TITLE

Synopsis 3: Perl 6 Operators

AUTHORS

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

VERSION

    Created: 8 Mar 2004

    Last Modified: 23 Sep 2010
    Version: 220

Overview

For a summary of the changes from Perl 5, see "Changes to Perl 5 operators".

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
    L  Additive          + - +| +^ ~| ~^ ?| ?^
    L  Replication       x xx
    X  Concatenation     ~
    X  Junctive and      &
    X  Junctive or       | ^
    L  Named unary       sleep abs sin 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 ... E
    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 ! 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 X cross operator and the 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.

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 S02 for longer descriptions of various terms. Here are some examples.

Int literal
```
    42
```
Num literal
```
    3.14
```
Non-interpolating Str literal
```
    '$100'
```
Interpolating Str literal
```
    "Answer = $answer\n"
```
Generalized Str literal
```
    q["$100"]
    qq["$answer"]
```

Heredoc

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

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.)
Hash composer
```
    { }
    { a => 42 }
```
Inside must be either empty, or a single list starting with a pair or a hash, otherwise you must use hash() or %() instead.
Closure
```
    { ... }
```
When found where a statement is expected, executes immediately. Otherwise always defers evaluation of the inside scope.
Capture composer
```
    \(@a,$b,%c)
```
An abstraction representing an argument list that doesn't yet know its context.

Sigiled variables

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

Sigils as contextualizer functions
```
    $()
    @()
    %()
    &()
```
Regexes in quote-like notation
```
    /abc/
    rx:i[abc]
    s/foo/bar/
```
Transliterations
```
    tr/a..z/A..Z/
```
Note ranges use .. rather than -.
Type names
```
    Num
    ::Some::Package
```
Subexpressions circumfixed by parentheses
```
    (1+2)
```
Parentheses are parsed on the inside as a semicolon-separated list of statements, which (unlike the statements in a block) returns the results of all the statements concatenated together as a List of Parcel. How that is subsequently treated depends on its eventual binding.
Function call with parens:
```
    a(1)
```
In term position, any identifier followed immediately by a parenthesized expression is always parsed as a term representing a function call even if that identifier also has a prefix meaning, so you never have to worry about precedence in that case. Hence:
```
    not($x) + 1         # means (not $x) + 1
    abs($x) + 1         # means (abs $x) + 1
```
Pair composers
```
    :limit(5)
    :!verbose
```
Signature literal
```
    :(Dog $self:)
```
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), .meth is a syntax error. (The .=meth form is allowed there only because there is a special .= infix assignment operator that is equivalent in semantics to the method call form but that allows whitespace between the = and the method name.)
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.

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 S12 for more discussion of single dispatch method calls.

Standard single-dispatch method calls
```
    $obj.meth
```
Variants of standard single-dispatch method call
```
    $obj.+meth
    $obj.?meth
    $obj.*meth
```
In addition to the ordinary . method invocation, there are variants .*, .?, and .+ to control how multiple related methods of the same name are handled.
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.
Mutating method call
```
    $obj.=meth
```
The .= operator does inplace modification of the object on the left.
Meta-method call
```
    $obj.^meth
```
The .^ operator calls a class metamethod; foo.^bar is short for foo.HOW.bar.
Method-like postcircumfixes
```
    $routine.()
    $array.[]
    $hash.{}
    $hash.<>
    $hash.«»
```
The dotless forms of these have exactly the same precedences.
Dotted form of any other postfix operator
```
    $x.++         # postfix:<++>($x)
```
Dotted postfix form of any other prefix operator
```
    $x.:<++>       # prefix:<++>($x)
```
There is specifically no infix:<.> operator, so
```
    $foo . $bar
```
will always result in a compile-time error indicating the user should use infix:<~> instead. This is to catch an error likely to be made by Perl 5 programmers learning Perl 6.

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 "Sequence points".

As with all postfix operators in Perl 6, no space is allowed between a term and its postfix. See 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 Scalar container) is allowed to mutate itself into an Int in order to support the common idiom:

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

Increment of a 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 <!after '.'> <rangechar>+ is incremented regardless of what comes before it.

The <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 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-Str types are defined in terms of the .succ and .pred methods on the type of object in the 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 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 %seen hash is actually a KeySet, in which case decrement actually deletes it from the KeySet.

Autoincrement prefix:<++> or postfix:<++> operator
```
    $x++
    ++$x;
```
Autodecrement prefix:<--> or postfix:<--> operator
```
    $x--
    --$x
```

Exponentiation precedence

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 Int**UInt is always exact, since Int supports arbitrary precision. Rat**UInt is accurate to the precision of 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 Str via Cool is likely to do the right thing, however.)

Symbolic unary precedence

prefix:<?>, boolean context
```
    ?$x
```
Evaluates the expression as a boolean and returns True if expression is true or False otherwise. See "so" below for a low-precedence alternative.
prefix:<!>, boolean negation
```
    !$x
```
Returns the opposite of what ? would. See "not" below for a low-precedence alternative.
prefix:<+>, numeric context
```
    +$x
```
Unlike in Perl 5, where + is a no-op, this operator coerces to numeric context in Perl 6. (It coerces only the value, not the original variable.) For values that do not already do the Numeric role, the narrowest appropriate type of Int, Rat, Num, or Complex will be returned; however, string containing two integers separated by a / will be returned as a Rat (or a FatRat if the denominator overflows an int64). Exponential notation and radix notations are recognized.
prefix:<->, numeric negation
```
    -$x
```
Coerces to numeric and returns the arithmetic negation of the resulting number.
prefix:<~>, string context
```
    ~$x
```
Coerces the value to a string, if it does not already do the Stringy role. (It only coerces the value, not the original variable.) As with numerics, it is guaranteed only to coerce to something Stringy, not necessarily Str.
prefix:<|>, flatten object into arglist
```
    | $capture
```
Interpolates the contents of the Capture (or 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.
prefix:<||>, flatten object into semicolon list
```
    || $parcel
```
Interpolates the elements of the Parcel (or any other ordered value) into the current argument list as if they had been specified literally, separated by semicolons, that is, at the multi-dimensional level. It is an error to use this operator outside of a lol context; in other words it must be bound into a ** (slice) parameter rather than a * (slurpy) parameter.
prefix:<+^>, numeric bitwise negation
```
    +^$x
```
Coerces to Int and then does bitwise negation on the number, returning an Int. (In order not to have to represent an infinitude of 1's, represents that value as some negative in 2's complement form.)
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).
prefix:<?^>, boolean negation
```
    ?^$x
```
Coerces to boolean and then flips the bit. (Same as !.)
prefix:<^>, upto operator
```
    ^$limit
```
Constructs a range of 0 ..^ +$limit or locates a metaclass as a shortcut for $limit.HOW. See "Range and RangeIter semantics".

Multiplicative precedence

infix:<*>
```
    $x*$y
```
Multiplication, resulting in wider type of the two.
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 type, the operator returns the corresponding Rat value.

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

Otherwise, if either operand is of Num type, converts both operands to Num and does division returning Num. If the denominator is zero, returns an object representing either +Inf, NaN, or -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.)
infix:<div>, integer division
```
    $numerator div $denominator
```
Dispatches to the 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, div should give the same result as
```
    $x div $y == floor($x/$y);
```
but the return value should be the same type as $x.
infix:<%>, modulo
```
    $x % $y
```
If necessary, coerces non-numeric arguments to an appropriate Numeric type, then calculates the remainder, which is defines as:
```
    $x % $y == $x - floor($x / $y) * $y
```
infix:<%%>, is divisible by
```
    $x %% $y
```
Performs a % and then tests the result for 0, returning Bool::True if the $x is evenly divisible by $y, and Bool::False otherwise.

You may use !%% to mean "not divisible by", though % itself generally has the same effect.
infix:<mod>, integer modulo
```
    $x mod $y
```
Dispatches to the 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
```
infix:['+&'], numeric bitwise and
```
    $x +& $y
```
Converts both arguments to Int and does a boolean AND between corresponding bits of each integer, returning an Int result.
infix:['+<'], numeric shift left
```
    $integer +< $bits
```
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 :signed or :!signed adverb.
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).
infix:['~<'], buffer bitwise shift left
```
    $buf ~< $bits
```
infix:['~>'], buffer bitwise shift right
```
    $buf ~> $bits
```
Sign extension is not done by default but may be enabled with a :signed adverb.
infix:<?&>, boolean and
```
    $x ?& $y
```
Converts both arguments to type Bool and then ANDs those, returning the resulting Bool.

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

Additive precedence

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 suitably "large" numeric type to hold the result. Do not overload the + 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.
infix:<->, numeric subtraction
```
    $x - $y
```
infix:<+|>, numeric bitwise inclusive or
```
    $x +| $y
```
Converts both arguments to Int and does a boolean OR between corresponding bits of each integer, returning an Int result.
infix:<+^> numeric bitwise exclusive or
```
    $x +^ $y
```
Converts both arguments to Int and does a boolean XOR between corresponding bits of each integer, returning an Int result.
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. 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).
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).
infix:<?|>, boolean inclusive or
```
    $x ?| $y
```
Converts both arguments to type Bool and then ORs those, returning the resulting Bool.
infix:<?^> boolean exclusive or
```
    $x ?^ $y
```
Converts both arguments to type Bool and then XORs those, returning the resulting Bool.

Replication

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 * because Perl 6 does not support infinite strings. (At least, not yet...) Note, however, that an infinite string may someday be emulated with cat($string xx *), in which case $string x * may be a shorthand for that.
infix:<xx>, list replication
```
    @list xx $count
```
Evaluates the left argument in list context, replicates the resulting Parcel value the number of times specified by the right argument and returns the result as a list of 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, (). If the count is *, returns an infinite list (lazily, since lists are lazy by default).

Concatenation

infix:<~>, string/buffer concatenation
```
    $x ~ $y
```

Junctive and (all) precedence

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 S metaoperator for force sequential evaluation, which will construct a list of ANDed patterns with the same semantics as 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
```

Junctive or (any) precedence

infix:<|>, any() 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 S metaoperator for force sequential evaluation, which will construct a list of ORed patterns with the same semantics as 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
```
infix:<^>, one() operator
```
    $a ^ $b ^ $c ...
```
The S^ variant guarantees left-to-right evaluation, and in boolean context short-circuits to false if it sees a second match.

Named unary precedence

Functions of one argument

    sleep
    abs
    sin
    ...         # see S29 Functions

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

There is no unary rand prefix in Perl 6, though there is a .rand method call and an argumentless rand term. There is no unary int prefix either; you must use a typecast to a type such as Int or 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 int is a type name now.

prefix:<int>

Deprecated, use the Int() coercion or the floor function.
prefix:<sleep>

Coerces to an appropriate Real type, then suspends the current thread of execution for the specified number of seconds, which may be fractional. Remember that although a Rat is capable of attosecond precision, your computer is probably not capable of attosecond accuracy.
prefix:<abs>

Returns the absolute value of the specified argument.

Nonchaining binary precedence

infix:<but>
```
    $value but Mixin
```
infix:<does>
```
    $object does Mixin
```
Sort comparisons
```
    $num1 <=> $num2
    $str1 leg $str2
    $obj1 cmp $obj2
```
These operators compare their operands using numeric, string, or eqv semantics respectively, and depending on the order return one of Order::Increase, Order::Same, or Order::Decrease (which numerify to -1, 0, or +1). See "Comparison semantics".
Range object constructor
```
    $min .. $max
    $min ^.. $max
    $min ..^ $max
    $min ^..^ $max
```
Constructs Range objects, optionally excluding one or both endpoints. See "Range and RangeIter semantics".

Chaining binary precedence

All operators on this precedence level may be chained; see "Chained comparisons". They all return a boolean value.

infix:<==> etc.
```
    == != < <= > >=
```
As in Perl 5, converts to Num before comparison. != is short for !==.
infix:<eq> etc.
```
    eq ne lt le gt ge
```
As in Perl 5, converts to Str before comparison. ne is short for !eq.
Generic ordering
```
    $a before $b
    $a after $b
```
Smart match
```
    $obj ~~ $pattern
```
Perl 5's =~ becomes the "smart match" operator ~~, with an extended set of semantics. See "Smart matching" for details.

To catch "brainos", the Perl 6 parser defines an infix:<=~> operator which always fails at compile time with a message directing the user to use ~~ or ~= (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 !~~.
Container identity
```
    VAR($a) =:= VAR($b)
```
See "Comparison semantics".
Value identity
```
    $x === $y
```
For objects that are not value types, their identities are their values. (Identity is returned by the .WHICH metamethod.) The actual contents of the objects are ignored. These semantics are those used by hashes that allow objects for keys. See also "Comparison semantics".

Note that === is defined with an (Any,Any) signature, and therefore autothreads over junctions; hence it cannot be used to determine if two objects are the same, if either or both of them are junctions. However, since .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
```
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 "Comparison semantics".

Note that 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 context forces junction collapse.)

Negated relational operators

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

See "Negated relational operators".

Tight and precedence

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 (). See and below for low-precedence version.

Tight or precedence

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 (). See or below for low-precedence version.
infix:<^^>, short-circuit exclusive-or
```
    $a ^^ $b ^^ $c ...
```
Returns the true argument if there is one (and only one). Returns Bool::False if all arguments are false or if more than one argument is true. In list context forces a false return to mean (). See 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.
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 (). See orelse below for a similar but not identical low-precedence version.
Minimum and maximum
```
    $a min $b min $c ...
    $a max $b max $c ...
```
These return the minimum or maximum value. See also the minmax listop.

Not all types can support the concept of infinity. Therefore any value of any type may be compared with +Inf or -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 +Inf and -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
```

Conditional operator precedence

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 =.
```
    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 2 to $x (because ($x = 1) is a valid lvalue).

And in any case, repeating the $x forces you to declare it earlier. The best don't-repeat-yourself solution is simply:
```
    my $x = hmm() ?? 1 !! 2;          # much better
```
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 ?? !! instead.

Flipflop ranges

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

Flipflop ranges (sed style)

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

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 == carefully, while

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

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

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

to apply the adverb to the == operator instead. We say that == 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 + operator happens last, so :foo would apply to that. Use

    +(%hash{$key} :foo)

to apply :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 eqv operator.

Item assignment precedence

infix:<=>
```
    $x = 1, $y = 2;
```
With simple lvalues, = has this precedence, which is tighter than comma. (List assignments have listop precedence below.)
infix:['=>'], Pair constructor
```
    foo => 1, bar => "baz"
```
Binary => is no longer just a "fancy comma". It now constructs a 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, => binds tighter than comma.
Assignment operators
```
    += -= **= xx= .= etc.
```
See "Assignment operators".

Loose unary precedence

prefix:<not>
```
    not any(@args) eq '-v' | '-V'
```
Returns a Bool value representing the logical negation of an expression.
prefix:<so>
```
    so any(@args) eq '-v' | '-V'
```
Returns a Bool value representing the logical non-negation of an expression. Mostly useful as documentation in parallel to a not when else isn't appropriate:
```
    if not $x { print "LOL"; }
    mumble();
    if so $x { print "SRSLY!" }
```

Comma operator precedence

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.)
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 .foo(): 1,2,3 down to .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.

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.

infix:<Z>, the zip operator
```
    1,2 Z 3,4   # (1,3),(2,4)
```
The Z operator is actually a degenerate case of the Z zipwith metaoperator (see "Zip operators" below).
infix:<minmax>, the minmax operator
```
    @a minmax @b
```
Returns a Range from the minimum element of @a and @b to the maximum element. Range elements in the input are treated as if their minimum and maximum values were passed individually, except that if the corresponding excludes flag is set in Range, the excludes flag is also set in the returned Range.
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 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 LoL in lol context:
```
    say flat(<a b> X <1 2>)
    '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.

Only the leftmost list may usefully be an infinite list. 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'.

Cross metaoperators

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

See "Cross operators".

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

As a list infix operator, ... 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 righthand list. This is the only value of the right list that the ... operator is actually interested in; any additional list elements are treasured up lazily to be returned after the ... 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 ... 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 ...^ 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 $x and the first element of the right side is in $limit, the two operators are implemented respectively as:
```
    ...     last($x) if $x ~~ $limit;
    ...^    last     if $x ~~ $limit;
```
Since this uses smartmatching via the ~~ operator (see "Smart matching" below), the usual smartmatching rules apply. If the limit is *, 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 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 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 $a, $b, and $c, and then define:
```
    $ab = $b - $a;
    $bc = $c - $b;
```
If $ab == $bc and $ab is not zero, then we deduce an arithmetic progression determined by the function *+$ab. If $ab is zero, and the three values look like numbers, then the function is *+0. If they do not look like numbers, then the function selected is either *.succ or *.pred depending on whether $b cmp $c appears to be Increasing or Decreasing. If cmp returns Same then an identity function is assumed.

If $ab != $bc and none($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 / $b;
```
If the two quotients are equal (and finite), then a geometric function of {$_ * $bc} is deduced.

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

If there is only one value, we always assume incrementation via .succ. (This may be forced to .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, .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 (), we use the function {()} 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 * 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 ... 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 *.succ or *.pred is more appropriate. The two values are compared with 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 Rat arithmetic, not Num, so the 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 ... 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 .succ/.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 justitifed, 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 seme 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 these 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 lower-case sigma, which you proably 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 '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 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 last call above returns no argument, so even though the internal test calls last($x), this call to last bypasses that as if the sequence had been specified with ...^ instead. Going the other way, a ...^ maybe be forced to have a final value by passing an argument to an explicit last($my-last-value). In the same way, that will bypass the argumentless internal last.

In a similar way, the sequence may be terminated by calling 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 * is considered to be of unknowable length (even if generated with a closure that has internal logic to terminate). However, by the definition of "mostly eager" in S07, the implementation may be able to determine that such a sequence is finite by conjectural evaluation; such workahead cannot, of course, 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 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 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 *, which indicates that it is to be treated as an infinite list in contexts which care. Similarly, any list ending with an operator that interprets * as infinity may be taken the same way, such as $n xx *, or 1..*.
infix:<E>, test for EMPTY iterator

Returns the list on the left unless any of them are EMPTY, in which case it executes the thunk on the right. Typically used in a loop with take:
```
    loop {
        take @iterators>>.get E last;
    }
```

Many of these operators return a list of Parcels, 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.

List prefix precedence

infix:<=>, list assignment
```
    @array = 1,2,3;
```
With compound targets, performs list assignment. The right side is looser than comma. You might be wondering why we've classified this as a prefix operator when its token name is 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 meaning depends 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 +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. :)

Assignment to a hash is not lazy (probably).
infix:<:=>, run-time binding
```
    $signature := $capture
```
A new form of assignment is present in Perl 6, called binding, used in place of typeglob assignment. It is performed with the := 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 $x and $y contain the string "Perl Hacker", since they are really just two different names for the same variable.

There is also an identity test, =:=, which tests whether two names are bound to the same underlying variable. $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 Scalar of Any, but since the Any type is not a real instantiable type but a generic (non)constraint, and Scalar of Any is sort of a double non-constraint similar to 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 ... *;
```
infix:<::=>, bind and make readonly
```
    $signature ::= $capture
```
This does the same as :=, then marks any destination parameters as readonly (unless the individual parameter overrides this with either the rw trait or the 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 doit wants to change $*OUT, it must declare its own dynamic variable. It may not simply assign to $*OUT.

Note that the semantics of ::= 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.

Normal listops

    print push say join split substr open etc.

Listop forms of junctional operators
```
    any all one none
```

Exception generators

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

Stubby exception generators
```
    ...
    !!! "fill this in later, Dave"
    ??? "oops in $?CLASS"
```
The ... 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 fail) if it is ever executed. Variant ??? calls warn, and !!! calls die. The argument is optional, but if provided, is passed onto the fail, warn, or 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 fail, warn, and die would say by default, since the latter operators typically point out bad data or programming rather than just an incomplete design.)
Reduce operators
```
    [+] [*] [<] [\+] [\*] etc.
```
See "Reduction operators" below.
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 @$a, these may only be applied with explicit parens around an argument that is processed as a bare 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 Parcel structure here, since there is no flattening.)

Since a Parcel with one argument is transparent, there can be no difference between the meaning of @($a) and @$a.
The item contextualizer
```
    item foo()
```
The new name for Perl 5's scalar contextualizer. Equivalent to $(...) (except that empty $() means $<? // Str($/)>, while empty item() yields 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 Seq object from it. The function is agnostic about any 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) )
```
The list contextualizer
```
    list foo()
```
Forces the subsequent expression to be evaluated in list context. Any flattening happens lazily.
The 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 Parcel objects.
The 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 LoL.
The hash contextualizer
```
    hash foo()
```
Forces the subsequent expression to be evaluated in hash context. The expression is evaluated in list context (flattening any Parcels), then a hash will be created from the list, taken as a list of Pairs. (Any element in the list that is not a Pair will pretend to be a key and grab the next value in the list as its value.) Equivalent to %(...) (except that empty %() means %($/), while empty hash() means an empty hash).

Loose and precedence

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 (). See && above for high-precedence version.
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 $_ 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.

Loose or precedence

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 (), or Nil. See || above for high-precedence version.
infix:<xor>, exclusive or
```
    $a xor $b xor $c ...
```
Returns the true argument if there is one (and only one). Returns Bool::False if all arguments are false or if more than one argument is true. In list context forces a false return to mean (), or Nil. See ^^ above for high-precedence version.
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 $! for the scope of the right side. That is,
```
    test1() orelse test2()
```
is equivalent to
```
    test1() orelse -> $! { test2() }
```
(The high-precedence // operator is similar, but does not set $! or treat blocks specially.)

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.)

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 Parcels, 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.)
Feed operators: <==, ==>, <<==, ==>>
```
    source() ==> filter() ==> sink()
```
The forms with the double angle append rather than clobber the sink's todo list. The ==>> 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 @(*) or @(**) target. This means you can stack multiple feeds onto one filter command:
```
    source1() ==>>
    source2() ==>>
    source3() ==>>
    filter(@(*)) ==> sink()
```
Similar semantics apply to <<== except it looks backward for an appropriate target to append to.
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.
Statement modifiers: if, unless, while, until, for

Statement modifiers terminate one expression and start another.
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 "Hyper operators").
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.

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.

Perl 5's ${...}, @{...}, %{...}, etc. dereferencing forms are now $(...), @(...), %(...), 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.
-> becomes ., like the rest of the world uses. There is a pseudo postfix:['->'] operator that produces a compile-time error reminding Perl 5 users to use dot instead. (The "pointy block" use of -> 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.)
The string concatenation . becomes ~. Think of it as "stitching" the two ends of its arguments together. String append is likewise ~=.
The filetest operators are gone. We now use a 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 "exists" }
```
is the same as
```
    if not $filename.IO.e { say "exists" }
```
The 1st form actually translates to the latter form, so the object's class decides how to dispatch methods. It just happens that the IO role defaults to the expected filetest semantics, but $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 ~~ 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 Bool, Int, or 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 IO object that will not be subject to timeout, and may be tested repeatedly just as a filename or handle can. An IO object has a .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.)
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 x().foo doesn't mean you can write x()foo. Likewise the ability to say $x.'foo' does not imply that $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 x().! is always the postfix operator, but x().'!' will always call !x(). In particular, you can say things like $array.'@'. This also includes any operator that would look like something with a special meaning if used after the method-calling dot. For example, If you defined a prefix:<=>, and you wanted to write it using the method-call syntax instead of =$object, the parser would take $object.= as the mutation syntax (see S12, "Mutating methods"). Writing $object.'=' will call your prefix operator.
Unary ~ now imposes a string (Stringy) context on its argument, and + imposes a numeric (Numeric) context (as opposed to being a no-op in Perl 5). Along the same lines, ? imposes a boolean (Bool) context, and the | unary operator imposes a function-arguments (Parcel or Capture) context on its argument. Unary sigils are allowed when followed by a $ sigil on a scalar variable; they impose the container context implied by their sigil. As with Perl 5, however, $$foo[bar] parses as ( $($foo) )[bar], so you need $($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.
Bitwise operators get a data type prefix: +, ~, or ?. For example, Perl 5's | becomes either +| or ~| or ?|, depending on whether the operands are to be treated as numbers, strings, or boolean values. Perl 5's left shift << becomes +< , and correspondingly with right shift. Perl 5's unary ~ (one's complement) becomes either +^ or ~^ or ?^, since a bitwise NOT is like an exclusive-or against solid ones. Note that ?^ is functionally identical to !, but conceptually coerces to boolean first and then flips the bit. Please use ! instead. As explained in "Assignment operators", a bitwise operator can be turned into its corresponding assignment operator by following it with =. For example Perl 5's <<= becomes +<= .

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

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

Bitwise string operators (those starting with ~) may only be applied to buf types or similar compact integer arrays, and treat the entire chunk of memory as a single huge integer. They differ from the + operators in that the + operators would try to convert the string to a number first on the assumption that the string was an ASCII representation of a number.
x splits into two operators: x (which concatenates repetitions of a string to produce a single string), and xx (which creates a list of repetitions of a list or item). "foo" xx * represents an arbitrary number of copies, useful for initializing lists. The left side of an xx is evaluated only once. (To call a block repeatedly, use a map instead.)
The ? : conditional operator becomes ?? !!. A pseudo operator, infix:<?>, catches migratory brainos at compile time.
qw{ ... } gets a synonym: < ... >, and an interpolating variant, «...». For those still living without the blessings of Unicode, that can also be written: << ... >>.
Comma , now constructs a Parcel object from its operands. In item context this turns into a Seq object. You have to use a [*-1] subscript to get the last one. (Note the *. Negative subscripts no longer implicitly count from the end; in fact, the compiler may complain if you use [-1] on an object known at compile time not to have negative subscripts.)
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 dereference this object in several ways to retrieve different parts of the arguments; see the definition of Capture in 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 S02 for details. However, oddly enough, because of that unspace rule, saying \\ $foo turns out to be equivalent to \$foo.)
The old .. flipflop operator is now done with ff operator. (.. now always produces a Range object even in item context.) The ff operator may take a caret on either end to exclude either the beginning or ending. There is also a corresponding fff operator with Perl 5's ... semantics. You may say
```
    /foo/ ff *
```
to indicate a flipflop that never flops once flipped.
All comparison operators are unified at the same precedence level. See "Chained comparisons" below.
The list assignment operator now parses on the right like any other list operator, so you don't need parens on the right side of:
```
    @foo = 1, 2, 3;
```
You do still need them on the left for
```
    ($a, $b, $c) = 1, 2, 3;
```
since assignment operators are tighter than comma to their left.

"Don't care" positions may be indicated by assigment to the * token. A final * 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 $ can ignore a single argument as well, and a bare *@ 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 * or the final iterator on the right is defined in terms of *. 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[$a]) = 1, 2;
```
assigns 2 to @b[0], not @b[1].
The item assignment operator expects a single expression with precedence tighter than comma, so
```
    loop ($a = 1, $b = 2; ; $a++, $b++) {...}
```
works as a C programmer would expect. The term on the right of the = 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 $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 = 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 item (or $ or + or ~) 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 foo() and 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.
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).

Other than parentheses, all other postfixes are disallowed immediately after a list operator, even if there are no arguments. To add a postfix to an argumentless list operator you must write it as a function call with empty parentheses:
```
    foo.[]      # ILLEGAL
    foo.()      # ILLEGAL
    foo++       # ILLEGAL
    foo().[]    # legal
    foo()++     # legal (if foo() is rw)
```
After the parentheses any postfix operators are allowed, and apply to the result of the function call. (Also note that the postfix restriction applies only to list operators; it doesn't apply to methods. It is legal to say
```
    $foo.bar<a b c>
```
to mean
```
    $foo.bar().{'a','b','c'}
```
because methods never assume there are arguments unless followed by parentheses or a colon.)

If the next item after the list operator is either an infix operator or a term, a syntax error is reported. [Conjecture: this may be relaxed in non-strict mode.]

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++;                          ILLEGAL, need parens

    say foo($bar+1),$baz                say(foo($bar+1), $baz);
    say foo.($bar+1),$baz               ILLEGAL, need space or parens
    say foo ($bar+1),$baz               say(foo($bar+1, $baz));
    say foo .($bar+1),$baz              say(foo($_.($bar+1), $baz));

    say foo[$bar+1],$baz                ILLEGAL, need foo()[]
    say foo.[$bar+1],$baz               ILLEGAL, need foo().[]
    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                ILLEGAL, need foo(){}
    say foo.{$bar+1},$baz               ILLEGAL, need foo().{}
    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                ILLEGAL, need foo()<>
    say foo.<$bar+1>,$baz               ILLEGAL, need foo().<>
    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 < accordingly:
```
    any <a b c>                 any('a','b','c')        # term
    any()<a b c>                (any).{'a','b','c'}     # postfix
    any() < $x                  (any) < $x              # infix
    any<a b c>                  ILLEGAL                 # stealth postfix
```
This will seem unfamiliar and "undwimmy" to Perl 5 programmers, who are used to a grammar that sloppily hardwires a few postfix operators at the price of extensibility. Perl 6 chooses instead to mandate a whitespace dependency in order to gain a completely extensible class of postfix operators.
A list operator's arguments are also terminated by a closure that is not followed by a comma or colon. (And a semicolon is implied if the closure is the final thing on a line. Use an "unspace" to suppress that.) This final closure may be followed by a postfix, in which case the postfix is applied to the result of the entire list operator.
A function predeclared with an empty signature is considered 0-ary at run time but is still parsed as a list prefix operator, and looks for a following argument list, which it may reject at run time.
```
    my sub foo () {...}
    foo;          # okay
    foo();        # okay
    foo (),(),(); # okay
    foo 1;        # fails to dispatch
```
The compiler is allowed to complain about anything it knows cannot succeed at run time. Note that a multi may contain () as one of its signatures, however:
```
    my multi foo () {...}
    my multi foo ($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 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, rand is a simple term in Perl 6 and does not allow parens, because there is no rand() function (though there's a $n.rand method). Most constant values such as e and 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 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 $x;     # ILLEGAL, two terms in a row
```
A non-multi sub predeclared with an arity of exactly 1 also still parses as a list prefix operator expecting multiple arguments. You must explicitly use the form prefix:<foo> to declare foo as a named unary in precedence; it must still take a single positional parameter (though any number of named parameters are allowed, which can be bound to adverbs). All other subs with arguments parse as list operators.
The && and || operators are smarter about list context and return () on failure in list context rather than Bool::False. The operators still short-circuit, but if either operator would return a false value, it is converted to the null list in list context so that the false results are self-deleting. (If this self-deleting behavior is not desired, put the expression into item context rather than list context.) This self-deletion is a behavior of the operators themselves, not a general property of boolean values in list context, so either of:
```
    @foo = so($a||$b);
    @foo = not($a||$b);
```
is guaranteed to insert exactly one boolean value into @foo.

Junctive operators

|, &, and ^ are no longer bitwise operators (see "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 any, all, one, and none.

This opens doors for constructions like:

     unless $roll == any(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 != and 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 .pairs) to make a junction of pairs.

Comparison semantics

Perl 5's comparison operators are basically unchanged, except that they can be chained because their precedence is unified.
Binary === tests immutable type and value correspondence: for two value types (that is, immutable types), tests whether they are the same value (eg. 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 [1,2] === [1,2] because those are different Array objects, but it is true that @a === @a because those are the same Array object).

Any object type may pretend to be a value type by defining a .WHICH method which returns a value type that can be recursively compared using ===, or in cases where that is impractical, by overloading === 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, eq always coerces to string, while == always coerces to numeric. In fact, $a eq $b really means "~$a === ~$b" and $a == $b means +$a === +$b.

Note also that, while string-keyed hashes use eq semantics by default, object-keyed hashes use === semantics, and general value-keyed hashes use eqv semantics.
Binary eqv tests equality much like === does, but does so with "snapshot" semantics rather than "eternal" semantics. For top-level components of your value that are of immutable types, eqv is identical in behavior to ===. For components of your value that are mutable, however, rather than comparing object identity using ===, the 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 ===.

If that's not enough flexibility, there is also an eqv() function that can be passed additional information specifying how you want canonical values to be generated before comparison. This gives eqv() the same kind of expressive power as a sort signature. (And indeed, the cmp operator from Perl 5 also has a functional analog, 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 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, eqv() reverts to standard eqv comparison. (Likewise for cmp().)
Binary cmp is no longer the comparison operator that forces stringification. Use the leg operator for the old Perl 5 cmp semantics. The cmp is just like the eqv above except that instead of returning Bool::False or Bool::True values it always returns Order::Increase, Order::Same, or Order::Decrease (which numerify to -1, 0, or +1).
The leg operator (less than, equal to, or greater than) is defined in terms of cmp, so $a leg $b is now defined as ~$a cmp ~$b. The sort operator still defaults to cmp rather than leg. The <=> operator's semantics are unchanged except that it returns an Order value as described above. In other words, $a <=> $b is now equivalent to +$a cmp +$b.
For boolean comparison operators with non-coercive cmp semantics, use the generic before and after infix operators. As ordinary infix operators these may be negated (!before and !after) as well as reduced ([before] and [after]).
Infix min and max may be used to select one or the other of their arguments. Reducing listop forms [min] and [max] are also available, as are the min= and max= assignment operators. By default min and max use cmp semantics. As with all cmp-based operators, this may be modified by an adverb specifying different semantics.
Note that, like most other operators, a comparison naturally throws an exception if either of its arguments is undefined. However, various parallelizable contexts such as sort and hyper suppress this, er, somehow.

Range and RangeIter semantics

The .. range operator has variants with ^ on either end to indicate exclusion of that endpoint from the range. It always produces a Range object. Range objects are immutable, and primarily used for matching intervals. 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 anything that does Iterable as implicitly numeric:

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

For ranges with other non-numeric types on the right, the right argument is coerced to the type of the left argument and treated as numeric. Hence, 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

Whatever types are also supported to represent -Inf/+Inf. If either endpoint is a WhateverCode, the range is curried into another 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, infix:<..>:(::T Any $x, T $y) is defined such that, if type T defines generic comparison (that is, by defining infix:<cmp> or equivalent), a range is constructed in that type. If T also defines .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 RangeIter.) Note that it is not necessary to define a range multimethod in type T, since the generic routine can usually auto-generate the range for you.

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

Range objects support .excludes_min and .excludes_max methods representing the exclusion (has ^) or inclusion (no ^) 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 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 ^. Hence 1..2 produces (1,2) but 1^..^2 is equivalent to 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 Range used as a list assumes .succ semantics, never .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 ... sequence operator. (The Range operator's :by adverb is hereby deprecated.)

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

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

Smart matching against a Range object smartmatches the endpoints in the domain of the object being matched, so fractional numbers are not truncated before comparison to integer ranges:

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

If a * (see the "Whatever" type in 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 * 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
    1.2.3..*    # Any version higher than 1.2.3.
    May..*      # May through December

An empty range cannot be iterated; it returns a Nil instead. An empty range still has a defined .min and .max, but one of the following is true: 1. The .min is greater than the .max. 2. The .min is equal to the .max and at least one of .excludes_min or .excludes_max is true. 3. Both .excludes_min and .excludes_max are true and .min and .max are consecutive values.

Ranges that are iterated transmute into the corresponding sequence operator, and hence use smartmatch semantics to determine an end to the sequence.

Unary ranges

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

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

If applied to a type name, it indicates the metaclass instance instead, so ^Moose is short for HOW(Moose) or Moose.HOW. It still kinda means "what is this thing's domain" in an abstract sort of way.

Auto-currying of ranges

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

Since use of Range objects in item context is usually non-sensical, a Range object used as an operand for scalar operators will generally attempt to distribute the operator to its endpoints and return another suitably modified Range instead, much like a junction of two items, only with proper interval semantics. (Notable exceptions to this autothreading include infix:<~~>, which does smart matching, and 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 Range objects.

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 < must have whitespace in front of it, or it will be interpreted as a hash subscript instead.

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 $_. In the table below, $_ represents the left side of the ~~ operator, or the argument to a given, or to any other topicalizer. X represents the pattern to be matched against on the right side of ~~, or after a when. (And, in fact, the ~~ operator works as a small topicalizer; that is, it binds $_ to the value of the left side for the evaluation of the right side. Use the underlying .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 ~~ 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 X pattern object.

In other words, smart matches are dispatched first on the basis of the pattern's form or type (the X below), and then that pattern itself decides whether and how to pay attention to the type of the topic ($_). So the second column below is really the primary column. The 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 $_)
    Any       Bool      simple truth            X
    Any       Numeric   numeric equality        +$_ == 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($_)
    Scalar    Hash      hash entry existence    X.{$_}: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)

    Any       Match     identity                $_

    Num       Range     in numeric range        X.min <= $_ <= X.max (mod ^'s)
    Str       Range     in string range         X.min le $_ le X.max (mod ^'s)
    Any       Range     in generic range        [!after] X.min,$_,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 ~~ and given/when provide item contexts to their arguments, and autothread any junctive matches so that the eventual dispatch to .ACCEPTS never sees anything "plural". So both $_ and X above are potentially container objects that are treated as scalars. (You may hyperize ~~ explicitly, though. In this case all smartmatching is done using the type-based dispatch to .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 X initially. The ACCEPTS method interface is defined by the Pattern role. Any class composing the Pattern role may choose to provide a single ACCEPTS method to handle everything, which corresponds to those pattern types that have only one entry with an Any on the left above. Or the class may choose to provide multiple ACCEPTS multi-methods within the class, and these will then redispatch within the class based on the type of $_.

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
    Match                       Capture
    Byte                        Str or Int
    Buf                         Str or Array of Int

(Note, however, that these mappings can be overridden by explicit definition of the appropriate 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 Buf type containing any bytes or integers outside the ASCII range may silently promote to a 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 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 integers is erroneous, and warnings may be generously issued.

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

Matching against a Signature does not actually bind any variables, but only tests to see if the signature could bind. To really bind to a signature, use the * pattern to delegate binding to the when statement's block instead. Matching against * 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 $_, so the final form above is equivalent to a 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 Any pattern, so if you find yourself in the situation of wanting a reversed smartmatch test with an Any on the right, you can almost always get it by explicit call to the underlying ACCEPTS method using $_ 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 $_:

    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:

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

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

Boolean expressions are those known to return a boolean value, such as comparisons, or the unary ? operator. They may reference $_ explicitly or implicitly. If they don't reference $_ 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 True case. Instead use something like a conditional context uses internally:

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

Better, just use an if statement. In any case, if you try to smartmatch with ~~ or when, it will recognize True or 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 $_, to the extent it can detect that.

In a similar vein, any function (such as grep) that takes a Matcher will not accept an argument of type Bool, since that almost always indicates a programming error. (One may always use * 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 not return a Bool, but merely a Match object that can be used as a boolean value. Use an explicit ? or true to force a Bool value if desired.

The primary use of the ~~ 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 Match object is a kind of Capture, which has these capabilities.

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

The Cat type allows you to have an infinitely extensible string. You can match an array or iterator by feeding it to a Cat, which is essentially a Str interface over an iterator of some sort. Then a Regex can be used against it as if it were an ordinary string. The 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 .* 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 cat operator takes a (potentially lazy) list and returns a 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 Cat interface allows the regex to match element boundaries with the <,> assertion, and the 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 shift or pop) are tracked by the 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.

Invocant marker

An appended : 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 :xxx adverb to the + operator, not the method call. This is not likely to succeed.

Feed operators

The new operators ==> and <== 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 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 S06 for more of the (less-than-obvious) details on these two operators.

Meta operators

Perl 6's operators have been greatly regularized, for instance, by consistently prefixing numeric, stringwise, and boolean operators with +, ~ and ? 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 ¬ operator, you'd have to add the +¬, ~¬, and ?¬ 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.

Assignment operators

Assignment operators are already familiar to C and Perl programmers. (Though the .= operator now means to call a mutating method on the object on the left, and ~= is string concatenation.) Most non-relational infix operators may be turned into their corresponding assignment operator by suffixing with =. 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 = 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 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 $f.

Negated relational operators

Any infix relational operator returning type Bool may be transformed into its negative by prefixing with !. 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 !! operator, you may not modify any operator already beginning with !.

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

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

Reversed operators

Any infix operator may be called with its two arguments reversed by prefixing with 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 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

Hyper operators

The Unicode characters » (\x[BB]) and « (\x[AB]) and their ASCII digraphs >> and << 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)

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. 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 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 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 * 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 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 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 « 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 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 Iterable semantics enable visitation:

    $tree.».foo;        # short for $tree.foo, $tree.list: { .».foo }

If not all nodes support the operation, you need a form of it that specifies the call is optional:

    $tree.».?foo;       # short for $tree.?foo, $tree.list: { .».?foo }
    $tree.».*foo;       # short for $tree.*foo, $tree.list: { .».*foo }

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 int or 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 int or num ops.)

Application-wide analysis of finalizable object types may also enable such optimizations to be applied to Int, 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 %inner keys that already exist in %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 %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 * 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 what order the processing happens in, only that the resulting structure ends up in a form consistent with the inputs. There is no promise from the system that the operation 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.

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 operator. In fact, a reduction operator really is a list operator, 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:

    proto prefix:<[+]> (*@args) {
        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 currying:

    &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 chain-associative operators (like <), 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 proto list operator definition 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, [+]() returns 0 and [*]() 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 < 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 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 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 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 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 ||.

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, infix:<\x> say, will make it impossible to write certain triangular reduction operators, since [\x] would mean the normal reduction of infix:<\x> operator, not the triangular reduction of infix:<x>. This is deemed to be an insignificant problem.

Triangular reductions of chaining operators always consist of one or more True values followed by 0 or more False values.

Cross operators

The cross metaoperator, 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 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 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, 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 X, operator is perhaps more clearly written as X[,]. However, this list form is common enough to have a shortcut, the ordinary infix 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 <== and ==> 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 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 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.

Zip operators

The zip metaoperator, 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 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 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 X and Z metaoperators a subprecedence within listop precedence corresponding to the original operator's precedence, so that Z~ and Z+ actually have different precedences within listop precedence. Then the above would parse as if you'd said <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 Z might be exactly what the naive user expects.]

The list concatenating form, Z,, when used like this:

    <a b> Z, 1,2 Z, <x y>

produces

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

The Z, operator is perhaps more clearly written as Z[,]. However, this list form is common enough to have a shortcut, the ordinary infix 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 <== and ==> 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 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 X operator, all the terms of a Z operator may reasonable 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.

Sequential operators

The sequence metaoperator, 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 S metaoperator that is provably redundant, such as the one in S||. The compiler is free to intuit an 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...]

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

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 & sigil:

    &infix:<+>
    &[+]

This is convenient for function application:

    1, 1, &[+] ... *       # fibonacci sequence
    sort &[Rleg], @list    # reverse sort as strings

The &[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 *:

    sort -*, @list        # sort reversed numerically

Declarators

The list of variable declarators has expanded from my and 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 my now take a signature as their argument. (The syntax of function signatures is described more fully in 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 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 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 our are different from Perl 5, where the initialization happens at the same time as a my. To get the same effect in Perl 6 you'd have to say "(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 "my $foo if 0" to get a static variable, because a 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 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 = 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 S06.] The syntax for constructing a 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 my, sub, method, 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 -> "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 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 rw by default rather than readonly. See Binding above.

Note that temp and let are not variable declarators, because their effects only take place at runtime. Therefore, they take an ordinary lvalue object as their argument. See 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 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 ::= 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

Argument List Interpolating

Perl 5 forced interpolation of a function's argument list by use of the & prefix. That option is no longer available in Perl 6, so instead the | prefix operator serves as an interpolator, by casting its operand to a Capture object and inserting the capture's parts into the current argument list. This operator can be used to interpolate an Array or 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 | 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);

| does not turn its argument into an Array, but instead directly converts its argument into a Capture:

    my @args = \$x, 1, 2, 3;
    say |@args;     # say(\$x, 1, 2, 3);

Because of this, |%args always produces named arguments, and |@args always produces positional arguments.

In list context, a Scalar holding an Array object does not flatten. Hence

    $bar = @bar;
    @foo.push($bar);

merely pushes a single Array object onto @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 push's signature flattens the 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 [] and .[] 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 {} and .{} on hashes, as well as the <>, .<>, «», and .«» constant and interpolating slice subscripting forms.

The | operator interpolates lazily for Array and Range objects. To get an immediate interpolation like Perl 5 does, add the 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 | 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 prefix:<|> operator:

    my (|$capture) := func();
    push |$capture;

Traversing arrays in parallel

In order to support parallel iteration over multiple arrays, Perl 6 has a zip function that builds a list of Seq objects from the elements of two or more arrays. In ordinary list context this behaves as a list of Captures and automatically flattens.

    for zip(@names; @codes) -> $name, $zip {
        print "Name: $name;   Zip code: $zip\n";
    }

zip has an infix synonym, the 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 zip function reads to the end of the shortest list, but a short list may always be extended arbitrarily by putting * 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 roundrobin instead:

    for roundrobin(@queue1; @queue2; @queue3) -> $next {
        ...
    }

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 unspace syntax (see 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 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 if() to also invoke a macro call, but if so, it's a prefix:<if> macro rather than a statement_control:<if> macro.

Sequence points

Certain operators are guaranteed to provide 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 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 +) 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.)

To install Perl6::Doc, copy and paste the appropriate command in to your terminal.

cpanm

cpanm Perl6::Doc

CPAN shell

perl -MCPAN -e shell
install Perl6::Doc

For more information on module installation, please visit the detailed CPAN module installation guide.

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Overview

Operator precedence

Term precedence

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Autoincrement precedence

Exponentiation precedence

Symbolic unary precedence

Multiplicative precedence

Additive precedence

Replication

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Junctive and (all) precedence

Junctive or (any) precedence

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Tight or precedence

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