tuesday and a half".)

An empty range evaluates to C<False> in boolean context; all other
ranges evaluate to C<True>.

Ranges that are iterated transmute into the corresponding sequence
operator, using C<.succ> semantics to find the next value, and the
appropriate inequality semantics to determine an end to the sequence.
For a non-discrete type with a discrete C<.succ> (such as C<Real>),
it is possible to write a range that, when iterated, produces no
values, but evaluates to true, because the C<.succ> function skips
over divisible intervals:

    say +( 0 ^..^ 1 )   # 0 elements
    say ?( 0 ^..^ 1 )   # True
    say 0.5 ~~ 0 ^..^ 1 # True; range contains non-integer values

=head2 Unary ranges

The unary C<^> operator generates a range from C<0> up to
(but not including) its argument.  So C<^4> is short for C<0..^4>.

    for ^4 { say $_ } # 0, 1, 2, 3

=head2 Auto-priming of ranges

[This section is conjectural, and may be ignored for 6.0.]

Since use of C<Range> objects in item context is usually
non-sensical, a C<Range> object used as an operand for scalar operators
will generally attempt to distribute the operator to its endpoints and
return another suitably modified C<Range> instead, much like a junction of two items,
only with proper interval semantics.  (Notable exceptions to this autothreading
include C<< infix:<~~> >>, which does smart matching, and C<< prefix:<+> >>
which returns the length of the range.)  Therefore if you wish to
write a slice using a length instead of an endpoint, you can say

    @foo[ start() + ^$len ]

which is short for:

    @foo[ start() + (0..^$len) ]

which is equivalent to something like:

    @foo[ list do { my $tmp = start(); $tmp ..^ $tmp+$len } ]

In other words, operators of numeric and other ordered types are
generally overloaded to do something sensible on C<Range> objects.

=head1 Chained comparisons

Perl 6 supports the natural extension to the comparison operators,
allowing multiple operands:

    if 1 < $a < 100 { say "Good, you picked a number *between* 1 and 100." }

    if 3 < $roll <= 6              { print "High roll" }

    if 1 <= $roll1 == $roll2 <= 6  { print "Doubles!" }

A chain of comparisons short-circuits if the first comparison fails:

    1 > 2 > die("this is never reached");

Each argument in the chain will evaluate at most once:

    1 > $x++ > 2    # $x increments exactly once

Note: any operator beginning with C<< < >> must have whitespace
in front of it, or it will be interpreted as a hash subscript instead.

=head1 Smart matching

Here is the table of smart matches for standard Perl 6
(that is, the dialect of Perl in effect at the start of your
compilation unit).  Smart matching is generally done on the current
"topic", that is, on C<$_>.  In the table below, C<$_> represents the
left side of the C<~~> operator, or the argument to a C<given>,
or to any other topicalizer.  C<X> represents the pattern to be
matched against on the right side of C<~~>, or after a C<when>.
(And, in fact, the C<~~> operator works as a small topicalizer; that is,
it binds C<$_> to the value of the left side for the evaluation
of the right side.  Use the underlying C<.ACCEPTS> form to avoid
this topicalization.)

The first section contains privileged syntax; if a match can be done
via one of those entries, it will be.   These special syntaxes are
dispatched by their form rather than their type.  Otherwise the rest
of the table is used, and the match will be dispatched according to
the normal method dispatch rules.  The optimizer is allowed to assume
that no additional match operators are defined after compile time,
so if the pattern types are evident at compile time, the jump table
can be optimized.  However, the syntax of this part of the table
is still somewhat privileged, insofar as the C<~~> operator is one
of the few operators in Perl that does not use multiple dispatch.
Instead, type-based smart matches singly dispatch to an underlying
method belonging to the C<X> pattern object.

In other words, smart matches are dispatched first on the basis of the
pattern's form or type (the C<X> below), and then that pattern itself
decides whether and how to pay attention to the type of the topic
(C<$_>).  So the second column below is really the primary column.
The C<Any> entries in the first column indicate a pattern that either
doesn't care about the type of the topic, or that picks that entry
as a default because the more specific types listed above it didn't match.

    $_        X         Type of Match Implied   Match if (given $_)
    ======    =====     =====================   ===================
    Any       True      ~~ True                 (parsewarn)
    Any       False     ~~ False match          (parsewarn)
    Any       *         block signature match   block successfully binds to |$_

    Any       Callable:($)  item sub truth          X($_)
    Any       Callable:()   simple closure truth    X() (ignoring $_)
    Any       Bool      simple truth            X
    Any       Match     match success           X
    Any       Numeric   numeric equality        +$_ == X
    Any       Stringy   string equality         ~$_ eq X
    Any       Whatever  always matches          True
    Any       Nil       is nil                  $_ === Nil

    Hash      Pair      test hash mapping       $_{X.key} ~~ X.value
    Any       Pair      test object attribute   ?."{X.key}" === ?X.value (e.g. filetests)

    Set       Set       identical sets          $_ === X
    Hash      Set       hash keys same set      $_.keys === X
    Any       Set       force set comparison    Set($_) === X

    Array     Array     arrays are comparable   $_ «===» X (dwims * wildcards!)
    Set       Array     array equiv to set      $_ === Set(X)
    Any       Array     lists are comparable    @$_ «===» X

    Hash      Hash      hash keys same set      $_.keys === X.keys
    Set       Hash      hash keys same set      $_ === X.keys
    Array     Hash      hash slice existence    X.{any @$_}:exists
    Regex     Hash      hash key grep           any(X.keys).match($_)
    Cool      Hash      hash entry existence    X.{$_}:exists
    Any       Hash      hash slice existence    X.{any @$_}:exists

    Str       Regex     string pattern match    .match(X)
    Hash      Regex     hash key "boolean grep" .any.match(X)
    Array     Regex     array "boolean grep"    .any.match(X)
    Any       Regex     pattern match           .match(X)

    Num       Range     in numeric range        X.min <= $_ <= X.max (mod ^'s)
    Str       Range     in string range         X.min le $_ le X.max (mod ^'s)
    Range     Range     subset range            !$_ or .bounds.all ~~ X (mod ^'s)
    Any       Range     in generic range        [!after] X.min,$_,X.max (etc.)

    Any       Type      type membership         $_.does(X)

    Signature Signature sig compatibility       $_ is a subset of X      ???
    Callable  Signature sig compatibility       $_.sig is a subset of X  ???
    Capture   Signature parameters bindable     $_ could bind to X (doesn't!)
    Any       Signature parameters bindable     |$_ could bind to X (doesn't!)

    Signature Capture   parameters bindable     X could bind to $_

    Any       Any       scalars are identical   $_ === X

The final rule is applied only if no other pattern type claims X.

All smartmatch types are "itemized"; both C<~~> and C<given>/C<when>
provide item contexts to their arguments, and autothread any
junctive matches so that the eventual dispatch to C<.ACCEPTS> never
sees anything "plural".  So both C<$_> and C<X> above are potentially
container objects that are treated as scalars.  (You may hyperize
C<~~> explicitly, though.  In this case all smartmatching is done
using the type-based dispatch to C<.ACCEPTS>, not the form-based
dispatch at the front of the table.)

The exact form of the underlying type-based method dispatch is:

    X.ACCEPTS($_)

As a single dispatch call this pays attention only to the type of
C<X> initially.  The C<ACCEPTS> method interface is defined by the
C<Pattern> role.  Any class composing the C<Pattern> role may choose
to provide a single C<ACCEPTS> method to handle everything, which
corresponds to those pattern types that have only one entry with
an C<Any> on the left above.  Or the class may choose to provide
multiple C<ACCEPTS> multi-methods within the class, and these
will then redispatch within the class based on the type of C<$_>.

The smartmatch table is primarily intended to reflect forms and types that
are recognized at compile time.  To avoid an explosion of entries,
the table assumes the following types will behave similarly:

    Actual type                 Use entries for
    ===========                 ===============
    Iterator Seq                Array
    KeySet KeyBag KeyHash       Hash
    named values created with
      Class, Enum, or Role,
      or generic type binding   Type
    Char Cat                    Str
    Int UInt etc.               Num
    Byte                        Str or Int
    Buf                         Str or Array of Int

(Note, however, that these mappings can be overridden by explicit
definition of the appropriate C<ACCEPTS> methods.
If the redefinition occurs at compile time prior to analysis of the
smart match then the information is also available to the optimizer.)

A C<Buf> type containing any bytes or integers outside the ASCII
range may silently promote to a C<Str> type for pattern matching if
and only if its relationship to Unicode is clearly declared or typed.
This type information might come from an input filehandle, or the
C<Buf> role may be a parametric type that allows you to instantiate
buffers with various known encodings.  In the absence of such typing
information, you may still do pattern matching against the buffer, but
(apart from assuming the lowest 7 bits represent ASCII) any attempt
to treat the buffer as other than a sequence of integers is erroneous,
and warnings may be generously issued.

Matching against a C<Grammar> treats the grammar as a typename,
not as a grammar.  You need to use the C<.parse> or C<.parsefile>
methods to invoke a grammar.

Matching against a C<Signature> does not actually bind any variables,
but only tests to see if the signature I<could> bind.  To really bind
to a signature, use the C<*> pattern to delegate binding to the C<when>
statement's block instead.  Matching against C<*> is special in that
it takes its truth from whether the subsequent block is bound against
the topic, so you can do ordered signature matching:

    given $capture {
        when * -> Int $a, Str $b { ... }
        when * -> Str $a, Int $b { ... }
        when * -> $a, $b         { ... }
        when *                   { ... }
    }

This can be useful when the unordered semantics of multiple dispatch
are insufficient for defining the "pecking order" of code.  Note that
you can bind to either a bare block or a pointy block.  Binding to a
bare block conveniently leaves the topic in C<$_>, so the final form
above is equivalent to a C<default>.  (Placeholder parameters may
also be used in the bare block form, though of course their types
cannot be specified that way.)

There is no pattern matching defined for the C<Any> pattern, so if you
find yourself in the situation of wanting a reversed smartmatch test
with an C<Any> on the right, you can almost always get it by an explicit
call to the underlying C<ACCEPTS> method using C<$_> as the pattern.
For example:

    $_      X    Type of Match Wanted   What to use on the right
    ======  ===  ====================   ========================
    Callable Any  item sub truth         .ACCEPTS(X) or .(X)
    Range   Any  in range               .ACCEPTS(X)
    Type    Any  type membership        .ACCEPTS(X) or .does(X)
    Regex   Any  pattern match          .ACCEPTS(X)
    etc.

Similar tricks will allow you to bend the default matching rules for
composite objects as long as you start with a dotted method on C<$_>:

    given $somethingordered {
        when .values.'[<=]'     { say "increasing" }
        when .values.'[>=]'     { say "decreasing" }
    }

In a pinch you can define a macro to do the "reversed when":

    my macro statement_control:<ACCEPTS> () { "when .ACCEPTS: " }
    given $pattern {
        ACCEPTS $a      { ... }
        ACCEPTS $b      { ... }
        ACCEPTS $c      { ... }
    }

Various proposed-but-deprecated smartmatch behaviors may be easily
(and we hope, more readably) emulated as follows:

    $_      X      Type of Match Wanted   What to use on the right
    ======  ===    ====================   ========================
    Array   Num    array element truth    .[X]
    Array   Num    array contains number  *,X,*
    Array   Str    array contains string  *,X,*
    Array   Seq    array begins with seq  X,*
    Array   Seq    array contains seq     *,X,*
    Array   Seq    array ends with seq    *,X
    Hash    Str    hash element truth     .{X}
    Hash    Str    hash key existence     .{X}:exists
    Hash    Num    hash element truth     .{X}
    Hash    Num    hash key existence     .{X}:exists
    Buf     Int    buffer contains int    .match(X)
    Str     Char   string contains char   .match(X)
    Str     Str    string contains string .match(X)
    Array   Scalar array contains item    .any === X
    Str     Array  array contains string  X.any
    Num     Array  array contains number  X.any
    Scalar  Array  array contains object  X.any
    Hash    Array  hash slice exists      .{X.all}:exists .{X.any}:exists
    Set     Set    subset relation        .{X.all}:exists
    Set     Hash   subset relation        .{X.all}:exists
    Any     Set    subset relation        .Set.{X.all}:exists
    Any     Hash   subset relation        .Set.{X.all}:exists
    Any     Set    superset relation      X.{.all}:exists
    Any     Hash   superset relation      X.{.all}:exists
    Any     Set    sets intersect         .{X.any}:exists
    Set     Array  subset relation        X,*          # (conjectured)
    Array   Regex  match array as string  .Cat.match(X)  cat(@$_).match(X)

(Note that the C<.cat> method and the C<Cat> type coercion both take a
single object, unlike the C<cat> function which, as a list operator,
takes a syntactic list (or multilist) and flattens it.  All of these
return a C<Cat> object, however.)

Boolean expressions are those known to return a boolean value, such
as comparisons, or the unary C<?> operator.  They may reference C<$_>
explicitly or implicitly.  If they don't reference C<$_> at all, that's
okay too--in that case you're just using the switch structure as a more
readable alternative to a string of elsifs.  Note, however, that this means
you can't write:

    given $boolean {
        when True  {...}
        when False {...}
    }

because it will always choose the C<True> case.  Instead use something like
a conditional context uses internally:

    given $boolean {
        when .Bool == 1 {...}
        when .Bool == 0 {...}
    }

Better, just use an C<if> statement.  In any case, if you try to smartmatch
with C<~~> or C<when>, it will recognize C<True> or C<False> syntactically
and warn you that it won't do what you expect.  The compiler is also allowed
to warn about any other boolean construct that does not test C<$_>, to the
extent it can detect that.

In a similar vein, any function (such as C<grep>) that takes a
C<Matcher> will not accept an argument of type C<Bool>, since that
almost always indicates a programming error.  (One may always use
C<*> to match anything, if that's what you really want.  Or use a closure
that returns a constant boolean value.)

Note also that regex matching does I<not> return a C<Bool>, but merely
a C<Match> object that can be used as a boolean value.  Use an explicit
C<?> or C<so> to force a C<Bool> value if desired.

The primary use of the C<~~> operator is to return a boolean value in
a boolean context.  However, for certain operands such as regular
expressions, use of the operator within item or list context transfers
the context to that operand, so that, for instance, a regular expression
can return a list of matched substrings, as in Perl 5.  This is done
by returning an object that can return a list in list context, or that
can return a boolean in a boolean context.  In the case regex matching
the C<Match> object is a kind of C<Capture>, which has these capabilities.

For the purpose of smartmatching, all C<Set> and C<Bag> values are
considered to be of type C<KeyHash>, that is, C<Hash> containers
where the keys represent the unique objects and the values represent
the replication count of those unique keys.  (Obviously, a C<Set> can
have only 0 or 1 replication because of the guarantee of uniqueness).

Despite the need for an implementation to examine the bounds of a
range in order to perform smartmatching, the result of smartmatching
two C<Range> objects is not actually defined in terms of bounds, but
rather as a subset relationship between two (potentially infinite) sets
of values encompassed by the intervals involved, for any orderable
type such as real numbers, strings, or versions.  The result is
defined as true if and only if all potential elements that would
be matched by the left range are also matched by the right range.
Hence it does not matter to what extent the bounds of a empty range
are "overspecified".  If the left range is empty, it always matches,
because there exists no value to falsify it.  If the right range is
empty, it can match only if the left range is also empty.

The C<Cat> type allows you to have an infinitely extensible string.
You can match an array or iterator by feeding it to a C<Cat>,
which is essentially a C<Str> interface over an iterator of some sort.
Then a C<Regex> can be used against it as if it were an ordinary
string.  The C<Regex> engine can ask the string if it has more
characters, and the string will extend itself if possible from its
underlying iterator.  (Note that such strings have an indefinite
number of characters, so if you use C<.*> in your pattern, or if you
ask the string how many characters it has in it, or if you even print
the whole string, it may be feel compelled to slurp in the rest of
the string, which may or may not be expeditious.)

The C<cat> operator takes a (potentially lazy) list and returns a
C<Cat> object.  In string context this coerces each of its elements
to strings lazily, and behaves as a string of indeterminate length.
You can search a gather like this:

    my $lazystr := cat gather for @foo { take .bar }

    $lazystr ~~ /pattern/;

The C<Cat> interface allows the regex to match element boundaries
with the C<< <,> >> assertion, and the C<StrPos> objects returned by
the match can be broken down into elements index and position within
that list element.  If the underlying data structure is a mutable
array, changes to the array (such as by C<shift> or C<pop>) are tracked
by the C<Cat> so that the element numbers remain correct.  Strings,
arrays, lists, sequences, captures, and tree nodes can all be pattern
matched by regexes or by signatures more or less interchangeably.

=head1 Invocant marker

An appended C<:> marks the invocant when using the indirect-object
syntax for Perl 6 method calls.  The following two statements are
equivalent:

    $hacker.feed('Pizza and cola');
    feed $hacker: 'Pizza and cola';

A colon may also be used on an ordinary method call to indicate that
it should be parsed as a list operator:

    $hacker.feed: 'Pizza and cola';

This colon is a separate token.  A colon prefixing an adverb is not
a separate token.  Therefore, under the longest-token rule,

    $hacker.feed:xxx('Pizza and cola');

is tokenized as an adverb applying to the method as its "toplevel preceding operator":

    $hacker.feed :xxx('Pizza and cola');

not as an xxx sub in the argument list of .feed:

    $hacker.feed: xxx('Pizza and cola');  # wrong

If you want both meanings of colon in order to supply both an adverb
and some positional arguments, you have to put the colon twice:

    $hacker.feed: :xxx('Pizza and cola'), 1,2,3;

(For similar reasons it's required to put whitespace after the colon of a label.)

Note in particular that because of adverbial precedence:

    1 + $hacker.feed :xxx('Pizza and cola');

will apply the C<:xxx> adverb to the C<+> operator, not the method call.
This is not likely to succeed.

=head1 Feed operators

The new operators C<< ==> >> and C<< <== >> are akin to UNIX pipes,
but work with functions or statements that accept and return lists.
Since these lists are composed of discrete objects and not liquids,
we call these I<feed> operators rather than pipes.  For example,

     @result = map { floor($^x / 2) },
                 grep { /^ \d+ $/ },
                   @data;

can also now be written with rightward feeds as:

     @data ==> grep { /^ \d+ $/ }
           ==> map { floor($^x / 2) }
           ==> @result;

or with leftward feeds as:

     @result <== map { floor($^x / 2) }
             <== grep { /^ \d+ $/ }
             <== @data;

Either form more clearly indicates the flow of data.  See L<S06> for
more of the (less-than-obvious) details on these two operators.

=head1 Meta operators

Perl 6's operators have been greatly regularized, for instance, by
consistently prefixing numeric, stringwise, and boolean operators
with C<+>, C<~> and C<?> respectively to indicate whether the bitwise
operation is done on a number, a string, or a single bit.
But that's just a naming convention, and if you wanted to add a new
bitwise C<¬> operator, you'd have to add the C<+¬>, C<~¬>, and C<?¬>
operators yourself.  Similarly, the carets that exclude the endpoints
on ranges are there by convention only.

In contrast to that, Perl 6 has eight standard metaoperators for
turning a given existing operator into a related operator that is
more powerful (or at least differently powerful).  These differ from a
mere naming convention in that Perl automatically generates these new
operators from user-defined operators as well as from builtins.
In fact, you're not generally supposed to define the individual
metaoperations--their semantics are supposed to be self-evident by
the transformation of the base operator.  In other words, these
metaoperators are really just shorthand for higher-order functions
(functions that take other functions as arguments).

Constructs containing metaoperators are considered "metatokens",
by which we mean that they are not subject to ordinary longest-token
matching rules, although their components are.  Like ordinary
tokens, however, metatokens do not allow whitespace between
their subparts.

=head2 Assignment operators

Assignment operators are already familiar to C and Perl programmers.  (Though the
C<.=> operator now means to call a mutating method on the object on
the left, and C<~=> is string concatenation.)  Most non-relational
infix operators may be turned into their corresponding assignment
operator by suffixing with C<=>.  The limitation is actually based
on whether the left side can function both as an rvalue and an lvalue
by the usual correspondence:

    A op= B;
    A = A op B;

Existing forms ending in C<=> may not be modified with this metaoperator.

Regardless of the precedence of the base operator, the precedence
of any assignment operator is forced to be the same as that of
ordinary assignment.  If the base operator is tighter than comma,
the expression is parsed as item assignment.  If the base operator is
the same or looser than comma, the expression is parsed as a list assignment:

    $a += 1, $b += 2    # two separate item assignments
    @foo ,= 1,2,3       # same as push(@foo,1,2,3)
    @foo Z= 1,2,3       # same as @foo = @foo Z 1,2,3

Note that metaassignment to a list does not automatically distribute
the right argument over the assigned list unless the base operator
does (as in the C<Z> case above).  Hence if you want to say:

    ($a,$b,$c) += 1;    # ILLEGAL

you must instead use a hyperoperator (see below):

    ($a,$b,$c) »+=» 1;  # add one to each of three variables

If you apply an assignment operator to a container containing a type object
(which is undefined), it is assumed that
you are implementing some kind of notional "reduction" to an accumulator
variable.  To that end, the operation is defined in terms
of the corresponding reduction operator, where the type object
autovivifies to the operator's identify value.  So if you say:

    $x -= 1;

it is more or less equivalent to:

    $x = [-]() unless defined $x;  # 0 for [-]()
    $x = $x - 1;

and $x ends up with -1 in it, as expected.

Hence you may correctly write:

    my Num $prod;
    for @factors -> $f {
        $prod *= $f;
    }

While this may seem marginally useful in the scalar variable case,
it's much more important for it to work this way when the modified
location may have only just been created by autovivification.  In other
words, if you write:

    %prod{$key} *= $f

you need not worry about whether the hash element exists yet.  If it
does not, it will simply be initialized with the value of C<$f>.

=head2 Negated relational operators

Any infix relational operator returning type C<Bool> may be transformed
into its negative by prefixing with C<!>.  A couple of these have
traditional shortcuts:

    Full form   Shortcut
    ---------   --------
    !==         !=
    !eq         ne

but most of them do not:

    !~~
    !<
    !>=
    !ge
    !===
    !eqv
    !=:=

To avoid visual confusion with the C<!!> operator, you may not modify
any operator already beginning with C<!>.

The precedence of any negated operator is the same as the base operator.

You may negate only those operators that return a C<Bool>.  Note that
logical operators such as C<||> and C<^^> do not return a C<Bool>,
but rather one of the operands.

=head2 Reversed operators

Any infix operator may be called with its two arguments reversed
by prefixing with C<R>.  For instance, to do reversed comparisons:

    Rcmp
    Rleg
    R<=>

The precedence of any reversed operator is the same as the base operator.
The associativity is I<not> reversed, so

    [R-] 1,2,3   # produces 2 from 3 - (2 - 1)

To get the other effect in a reduce, reverse the list:

    [-] reverse 1,2,3  # produces 0

=head2 Hyper operators

The Unicode characters C<»> (C<\x[BB]>) and C<«> (C<\x[AB]>) and
their ASCII digraphs C<<< >> >>> and C<<< << >>> are used to denote a
"list operation" that operates on each element of its list (or array)
argument (or arguments) and returns a single list (or array) of
the results.  In other words, a hyper operator evaluates its arguments in
item context but then distributes the operator over them as lists.

When writing a hyper operator, spaces are not allowed on the inside,
that is, between any "hyper" marker and the operator it's modifying.
On the outside the spacing policy is the same as the base operator.
Likewise the precedence of any hyperoperator is the same as its
base operator.  This means that you must parenthesize your comma
lists for most operators.  For example:

     -« (1,2,3);                   # (-1, -2, -3)
     (1,1,2,3,5) »+« (1,2,3,5,8);  # (2,3,5,8,13)

(If you find yourself doing this, ask yourself whether you are really
working with objects or lists; in the latter case, there may be other
metaoperators such as Z or X that are more appropriate, and will not
require parens.)

A unary hyper operator (either prefix or postfix) has only one
hyper marker, located on its argument side, while an infix operator
always has one on each side to indicate there are two arguments.
Unary operators always produce a list or array of exactly the same
shape as their single argument (at least down to the level that the operator
may be applied).  When infix operators are presented with
two lists or arrays of identical shape, a result of that same shape is
produced.  Otherwise the result depends on how you write the hyper
markers.

For an infix operator, if either argument is insufficiently
dimensioned, Perl "upgrades" it, but only if you point the "sharp" end
of the hypermarker at it.

     (3,8,2,9,3,8) >>->> 1;          # (2,7,1,8,2,7)
     @array »+=» 42;                 # add 42 to each element

In fact, an upgraded scalar is the only thing that will work for an
unordered type such as a C<Bag>:

     Bag(3,8,2,9,3,8) >>->> 1;       # Bag(2,7,1,8,2,7) === Bag(1,2,2,7,7,8)

In other words, pointing the small end at an argument tells the hyperoperator
to "dwim" on that side.  If you don't know whether one side or the other will
be underdimensioned, you can dwim on both sides:

    $left «*» $right

[Note: if you are worried about Perl getting confused by something like this:

    func «*»

then you shouldn't worry about it, because unlike previous versions,
Perl 6 never guesses whether the next thing is a term or operator.
In this case it is always expecting a term unless C<func> is predeclared
to be a type or value name.]

The upgrade never happens on the "blunt" end of a hyper.  If you write

    $bigger «*« $smaller
    $smaller »*» $bigger

an exception is thrown, and if you write

    $foo »*« $bar

you are requiring the shapes to be identical, or an exception will be thrown.

For all hyper dwimminess, if a scalar is found where the other side expects a list,
the scalar is considered to be a list of one element repeated C<*> times.

Once we have two lists to process, we have to decide how to put the elements
into correspondence.  If both sides are dwimmy, the short list will have be repeated
as many times as necessary to make the appropriate number of elements.

If only one side is dwimmy, then the list on that side only will be
grown or truncated to fit the list on the non-dwimmy side.

Regardless of whether the dwim is forced or emergent from the shapes
of the arrays, once the side to dwim on has been chosen, the dwim
semantics on the dwimmy side are always:

    (@dwimmyside xx *).batch(@otherside.elems)

This produces a list the same length as the corresponding dimension
on the other side.  The original operator is then recursively applied
to each corresponding pair of elements, in case there are more dimensions
to handle.

Here are some examples:

    (1,2,3,4) »+« (1,2)   # always error
    (1,2,3,4) «+» (1,2)   # 2,4,4,6     rhs dwims to 1,2,1,2
    (1,2,3)   «+» (1,2)   # 2,4,4       rhs dwims to 1,2,1
    (1,2,3,4) «+« (1,2)   # 2,4         lhs dwims to 1,2
    (1,2,3,4) »+» (1,2)   # 2,4,4,6     rhs dwims to 1,2,1,2
    (1,2,3)   »+» (1,2)   # 2,4,4       rhs dwims to 1,2,1
    (1,2,3)   »+» 1       # 2,3,4       rhs dwims to 1,1,1

Another way to look at it is that the dwimmy list's elements are
indexed modulo its number of elements so as to produce as many or as
few elements as necessary.

Note that each element of a dwimmy list may in turn be expanded into
another dimension if necessary, so you can, for instance, add one to
all the elements of a matrix regardless of its dimensionality:

    @fancy »+=» 1

On the non-dwimmy side, any scalar value that does not know how to
do C<Iterable> will be treated as a list of one element, and for infix
operators must be matched by an equivalent one-element list on the
other side.  That is, a hyper operator is guaranteed to degenerate
to the corresponding scalar operation when all its arguments are
non-list arguments.

When using a unary operator, you always aim the blunt end at the
single operand, because no replicative dwimmery ever happens:

     @negatives = -« @positives;

     @positions»++;            # Increment all positions

     @positions.»++;           # Same thing, dot form
     @positions».++;           # Same thing, dot form
     @positions.».++;          # Same thing, dot form
     @positions\  .»\  .++;    # Same thing, unspace form

     @objects.».run();
     ("f","oo","bar").>>.chars;   # (1,2,3)

Note that method calls are really postfix operators, not infix, so you
shouldn't put a C<«> after the dot.

Hyper operators are defined recursively on nested arrays, so:

    -« [[1, 2], 3]               #    [-«[1, 2], -«3]
                                 # == [[-1, -2], -3]

Likewise the dwimminess of dwimmy infixes propagates:

    [[1, 2], 3] «+» [4, [5, 6]]  #    [[1,2] «+» 4, 3 «+» [5, 6]]
                                 # == [[5, 6], [8, 9]]

More generally, a dwimmy hyper operator works recursively for any object
matching the C<Iterable> role even if the object itself doesn't support
the operator in question:

    Bag(3,8,[2,Seq(9,3)],8) >>->> 1;         # Bag(2,7,[1,Seq(8,2)],7)
    Seq(3,8,[2,Seq(9,3)],8) >>->> (1,1,2,1); # Seq(2,7,[0,Seq(7,1)],7)

In particular, tree node types with C<Iterable> semantics enable visitation:

    $node.».foo;

which means something like:

    my $type = $node.WHAT;
    $node.?foo // $type($node.map: { .».foo })

When processing recursive structures, there is an ambiguity when a node
could be processed either directly by the operator or recursively
by iterating a contained structure.  For unary hypers, we use a
policy called "duck mapping", which says that when a node responds
directly to the operator supplied, it is considered a leaf node,
and any Iterable components of the node are ignored.  If and only if
a node does not respond to the operator, it is examined to see if is
Iterable, and recursion occurs.  (For this meaning of "responds to",
we ignore any multi candidates defined in Cool, or the negation
above would not work, since Array responds to negation via Cool.
[Conjecture: there's a C<use strict :multi> pragma that can enable
these dispatch semantics in a lexical scope.])

A declaratively shaped array or hash with multiple dimensions is
considered a single level of tree node for this purpose.  You must
use subscripting if you wish to isolate a 1-dimensional slice of such
a shaped object.

The main upshot of this duck mapping policy is that it is possible
to use array or hash operators that make sense on a node of the tree,
and the requested operator will take precedence over recursion.  For
example, if you have an array of hashes, you can subscript into
each of the hashes in parallel without caring whether the value
produced is iterable:

    @AoHoA».<foo>;  # a list of all the 'foo' Arrays

This would not be possible if recursion took precedence over subscripting.
Since duck mapping stops recursing whenever the operator is applicable,
duck mapping can be considered to have a shallow bias.  If you wish to have
a deep mapping where the recursion takes precedence over the operator,
so that all the leaves are found first, and then the operator applied,
you need to use the C<.deepmap> method instead:

    $node.deepmap: *.foo;
    
which means something like:
    
    my $type = $node.WHAT;
    $node ~~ Iterable ?? $type($node.map({ .deepmap: *.foo })) !! $node.?foo

[Conjecture: we could allow C<««> and C<»»> hypers which did deep mapping.]

You are not allowed to define your own hyper operators, because they
are supposed to have consistent semantics derivable entirely from
the modified scalar operator.  If you're looking for a mathematical
vector product, this isn't where you'll find it.  A hyperoperator
is one of the ways that you can promise to the optimizer that your
code is parallelizable.  (The tree visitation above is allowed to
have side effects, but it is erroneous for the meaning of those side
effects to depend on the order of visitation in any way.  Hyper tree
visitation is not required to follow DAG semantics, at least by default.)

Even in the absence of hardware that can do parallel processing,
hyperoperators may be faster than the corresponding scalar operators
if they can factor out looping overhead to lower-level code, or
can apply loop-unrolling optimizations, or can factor out some or
all of the MMD dispatch overhead, based on the known types of the
operands (and also based on the fact that hyper operators promise
no interaction among the "iterations", whereas the corresponding
scalar operator in a loop cannot make the same promise unless all
the operations within the loop are known to be side-effect free.)

In particular, infix hyperops on two C<int> or C<num> arrays need
only do a single MMD dispatch to find the correct function to call for
all pairs, and can further bypass any type-checking or type-coercion
entry points to such functions when there are known to be low-level
entry points of the appropriate type.  (And similarly for unary C<int>
or C<num> ops.)

Application-wide analysis of finalizable object types may also enable
such optimizations to be applied to C<Int>, C<Num>, and such.  In the
absence of that, run-time analysis of partial MMD dispatch may save
some MMD searching overhead.  Or particular object arrays might even
keep track of their own run-time type purity and cache partial MMD
dispatch tables when they know they're likely to be used in hyperops.

Beyond all that, "array of scalar" types are known at compile time not to
need recursive hypers, so the operations can be vectorized aggressively.

Hypers may be applied to hashes as well as to lists.  In this case
"dwimminess" says whether to ignore keys that do not exist
in the other hash, while "non-dwimminess" says to use all keys that are
in either hash.  That is,

    %foo «+» %bar;

gives you the intersection of the keys, while

    %foo »+« %bar;

gives you the union of the keys.  Asymmetrical hypers are also useful;
for instance, if you say:

    %outer »+» %inner;

only the C<%inner> keys that already exist in C<%outer> will occur in the result.
Note, however, that you want

    %outer »+=« %inner;

in order to pass accumulated statistics up a tree, assuming you want C<%outer>
to have the union of keys.

Unary hash hypers and binary hypers that have only one hash operand
will apply the hyper operator to just the values but return a new
hash value with the same set of keys as the original hash.

For any kind of zip or dwimmy hyper operator, any list ending with C<*>
is assumed to be infinitely extensible by taking its final element
and replicating it:

    @array, *

is short for something like:

    @array[0..^@array], @array[*-1] xx *

Note that hypers promise that you don't care in what order the processing
happens, only that the resulting structure ends up in a form consistent
with the inputs.  There is no promise from the system that the operation
I<will> be parallelized.  Effective parallelization requires some means
of partitioning the work without doing more extra work than you save.
This will differ from structure to structure.  In particular, infinite
structures cannot be completely processed, and the system is allowed to
balance out the demands of laziness with parallel processing.  For instance,
an algorithm that wants to divide a list into two equal sublists will not
work if you have to calculate the length in advance, since you can't always
calculate the length.  Various approaches can be taken: handing off batches
to be processed in parallel on demand, or interleaving roundrobin with a
set of N processors, or whatever.  In the limit, a simple, non-parallel,
item-by-item lazy implementation is within spec, but unlikely to use multiple
cores efficiently.  Outside of performance requirements, if the algorithm
depends on which of these approaches is taken, it is erroneous.

=head2 Reduction operators

Any infix operator (except for non-associating operators)
can be surrounded by square brackets in term position to
create a list operator that reduces using that operation:

    [+] 1, 2, 3;      # 1 + 2 + 3 = 6
    my @a = (5,6);
    [*] @a;           # 5 * 6 = 30

As with all the metaoperators, space is not allowed inside a metatoken.

A reduction operator has the same precedence as a list prefix.  In fact,
a reduction operator really is a list prefix, and is invoked as one.
Hence, you can implement a reduction operator in one of two ways.  Either
you can write an explicit list operator:

    multi prefix:<[+]> (*@args) is default {
        my $accum = 0;
        while (@args) {
            $accum += @args.shift();
        }
        return $accum;
    }

or you can let the system autogenerate one for you based on the
corresponding infix operator, probably by priming:

    &prefix:<[*]> ::= &reduce.assuming(&infix:<*>, 1);
    &prefix:<[**]> ::= &reducerev.assuming(&infix:<**>);

If the reduction operator is defined separately from the infix operator,
it must associate the same way as the operator used:

    [-] 4, 3, 2;      # 4-3-2 = (4-3)-2 = -1
    [**] 4, 3, 2;     # 4**3**2 = 4**(3**2) = 262144

For list-associative operator (the ones with X in the precedence table), the
implementation must take into account the listiness of the arguments; that is,
if repeatedly applying a binary version of the operator would produce the
wrong results, then it cannot be implemented that way.  For instance:

    [^^] $a, $b, $c;  # means ($a ^^ $b ^^ $c), NOT (($a ^^ $b) ^^ $c)

For chain-associative operators (like C<< < >>), all arguments are taken
together, just as if you had written it out explicitly:

    [<] 1, 3, 5;      # 1 < 3 < 5

If fewer than two arguments are given, a dispatch is still attempted
with whatever arguments are given, and it is up to the receiver of that
dispatch to deal with fewer than two arguments.  Note that the default
list operator signature is the most general, so you are allowed to define
different ways to handle the one argument case depending on type:

    multi prefix:<[foo]> (Int $x) { 42 }
    multi prefix:<[foo]> (Str $x) { fail "Can't foo a single Str" }

However, the zero argument case cannot be defined this way, since there
is no type information to dispatch on.  Operators that wish to specify an
identity value should do so by specifying a multi variant that takes zero
arguments:

    multi prefix:<[foo]> () { 0 }

Among the builtin operators, C<[+]()> returns 0 and C<[*]()> returns 1,
for instance.

By default, if there is one argument, the built-in reduce operators
return that one argument.  However, this default doesn't make sense
for operators like C<< < >> that don't return the same type as they
take, so these kinds of operators overload the single-argument case
to return something more meaningful.  To be consistent with chaining
semantics, all the comparison operators return C<Bool::True> for 1 or 0 arguments.

You can also make a reduce operator of the comma operator.  This is just
the list operator form of the C<< circumfix:<[ ]> >> anonymous array composer:

    [1,2,3]     # make new Array: 1,2,3
    [,] 1,2,3   # same thing

Builtin reduce operators return the following identity values:

    [**]()      # 1     (arguably nonsensical)
    [*]()       # 1
    [/]()       # fail  (reduce is nonsensical)
    [%]()       # fail  (reduce is nonsensical)
    [x]()       # fail  (reduce is nonsensical)
    [xx]()      # fail  (reduce is nonsensical)
    [+&]()      # -1    (from +^0, the 2's complement in arbitrary precision)
    [+<]()      # fail  (reduce is nonsensical)
    [+>]()      # fail  (reduce is nonsensical)
    [~&]()      # fail  (sensical but 1's length indeterminate)
    [~<]()      # fail  (reduce is nonsensical)
    [~>]()      # fail  (reduce is nonsensical)
    [+]()       # 0
    [-]()       # 0
    [~]()       # ''
    [+|]()      # 0
    [+^]()      # 0
    [~|]()      # ''    (length indeterminate but 0's default)
    [~^]()      # ''    (length indeterminate but 0's default)
    [&]()       # all()
    [|]()       # any()
    [^]()       # one()
    [!==]()     # Bool::True    (also for 1 arg)
    [==]()      # Bool::True    (also for 1 arg)
    [before]()  # Bool::True    (also for 1 arg)
    [after]()   # Bool::True    (also for 1 arg)
    [<]()       # Bool::True    (also for 1 arg)
    [<=]()      # Bool::True    (also for 1 arg)
    [>]()       # Bool::True    (also for 1 arg)
    [>=]()      # Bool::True    (also for 1 arg)
    [~~]()      # Bool::True    (also for 1 arg)
    [!~~]()     # Bool::True    (also for 1 arg)
    [eq]()      # Bool::True    (also for 1 arg)
    [!eq]()     # Bool::True    (also for 1 arg)
    [lt]()      # Bool::True    (also for 1 arg)
    [le]()      # Bool::True    (also for 1 arg)
    [gt]()      # Bool::True    (also for 1 arg)
    [ge]()      # Bool::True    (also for 1 arg)
    [=:=]()     # Bool::True    (also for 1 arg)
    [!=:=]()    # Bool::True    (also for 1 arg)
    [===]()     # Bool::True    (also for 1 arg)
    [!===]()    # Bool::True    (also for 1 arg)
    [eqv]()     # Bool::True    (also for 1 arg)
    [!eqv]()    # Bool::True    (also for 1 arg)
    [&&]()      # Bool::True
    [||]()      # Bool::False
    [^^]()      # Bool::False
    [//]()      # Any
    [min]()     # +Inf
    [max]()     # -Inf
    [=]()       # Nil    (same for all assignment operators)
    [,]()       # []
    [Z]()       # []

User-defined operators may define their own identity values, but
there is no explicit identity property.  The value is implicit in the
behavior of the 0-arg reduce, so mathematical code wishing to find
the identity value for an operation can call C<prefix:["[$opname]"]()>
to discover it.

To call some other non-infix function as a reduce operator, you may
define an alias in infix form.  The infix form will parse the right
argument as an item even if the aliased function would have parsed it
as a list:

    &infix:<dehash> ::= postcircumfix:<{ }>;
    $x = [dehash] $a,'foo','bar';  # $a<foo><bar>, not $a<foo bar>

Alternately, just define your own C<< prefix:<[dehash]> >> routine.

Note that, because a reduce is a list operator, the argument list is
evaluated in list context.  Therefore the following would be incorrect:

    $x = [dehash] %a,'foo','bar';

You'd instead have to say one of:

    $x = [dehash] \%a,'foo','bar';
    $x = [dehash] %a<foo>,'bar';

On the plus side, this works without a star:

    @args = (\%a,'foo','bar');
    $x = [dehash] @args;

Likewise, from the fact that list context flattens inner arrays and
lists, it follows that a reduced assignment does no special syntactic
dwimmery, and hence only scalar assignments are supported.  Therefore

    [=] $x, @y, $z, 0
    [+=] $x, @y, $z, 1

are equivalent to

    $x = @y[0] = @y[1] = @y[2] ... @y[*-1] = $z = 0
    $x += @y[0] += @y[1] += @y[2] ... @y[*-1] += $z += 1

rather than

    $x = @y = $z = 0;
    $x += @y += $z += 1;

(And, in fact, the latter are already easy to express anyway,
and more obviously nonsensical.)

Similarly, list-associative operators that have the thunk-izing characteristics of
macros (such as short-circuit operators) lose those macro-like characteristics.
You can say

    [||] a(), b(), c(), d()

to return the first true result, but the evaluation of the list is controlled
by the semantics of the list, not the semantics of C<||>.  The operator still
short-circuits, but only in the sense that it does not need to examine all
the values returned by the list.  This is still quite useful for performance,
especially if the list could be infinite.

Most reduce operators return a simple scalar value, and hence do not care
whether they are evaluated in item or list context.  However, as with
other list operators and functions, a reduce operator may return a list
that will automatically be interpolated into list context, so you may
use it on infix operators that operate over lists as well as scalars:

    my ($min, $max) = [minmax] @minmaxpairs;

A variant of the reduction metaoperator is pretty much guaranteed
to produce a list; to lazily generate all intermediate results along
with the final result, you can backslash the operator:

    say [\+] 1..*  #  (1, 3, 6, 10, 15, ...)

The visual picture of a triangle is not accidental.  To produce a triangular
list of lists, you can use a "triangular comma":

    [\,] 1..5
    [1],
    [1,2],
    [1,2,3],
    [1,2,3,4],
    [1,2,3,4,5]

If there is ambiguity between a triangular reduce and an infix operator
beginning with backslash, the infix operator is chosen, and an extra backslash
indicates the corresponding triangular reduce.  As a consequence, defining an
infix operator beginning with backslash, C<< infix:<\x> >> say, will make it
impossible to write certain triangular reduction operators, since C<[\x]> would
mean the normal reduction of C<< infix:<\x> >> operator, not the triangular
reduction of C<< infix:<x> >>.  This is deemed to be an insignificant problem.

Triangular reductions of chaining operators always consist of one or
more C<True> values followed by 0 or more C<False> values.

=head2 Cross operators

The cross metaoperator, C<X>, may be followed by any infix operator.
It applies the modified operator across all groupings of its list
arguments as returned by the ordinary C<< infix:<X> >> operator.
All generated cross operators are of list infix precedence, and are
list associative.

The string concatenating form is:

    <a b> X~ 1,2           #  'a1', 'a2', 'b1', 'b2'

The C<X~> operator desugars to:

    (<a b>; 1,2).crosswith(&[~])

which in turn means

    (<a b>; 1,2).cross.lol.map { .reduce(&[~]) }

Note that

    <a b> X~ 1,2 X+ 3,4

could mean something like

    (<a b>; 1,2; 3,4).cross.lol.map { .reduce({$^a ~ $^b + $^c}) }

but it is currently illegal as a non-identical list associative
operator, which is considered non-associative.  You can, however,
always use parens to be explicit:

    <a b> X~ (1,2 X+ 3,4)

The list concatenating form, C<X,>, when used like this:

    <a b> X, 1,2 X, <x y>

produces

    ('a', 1, 'x'),
    ('a', 1, 'y'),
    ('a', 2, 'x'),
    ('a', 2, 'y'),
    ('b', 1, 'x'),
    ('b', 1, 'y'),
    ('b', 2, 'x'),
    ('b', 2, 'y')

The C<X,> operator is perhaps more clearly written as C<X[,]>.  However,
this list form is common enough to have a shortcut, the ordinary infix
C<X> operator described earlier.

For the general form, any existing, non-mutating infix operator
may be used.

    1,2 X* 3,4               # 3,4,6,8

(Note that C<< <== >> and C<< ==> >> are considered mutating, as well as
all assignment operators.)

If the underlying operator is non-associating, so is the cross operator:

    @a Xcmp @b Xcmp @c       # ILLEGAL
    @a Xeq @b Xeq @c         # ok

In fact, though the C<X> operators are all list associative
syntactically, the underlying operator is always applied with its
own associativity, just as the corresponding reduce operator would do.

Note that only the first term of an C<X> operator may reasonably be
an infinite list.

All lists are assumed to be flat; multidimensional lists are
handled by treating the first dimension as the only dimension.

=head2 Zip operators

The zip metaoperator, C<Z>, may be followed by any infix operator.
It applies the modified operator across all groupings of its list
arguments as returned by the ordinary C<< infix:<Z> >> operator.
All generated zip operators are of list infix precedence, and are
list associative.

The string concatenating form is:

    <a b> Z~ 1,2           #  'a1', 'b2'

The C<Z~> operator desugars to:

    (<a b>; 1,2).zipwith(&[~])

which in turn means

    (<a b>; 1,2).zip.lol.map: { .reduce(&[~]) }

Note that

    <a b> Z~ 1,2 Z+ 3,4

could mean something like

    (<a b>; 1,2; 3,4).zip.lol.map: { .reduce({$^a ~ $^b + $^c}) }

but it is currently illegal as a non-identical list associative
operator, which is considered non-associative.  You can, however,
always use parens to be explicit:

    <a b> Z~ (1,2 Z+ 3,4)

[Conjecture: another approach would involve giving C<X> and C<Z> metaoperators a
subprecedence within listop precedence corresponding to the original
operator's precedence, so that C<Z~> and C<Z+> actually have different
precedences within listop precedence.  Then the above would parse as if
you'd said C<< <a b> Z~ ( 1,2 Z+ 3,4> ) >>, but the lists would still
parse at list infix precedence, with comma tighter than the zips.
(This would actually be fairly trivial to implement, given how we
represent our precedence as strings.)  Also, though it's complicated to
explain, subprecedence within C<Z> might be exactly what the naive user expects.]

The list concatenating form, C<Z,>, when used like this:

    <a b> Z, 1,2 Z, <x y>

produces

    ('a', 1, 'x'),
    ('b', 2, 'y')

The C<Z,> operator is perhaps more clearly written as C<Z[,]>.  However,
this list form is common enough to have a shortcut, the ordinary infix
C<Z> operator described earlier.

For the general form, any existing, non-mutating infix operator
may be used.

    1,2 Z* 3,4               # 3,8

(Note that C<< <== >> and C<< ==> >> are considered mutating, as well as
all assignment operators.)

If the underlying operator is non-associating, so is the cross operator:

    @a Zcmp @b Zcmp @c       # ILLEGAL
    @a Zeq @b Zeq @c         # ok

In fact, though the C<Z> operators are all list associative
syntactically, the underlying operator is always applied with its
own associativity, just as the corresponding reduce operator would do.

Note that, unlike the C<X> operator, all the terms of a C<Z> operator
may reasonably be infinite lists, since zipping is lazy.

All lists are assumed to be flat; multidimensional lists are
handled by treating the first dimension as the only dimension.

=head2 Sequential operators

The sequence metaoperator, C<S>, may be followed by any non-fiddly infix operator.
It suppresses any explicit or implicit parallelism, and prevents the optimizer
from reordering the operand evaluations.  The 'S' can be thought of as standing
for Sequential, Serial, Synchronous, Short-circuit, Single-thread, and Safe.
Among other things.  In particular, we can have:

    a S& b S& c         short-circuited AND junction
    a S| b S| c         short-circuited OR junction
    a S^ b S^ c         short-circuited XOR junction
    a S»op« b           single-threaded hyperop
    a SX* b             single-threaded X*
    a SX[*] b           single-threaded X*
    a S[X*] b           single-threaded X*
    a S+ b              suppress arg reordering by ignorant optimizer 

This metaoperator has the same precedence and associativity as its base operator.
The compiler is free to discard any C<S> metaoperator that is provably redundant,
such as the one in C<S||>.  The compiler is free to intuit an C<S> on any
operator involving known volatile operands where that does not otherwise
change the semantics of the operator.

[Conjectural: since metaoperators are notionally applied from inside
to outside, the semantics of serializing and reversing depends on
the order of the metaoperators:

    a SR/ b             evaluates b, then a, then does b/a
    a RS/ b             evaluates a, then b, then does b/a
    a RSR/ b            evaluates b, then a, then does a/b

...maybe. Can argue it all the other way too...]

=head2 Nesting of metaoperators

Anywhere you may use an ordinary infix operator, you may use the infix operator enclosed in square brackets
with the same meaning.  (No whitespace is allowed.)  You may therefore use square brackets
within a metatoken to disambiguate sequences that might
otherwise be misinterpreted, or to force a particular order
of application when there are multiple metaoperators in the metatoken:

    @a [X+]= @b
    @a X[+=] @b

Since metatokens may never be disambiguated with internal whitespace,
use of brackets is especially useful when the operator and its
associated metaoperator share characters that would be confusing to the
reader, even if not to the compiler:

    @a >>>>> $b        # huh?
    @a >>[>]>> $b      # oh yeah

=head2 Turning an infix operator into a noun

Any infix function may be referred to as a noun either by the normal long
form or a short form using square brackets directly after the C<&> sigil:

    &infix:<+>
    &[+]

This is convenient for function application:

    1, 1, &[+] ... *       # fibonacci sequence
    sort &[Rleg], @list    # reverse sort as strings

The C<&[op]> form always refers to a binary function of the operator,
even if it is underlyingly defined as a variadic list-associative operator.

There is no corresponding form for unary operators, but those may
usually be constructed by applying an operator to C<*>:

    sort -*, @list        # sort reversed numerically

=head2 Turning a binary function into an infix

By using the noun form of a binary function inside square brackets,
it is possible to turn any function that accepts at least two arguments
into an infix operator.  For instance:

    $y [&atan2] $x        # same as atan2($y, $x)

By itself this may seem relatively useless, but note that it allows
composition of normal 2-arg functions with all the infix metaoperators.
Since it is primarily intended for composition with metaoperators,
this form always assumes a binary function, even if the function could
accept more arguments; functions that accept more than 2 arguments do
not thereby accept multiple arguments on the right side.  You must use
the normal functional form to pass three or more positional arguments.

This form of operator is parsed with a precedence of addition.
A C<$> is acceptable in place of C<&>, but in either case the
next character must be either alphabetic or a left parenthesis.
Otherwise a normal infix operator starting with that character will
be assumed.  Hence C<[&&]> parses as a form of the C<&&> operator.

=head1 Declarators

The list of variable declarators has expanded from C<my> and C<our>
to include:

    my $foo             # ordinary lexically scoped variable
    our $foo            # lexically scoped alias to package variable
    has $foo            # object attribute
    state $foo          # persistent lexical (cloned with closures)

Variable declarators such as C<my> now take a I<signature> as their
argument.  (The syntax of function signatures is described more fully in L<S06>.)

The parentheses around the signature may be omitted for a
simple declaration that declares a single variable, along with its
associated type, traits and the initializer:

    my Dog $foo is woof = 123;    # okay: initializes $foo to 123
    my (Dog $foo is woof = 123);  # same thing (with explicit parens)
    my :(Dog $foo is woof = 123); # same thing (full Signature form)

The C<constant> declarator can declare either variables or names
as compile-time constants:

    constant $foo = 1;      # compile-time constant variable
    constant bar = 2;       # compile-time constant symbol

Because it can declare names in "type" space, the C<constant>
declarator may not declare using the signature, which would be
ambiguous.

Each declarator can take an initializer following an equals
sign (which should not be confused with a normal assignment, because
the timing of the initialization depends on the natural lifetime of the
container, which in turn depends on which declarator you use).

    my $foo = 1;         # happens at the same time as normal assignment
    our $foo = 1;        # happens at INIT time
    has $foo = 1;        # happens at BUILD time
    state $foo = 1;      # happens at START time
    constant $foo = 1;   # happens at BEGIN time

(Note that the semantics of C<our> are different from Perl 5, where the
initialization happens at the same time as a C<my>.  To get the same
effect in Perl 6 you'd have to say "C<(our $foo) = 1;>" instead.)

If you do not initialize a container, it starts out undefined at the
beginning of its natural lifetime.  (In other words, you can't use
the old Perl 5 trick of "C<my $foo if 0>" to get a static variable,
because a C<my> variable starts out uninitialized every time through
in Perl 6 rather than retaining its previous value.)  Native integer
containers that do not support the concept of undefined should be
initialized to 0 instead.  (Native floating-point containers are
by default initialized to C<NaN>.)  Typed object containers start
out containing an undefined type object of the correct type.

List-context pseudo-assignment is supported for simple declarations but
not for signature defaults:

    my @foo = 1,2,3;      # okay: initializes @foo to (1,2,3)
    my (@foo = 1,2,3);    # wrong: 2 and 3 are not variable names

When parentheses are omitted, you may use any infix assignment operator
instead of C<=> as the initializer.  In that case, the left hand side of
the infix operator will be the variable's prototype object:

    my Dog $fido .= new;      # okay: a Dog object
    my Dog $fido = Dog.new;   # same thing
    my Dog $fido = $fido.new; # wrong: invalid self-reference
    my (Dog $fido .= new);    # wrong: cannot use .= inside signature

Note that very few mutating operators make sense on a type object, however,
since type objects are a kind of undefined object.  (Those operators with
an identity value are an exception, as noted above.)

Parentheses must always be used when declaring multiple parameters:

    my $a;                  # okay
    my ($b, $c);            # okay
    my ($b = 1, $c = 2);    # okay - "my" initializers assign at runtime
    my $b, $c;              # wrong: "Use of undeclared variable: $c"

Types occurring between the declarator and the signature are distributed into
each variable:

    my Dog ($b, $c);
    my (Dog $b, Dog $c);    # same thing

[XXX the following probably belongs in L<S06>.]
The syntax for constructing a C<Signature> object when the parser isn't already
expecting one is:

    :(Dog $a, *@c)

This might be used like this:

    my $sig = :(Dog $a, *@c);

Signatures are expected after declarators such as C<my>, C<sub>, C<method>,
C<rule>, etc.  In such declarators the colon may be omitted.  But it's
also legal to use it:

    my :($b, $c);               # okay
    sub foo :($a,$b) {...}      # okay

The C<< -> >> "pointy block" token also introduces a signature, but
in this case you must omit both the colon and the parens.  For instance,
if you're defining the "loop variable" of a loop block:

    for @dogpound -> Dog $fido { ... }

If a signature is assigned to (whether declared or colon form), the
signature is converted to a list of lvalue variables and the ordinary
rules of assignment apply, except that the evaluation of the right
side and the assignment happens at time determined by the declarator.
(With C<my> this is always when an ordinary assignment would happen.)
If the signature is too complicated to convert to an assignment,
a compile-time error occurs.  Assignment to a signature makes the
same item/list distinction as ordinary assignment, so

    my $a = foo();      # foo in item context
    my ($a) = foo();    # foo in list context

If a signature is bound to an argument list, then the binding of the
arguments proceeds as if the signature were the formal parameters for
a function, except that, unlike in a function call, the parameters
are bound C<rw> by default rather than C<readonly>.  See Binding above.

Note that C<temp> and C<let> are I<not> variable declarators, because
their effects only take place at runtime.  Therefore, they take an ordinary
lvalue object as their argument.  See L<S04> for more details.

There are a number of other declarators that are not variable
declarators.  These include both type declarators:

    package Foo
    module Foo
    class Foo
    role Foo
    subset Foo
    enum Foo
    constant Foo

and code declarators:

    sub foo
    method foo
    submethod foo
    multi foo
    proto foo
    macro foo
    quote qX
    regex foo
    rule foo
    token foo

These all have their uses and are explained in subsequent Synopses.

Note that since C<constant> is parsed as a type declarator (essentially
declaring a type with a single value), it can actually take a scope
declarator in front:

    my constant companion = 'Fido';
    has constant $.pi = 22/7;
    state constant $latch = snapshot(); # careful with this!

However, the constant declarator is intended to create values the
compiler can inline, so it always evaluates its value at BEGIN time.
Thus, while the extra scope declarator may say where the value is
stored and when that storage is initialized, it cannot change the value
of that from instance to instance.  In general, if you want something
that doesn't vary over the normal lifetime of a scope declarator,
initialize it to a readonly value using C<::=> rather than declaring
it as a constant.  Then each time the scope declarator is used,
it can initialize to a different readonly value:

    state $latch ::= snapshot();  # each clone gets its own value of $latch

=head1 Argument List Interpolating

Perl 5 forced interpolation of a function's argument list by use of
the C<&> prefix.  That option is no longer available in Perl 6, so
instead the C<|> prefix operator serves as an
interpolator, by casting its operand to a C<Capture> object
and inserting the capture's parts into the current argument list.
This operator can be used to interpolate an C<Array> or C<Hash>
into the current call, as positional and named arguments respectively.

Note that the resulting arguments still must comply with the subroutine's
signature, but the presence of C<|> defers that test until run time for
that argument (and for any subsequent arguments):

    my $args = \(@foo, @bar);
    push |$args;

is equivalent to:

    push @foo, @bar;

However,

    my $args = \(@foo: @bar);
    push |$args;

is instead equivalent to:

    @foo.push(@bar);

C<|> does not turn its argument into an C<Array>, but instead directly
converts its argument into a C<Capture>:

    my @args = \$x, 1, 2, 3;
    say |@args;     # say(\$x, 1, 2, 3);

Because of this, C<|%args> always produces named arguments, and
C<|@args> always produces positional arguments.

In list context, a C<Scalar> holding an C<Array> object does not flatten.  Hence

    $bar = @bar;
    @foo.push($bar);

merely pushes a single C<Array> object onto C<@foo>.  You can
explicitly flatten it in one of these ways:

    @foo.push(@$bar);
    @foo.push($bar[]);
    @foo.push(|$bar);

Those three forms work because the slurpy array in C<push>'s signature
flattens the C<Array> object into a list argument.

Note that the first two forms also allow you to specify list context on
assignment:

    @$bar = 1,2,3;
    $bar[] = 1,2,3;

For long expressions that need to be cast to an array lvalue, the
second form can keep the "arrayness" of the lvalue close to the
assignment operator:

    $foo.bar.baz.bletch.whatever.attr[] = 1,2,3;

The empty C<[]> and C<.[]> postfix operators are interpreted as a
zero-dimensional subscript returning the entire array, not as a one-dimensional
null slice returning no elements.  Likewise for C<{}> and C<.{}> on hashes,
as well as the C<< <> >>, C<< .<> >>, C<«»>, and C<.«»> constant and
interpolating slice subscripting forms.

The C<|> operator interpolates lazily for C<Array> and C<Range> objects.
To get an immediate interpolation like Perl 5 does, add the C<eager> list
operator:

    func(|(1..Inf));       # works fine
    func(|eager 1..Inf);   # never terminates (well, actually...)

To interpolate a function's return value, you can say:

    push |func();

Within such an argument list, function return values are
automatically exploded into their various parts, as if you'd said:

    my $capture = \(func());
    push $$capture: @$capture, %$capture;

or some such.  The C<|> then handles the various zones appropriately
depending on the context.  An invocant only makes sense as the first
argument to the outer function call.  An invocant inserted anywhere
else just becomes a positional argument at the front of its list,
as if its colon changed back to a comma.

If you already have a capture variable, you can interpolate all of
its bits at once using the C<< prefix:<|> >> operator:

    my (|$capture) := func();
    push |$capture;

=head1 Traversing arrays in parallel

In order to support parallel iteration over multiple arrays, Perl 6
has a C<zip> function that builds a list of C<Seq> objects from the
elements of two or more arrays.  In ordinary list context this behaves
as a list of C<Captures> and automatically flattens.

    for zip(@names; @codes) -> $name, $zip {
        print "Name: $name;   Zip code: $zip\n";
    }

C<zip> has an infix synonym, the C<Z> operator.

In an explicitly multidimensional list context, however, the sequences
turn into subarrays, and each element would then have to be unpacked
by the signature:

    for lol(zip(@names; @codes)) -> [$name, $zip] {
        print "Name: $name;   Zip code: $zip\n";
    }

By default the C<zip> function reads to the end of the shortest list,
but a short list may always be extended arbitrarily by putting C<*>
after the final value, which replicates the final value as many times
as necessary.  If instead of supplying a default value for short lists,
you just wish to skip missing entries, use C<roundrobin> instead:

    for roundrobin(@queue1; @queue2; @queue3) -> $next {
        ...
    }

=head1 Minimal whitespace DWIMmery

Whitespace is no longer allowed before the opening bracket of an array
or hash subscript, or the opening parenthesis of an argument list.  That is:

    @deadbeef[$x]         # okay
    @a       [$b]         # WRONG
    %monsters{'cookie'}   # okay
    %people  {'john'}     # WRONG
    saymewant('cookie')   # okay
    mewant   ('cookie')   # WRONG

One of the several useful side-effects of this restriction is that
parentheses are no longer required around the condition of control
constructs:

    if $value eq $target {
        print "Bullseye!";
    }
    while $i < 10 { $i++ }

It is, however, still possible to align subscripts and other postfix
operators by explicitly using the I<unspace> syntax (see L<S02>):

     %squirrels{'fluffy'} = Squirrel.new;
     %monsters.{'cookie'} = Monster.new;
     %beatles\.{'ringo'}  = Beatle.new;
     %people\ .{'john'}   = Person.new;

Whitespace is in general required between any keyword and any opening
bracket that is I<not> introducing a subscript or function arguments.
Any keyword followed directly by parentheses will be taken as a
function call instead.

    if $a == 1 { say "yes" }            # preferred syntax
    if ($a == 1) { say "yes" }          # P5-ish if construct
    if($a,$b,$c)                        # if function call

It is possible for C<if()> to also invoke a macro call, but if so, it's a
C<< prefix:<if> >> macro rather than a C<< statement_control:<if> >> macro.

=head1 Sequence points

Certain operators are guaranteed to provide I<sequence points>.
Sequence points are guaranteed whenever some thunk (a lazy chunk of code) is
conditionally evaluated based on the result of some other evaluation,
so the short-circuit and conditional operators all provide sequence
points.

Certain other operators guarantee the I<absence> of sequence points,
including junctional operators, hyperoperators, and feed operators.
These operators promise the compiler that you consider the bits of
code not to be dependent on each other so that they can operate
in parallel if they like.

A large number of operators (such as C<+>) are stuck in the middle,
and may exhibit sequential behavior today, but might not tomorrow.
A program that relies on either sequential or parallel behavior for one
of these operators is erroneous.  As we get more feedback from people
writing parallelizing optimizers, we reserve the right to classify
various of the unclassified operators into one of the two specified
sets.  (We need to give these three sets of operators good names.)


=for vim:set expandtab sw=4: