# class Backtrace

Snapshot of the dynamic call stack

```
class Backtrace is List { ... }
```

A backtrace shows the dynamic call stack, usually leading up to a point where an exception was thrown.

It is a List of Backtrace::Frame objects. Its default stringification excludes backtrace frames that are deemed unnecessary or confusing, for example routines like `&die`

are hidden by default.

# Methods

## method new

```
proto method new(*@, *%) {*}
multi method new()
```

Creates a new backtrace, using its calling location as the origin of the backtrace.

## method Str

```
multi method Str(Backtrace:D:) returns Str:D:
```

Returns a concise string representation of the backtrace, omitting routines marked as `is hidden-from-backtrace`

, and at the discretion of the implementor, also some routines from the setting.

## method full

```
multi method full(Backtrace:D:) returns Str:D:
```

Returns a full string representation of the backtrace, including hidden frames, compiler-specific frames and those from the setting.

# Type graph

Below you should see a clickable image showing the type relations for Backtrace that links to the documentation pages for the related types. If not, try the PNG version instead.

# Routines supplied by class List

Backtrace inherits from class List, which provides the following methods:

## routine elems

```
multi sub elems($list) returns Int:D
multi method elems(List:D:) returns Int:D
```

Returns the number of elements in the list.

## routine end

```
multi sub end($list) returns Int:D
multi method end(List:D:) returns Int:D
```

Returns the index of the last element.

## routine keys

```
multi sub keys($list) returns List:D
multi method keys(List:D:) returns List:D
```

Returns a list of indexes into the list (e.g., 0..(@list.elems-1)).

## routine values

```
multi sub values($list) returns List:D
multi method values(List:D:) returns List:D
```

Returns a copy of the list.

## routine kv

```
multi sub kv($list) returns List:D
multi method kv(List:D:) returns List:D
```

Returns an interleaved list of indexes and values. For example

```
<a b c>.kv
```

Returns

```
0, 'a', 1, 'b', 2, 'c'
```

## routine pairs

```
multi sub pairs($list) returns List:D
multi method pairs(List:D:) returns List:D
```

Returns a list of pairs, with the indexes as keys and the list values as values.

```
<a b c>.pairs # 0 => 'a', 1 => 'b', 2 => 'c'
```

## routine join

```
multi sub join($separator, *@list) returns Str:D
multi method join(List:D: $separator) returns Str:D
```

Treats the elements of the list as strings, interleaves them with `$separator`

and concatenates everything into a single string.

Example:

```
join ', ', <a b c>; # a, b, c
```

Note that the method form does not flatten sublists:

```
say (1, <a b c>).join('|'); # 1|a b c
```

## routine map

```
multi sub map(&code, *@elems) returns List:D
multi method map(List:D: &code) returns List:D
```

Invokes `&code`

for each element and gathers the return values in another list and returns it. This happens lazily, i.e. `&code`

is only invoked when the return values are accessed.

Examples:

```
> ('hello', 1, 22/7, 42, 'world').map: { .WHAT.perl }
Str Int Rat Int Str
> map *.Str.chars, 'hello', 1, 22/7, 42, 'world'
5 1 8 2 5
```

`map`

inspects the arity of the code object, and tries to pass as many arguments to it as expected:

```
sub b($a, $b) { "$a before $b" };
say <a b x y>.map(&b).join(', '); # a before b, x before y
```

iterates the list two items at a time.

Note that `map`

does not flatten embedded lists and parcels, so

```
((1, 2), <a b>).map({ .join(',')})
```

passes `(1, 2)`

and `<a b> `

in turn to the block, leading to a total of two iterations and the result list `"1,2", "a,b"`

. See method flatmap for an alternative that flattens.

## method flatmap

```
method flatmap(List:D: &code) returns List:D
```

Like `map`

iterates over the elements of the invocant list, feeding each element in turn to the code reference, and assembling the return values from these invocations in a result list.

Unlike `map`

it flattens non-itemized lists and parcels, so

```
say ((1, 2), <a b>).flatmap(&uc).join('|'); # 1|2|A|B
```

invokes `uc|/type/Str#routine uc`

four times.

## routine grep

```
multi sub grep(Mu $matcher, *@elems) returns List:D
multi method grep(List:D: Mu $matcher) returns List:D
```

Returns a lazy list of elements against which `$matcher`

smart-matches. The elements are returned in the order in which they appear in the original list.

Examples:

```
> ('hello', 1, 22/7, 42, 'world').grep: Int
1 42
> grep { .Str.chars > 3 }, 'hello', 1, 22/7, 42, 'world'
hello 3.142857 world
```

## routine grep-index

```
multi method grep-index(List:D: Mu $matcher) returns List:D
```

Returns a lazy list of indices against which the associated elements smart-match. The indices are returned in order.

## routine first

```
multi sub first(Mu $matcher, *@elems)
multi method first(List:D: Mu $matcher)
```

Returns the first item of the list which smart-matches against `$matcher`

, fails when no values match.

Examples:

```
say (1, 22/7, 42).first: * > 5; # 42
say $f = ('hello', 1, 22/7, 42, 'world').first: Complex;
say $f.perl; # Failure.new(exception => X::AdHoc.new(payload => "No values matched"))
```

## routine first-index

```
multi method first-index(List:D: Mu $matcher)
```

Returns the first index against which `$matcher`

smart-matches, or `Nil`

if no match was found.

## routine last-index

```
multi method last-index(List:D: Mu $matcher)
```

Returns the last index against which `$matcher`

smart-matches, or `Nil`

if no match was found.

## routine classify

```
multi sub classify(&mapper, *@values) returns Hash:D
multi method classify(List:D: &mapper) returns Hash:D
```

Transforms a list of values into a hash representing the classification of those values according to a mapper; each hash key represents the classification for one or more of the incoming list values, and the corresponding hash value contains an array of those list values classified by the mapper into the category of the associated key.

Example:

```
say classify { $_ %% 2 ?? 'even' !! 'odd' }, (1, 7, 6, 3, 2);
#-> even => 6 2, odd => 1 7 3
say ('hello', 1, 22/7, 42, 'world').classify: { .Str.chars };
#-> 1 => 1, 2 => 42, 5 => hello world, 8 => 3.142857
```

## method Bool

```
multi method Bool(List:D:) returns Bool:D
```

Returns `True`

if the list has at least one element, and `False`

for the empty list.

## method Str

```
multi method Str(List:D:) returns Str:D
```

Stringifies the elements of the list and joins them with spaces (same as `.join(' ')`

).

## method Int

```
multi method Int(List:D:) return Int:D
```

Returns the number of elements in the list (same as `.elems`

).

## method Numeric

```
multi method Numeric(List:D:) return Int:D
```

Returns the number of elements in the list (same as `.elems`

).

## routine pick

```
multi sub pick($count, *@list) returns List:D
multi method pick(List:D: $count = 1)
```

Returns `$count`

elements chosen at random and without repetition from the invocant. If `*`

is passed as `$count`

, or `$count`

is greater than or equal to the size of the list, then all elements from the invocant list are returned in a random sequence.

Examples:

```
say <a b c d e>.pick; # b
b
say <a b c d e>.pick: 3; # c a e
say <a b c d e>.pick: *; # e d a b c
```

## routine roll

```
multi sub roll($count, *@list) returns List:D
multi method roll(List:D: $count = 1)
```

Returns a lazy list of `$count`

elements, each randomly selected from the list. Each random choice is made independently, like a separate die roll where each die face is a list element.

If `*`

is passed to `$count`

, returns a lazy, infinite list of randomly chosen elements from the original list.

Examples:

```
say <a b c d e>.roll; # b
b
say <a b c d e>.roll: 3; # c c e
say roll 8, <a b c d e>; # b a e d a e b c
my $random_digits := (^10).roll(*);
say $random_digits[^15]; # 3 8 7 6 0 1 3 2 0 8 8 5 8 0 5
```

## routine eager

```
multi method eager(List:D:) returns List:D
sub eager(*@elems) returns List:D
```

Evaluates all elements in the list eagerly, and returns them as a list. If a List signals that it is "known infinite", eager evaluation may stop at the point where the infinity is detected.

## routine reverse

```
multi sub reverse(*@list ) returns List:D
multi method reverse(List:D:) returns List:D
```

Returns a list with the same elements in reverse order.

Note that `reverse`

always refers to reversing elements of a list; to reverse the characters in a string, use flip.

Examples:

```
say <hello world!>.reverse # world! hello
say reverse ^10 # 9 8 7 6 5 4 3 2 1 0
```

## routine rotate

```
multi sub rotate(@list, Int:D $n = 1) returns List:D
multi method rotate(List:D: Int:D $n = 1) returns List:D
```

Returns the list rotated by `$n`

elements.

Examples:

```
<a b c d e>.rotate(2); # <c d e a b>
<a b c d e>.rotate(-1); # <e a b c d>
```

## routine sort

```
multi sub sort(*@elems) returns List:D
multi sub sort(&by, *@elems) returns List:D
multi method sort(List:D:) returns List:D
multi method sort(List:D:, &by) returns List:D
```

Sorts the list, smallest element first. By default `infix:<cmp> `

is used for comparing list elements.

If `&by`

is provided, and it accepts two arguments, it is invoked for pairs of list elements, and should return `Order::Increase`

, `Order::Same`

or `Order::Decrease`

.

If `&by`

accepts only one argument, the list elements are sorted according to `by($a) cmp by($b) `

. The return values of `&by`

are cached, so that `&by`

is only called once per list element.

Examples:

```
say (3, -4, 7, -1, 2, 0).sort; # -4 -1 0 2 3 7
say (3, -4, 7, -1, 2, 0).sort: *.abs; # 0 -1 2 3 -4 7
say (3, -4, 7, -1, 2, 0).sort: { $^b leg $^a }; # 7 3 2 0 -4 -1
```

## routine unique

```
multi sub unique(*@values, :&as) returns List:D
multi method unique(List:D:, :&as) returns List:D
```

Returns a list of unique values from the invocant/argument list, such that only the first occurrence of each duplicated value remains in the result list. `unique`

uses the semantics of the === operator to decide whether two objects are the same. The order of the original list is preserved even as duplicates are removed.

Examples:

```
say <a a b b b c c>.unique # a b c
say <a b b c c b a>.unique # a b c
```

(Use `squish`

instead if you know the input is sorted such that identical objects are adjacent.)

The optional `:as`

parameter allows you to normalize/canonicalize the elements before unique-ing. The values are transformed for the purposes of comparison, but it's still the original values that make it to the result list:

Example:

```
say <a A B b c b C>.unique(:as(&lc)) # a B c
```

## routine squish

```
multi sub squish(*@values, :&as) returns List:D
multi method squish(List:D:, :&as) returns List:D
```

Returns a list of values from the invocant/argument list where runs of more than one value are replaced with only the first instance. Like `unique`

, `squish`

uses the semantics of the === operator to decide whether two objects are the same. Unlike `unique`

, this function only removes adjacent duplicates; identical values further apart are still kept. The order of the original list is preserved even as duplicates are removed.

Examples:

```
say <a a b b b c c>.squish # a b c
say <a b b c c b a>.squish # a b c b a
```

The optional `:as`

parameter, just like with `unique`

, allows values to be temporarily transformed before comparison.

## routine reduce

```
multi sub reduce(&with, *@elems)
multi method reduce(List:D: &with)
```

Applies `&with`

to the first and the second value of the list, then to the result of that calculation and the third value and so on. Returns a single item generated that way.

Note that `reduce`

is an implicit loop, and thus responds to `next`

, `last`

and `redo`

statements.

Example:

```
say (1, 2, 3).reduce: * - *; # -4
```

## routine splice

```
multi sub splice(@list, $start, $elems?, *@replacement) returns List:D
multi method splice(List:D: $start, $elems?, *@replacement) returns List:D
```

Deletes `$elems`

elements starting from index `$start`

from the list, returns them and replaces them by `@replacement`

. If `$elems`

is omitted, all the elements starting from index `$start`

are deleted.

Example:

```
my @foo = <a b c d e f g>;
say @foo.splice(2, 3, <M N O P>); # c d e
say @foo; # a b M N O P f g
```

## routine pop

```
multi sub pop(List:D )
multi method pop(List:D:)
```

Removes and returns the last item from the list, fails for an empty list.

Example:

```
> my @foo = <a b>;
a b
> @foo.pop;
b
> pop @foo
a
> pop @foo
Element popped from empty list
```

## routine push

```
multi sub push(List:D, *@values) returns List:D
multi method push(List:D: *@values) returns List:D
```

Adds the `@values`

to the end of the list, and returns the modified list. Fails for infinite lists.

Example:

```
my @foo = <a b c>;
@foo.push: 1, 3 ... 11;
say @foo; # a b c 1 3 5 7 9 11
```

## routine shift

```
multi sub shift(List:D )
multi method shift(List:D:)
```

Removes and returns the first item from the list. Fails for an empty list.

Example:

```
my @foo = <a b>;
say @foo.shift; # a
say @foo.shift; # b
say @foo.shift; # Element shifted from empty list
```

## routine unshift

```
multi sub unshift(List:D, *@values) returns List:D
multi method unshift(List:D: *@values) returns List:D
```

Adds the `@values`

to the start of the list, and returns the modified list. Fails if `@values`

is infinite.

Example:

```
my @foo = <a b c>;
@foo.unshift: 1, 3 ... 11;
say @foo; # 1 3 5 7 9 11 a b c
```

## routine combinations

```
multi method combinations (List:D: Int:D $of) returns List:D
multi method combinations (List:D: Range:D $of = 0..*) returns List:D
multi sub combinations ($n, $k) returns List:D
```

The `Int`

variant returns all `$of`

-combinations of the invocant list. For example

```
say .join('|') for <a b c>.combinations(2);
```

prints

```
a|b
a|c
b|c
```

because all the 2-combinations of `'a', 'b', 'c'`

are `['a', 'b'], ['a', 'c'], ['b', 'c']`

.

The `Range`

variant combines all the individual combinations into a single list, so

```
say .join('|') for <a b c>.combinations(2..3);
```

prints

```
a|b
a|c
b|c
a|b|c
```

because that's the list of all 2- and 3-combinations.

The subroutine form `combinations($n, $k)`

is equivalent to `(^$n).combinations($k)`

, so

```
.say for combinations(4, 2)
```

prints

```
0 1
0 2
0 3
1 2
1 3
2 3
```

## routine permutations

```
multi method permutations(List:D:) returns List:D
multi sub permutations($n) returns List:D
```

Returns all possible permutations of a list as a list of arrays. So

```
say .join('|') for <a b c>.permutations
```

prints

```
a|b|c
a|c|b
b|a|c
b|c|a
c|a|b
c|b|a
```

`permutations`

treats all list elements as distinguishable, so `(1, 1, 2).permutations`

still returns a list of 6 elements, even though there are only three distinct permutations.

The subroutine form `permutations($n)`

is equivalent to `(^$n).permutations`

, so

```
.say for permutations 3;
```

prints

```
1 2 3
1 3 2
2 1 3
2 3 1
3 1 2
3 2 1
```

## method rotor

```
method rotor(*@cycle, Bool() :$partial)
```

Returns a list of lists, where each sublist is made up of elements of the invocant.

In the simplest case, `@cycle`

contains just one integer, in which case the invocant list is split into sublists with as many elements as the integer specifies. If `:$partial`

is True, the final chunk is included even if it doesn't satisfy the length requirement:

```
say ('a'..'h').rotor(3).join('|'); # a b c|d e f
say ('a'..'h').rotor(3, :partial).join('|'); # a b c|d e f|g h
```

If the element of `@cycle`

is a /type/Pair instead, the key of the pair specifies the length of the return sublist, and the value the gap between sublists; negative gaps produce overlap:

```
say ('a'..'h').rotor(2 => 1).join('|'); # a b|d e|g h
say ('a'..'h').rotor(3 => -1).join('|'); # a b c|c d e|e f g
```

If `@cycle`

contains more than element, `rotor`

cycles through it to find the number of elements for each sublist:

```
say ('a'..'h').rotor(2, 3).join('|'); # a b|c d e|f g
say ('a'..'h').rotor(1 => 1, 3).join('|'); # a|c d e|f
```

Combining multiple cycles and `:partial`

also works:

```
say ('a'..'h').rotor(1 => 1, 3 => -1, :partial).join('|');
# a|c d e|e|g h
```

Note that assigning the list of lists returned from `rotor`

to a variable will flatten to an `Array`

:

```
my @maybe_lol = ('a'..'h').rotor(2 => 1);
@maybe_lol.perl.say; #-> ["a", "b", "d", "e", "g", "h"]<>
```

Which probably isn't what one wanted, since the `rotor`

-ed output looks like this:

```
say ('a'..'h').rotor(2 => 1).perl; #-> (("a", "b"), ("d", "e"), ("g", "h"))
```

To force a `List`

of `List`

s to be returned, *bind* the output instead of assigning it:

```
my @really_lol := ('a'..'h').rotor(2 => 1);
@really_lol.perl.say; #-> (("a", "b"), ("d", "e"), ("g", "h"))
```

## routine zip

```
sub zip(List:D:, List:D:, ...) returns List:D
```

Zip two or more lists together by interleaving their elements. If the lists have different lengths, then the lists are zipped to the length of the shortest list; elements of the longer list(s) are discarded.

In order to support parallel iteration over multiple arrays, Perl 6 has a `zip`

function that builds a list of `Parcel`

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 {
say "Name: $name; Zip code: $zip";
}
```

`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] {
say "Name: $name; Zip code: $zip";
}
```

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 {
...
}
```

## sub roundrobin

```
multi roundrobin(List:D: --> Parcel)
```

`roundrobin`

is very similar to zip. The difference is that `roundrobin`

will not stop on lists that run out of elements but simply skip any undefined value:

```
my @a = 1;
my @b = 1..2;
my @c = 1..3;
for roundrobin(@a; @b; @c) -> $x { $x.say }
```

will display the following values: `1, 1, 1, 2, 2, 3`

# Methods supplied by role Positional

Backtrace inherits from class List, which does role Positional, which provides the following methods:

## method of

```
method of()
```

Returns the type constraint for elements of the positional container. Defaults to Mu.

# Routines supplied by class Cool

Backtrace inherits from class Cool, which provides the following methods:

## routine abs

```
method abs()
sub abs(Numeric() $x)
```

Coerces the invocant (or in the sub form, the argument) to Numeric and returns the absolute value (that is, a non-negative number).

```
say (-2).abs; # 2
say abs "6+8i"; # 10
```

## method conj

```
method conj()
```

Coerces the invocant to Numeric and returns the complex conjugate (that is, the number with the sign of the imaginary part negated).

```
say (1+2i).conj; # 1-2i
```

## routine sqrt

```
method sqrt()
sub sqrt(Numeric(Cool) $x)
```

Coerces the invocant to Numeric (or in the sub form, the argument) and returns the square root, that is, a non-negative number that, when multiplied with itself, produces the original number.

```
say 4.sqrt; # 2
say sqrt(2); # 1.4142135623731
```

## method sign

```
method sign()
```

Coerces the invocant to Numeric and returns its sign, that is, 0 if the number is 0, 1 for positive and -1 for negative values.

```
say 6.sign; # 1
say (-6).sign; # -1
say "0".sign; # 0
```

## method rand

```
method rand()
```

Coerces the invocant to Num and returns a pseudo-random value between zero and the number.

```
say 1e5.rand; # 33128.495184283
```

## routine sin

```
method sin()
sub sin(Numeric(Cool))
```

Coerces the invocant (or in the sub firm, the argument) to Numeric, interprets it as radians, returns its sine.

```
say sin(0); # 0
say sin(pi/4); # 0.707106781186547
say sin(pi/2); # 1
```

Note that Perl 6 is no computer algebra system, so `sin(pi)`

typically does not produce an exact 0, but rather a very small floating-point number.

## routine asin

```
sub asin(Numeric(Cool))
method asin()
```

Coerces the invocant (or in the sub firm, the argument) to Numeric, and returns its arc-sine in radians.

```
say 0.1.asin; # 0.10016742116156
```

## routine cos

```
method cos()
sub cos(Numeric(Cool))
```

Coerces the invocant (or in sub form, the argument) to Numeric, interprets it as radians, returns its sine.

```
say 0.cos; # 1
say pi.cos; # -1
say cos(pi/2); # 6.12323399573677e-17
```

## routine acos

```
method acos()
sub acos(Numeric(Cool))
```

Coerces the invocant (or in sub form, the argument) to Numeric, and returns its arc-cosine in radians.

## routine tan

```
method tan()
sub tan(Numeric(Cool))
```

Coerces the invocant (or in sub form, the argument) to Numeric, interprets it as radians, returns its tangens.

## routine atan

```
method atan()
sub atan(Numeric(Cool))
```

Coerces the invocant (or in sub form, the argument) to Numeric, and returns its arc-tangens in radians.

## routine atan2

```
method atan2($y = 1e0)
sub atan2(Numeric() $x, Numeric() $y = 1e0)
```

Coerces the arguments (including the invocant in the method form) to Numeric, and returns their two-argument arc-tangens in radians.

## method sec

```
method sec()
sub sec(Numeric(Cool))
```

Coerces the invocant (or in sub form, its argument) to Numeric, interprets it as radians, returns its secans, that is, the reciprocal of its cosine.

## routine asec

```
method asec()
sub asec(Numeric(Cool))
```

Coerces the invocant (or in sub form, its argument) to Numeric, and returns its arc-secans in radians.

## routine cosec

```
method cosec()
sub cosec(Numeric(Cool))
```

Coerces the invocant (or in sub form, its argument) to Numeric, interprets it as radians, returns its cosecans, that is, the reciprocal of its sine.

## routine acosec

```
method acosec()
sub acosec(Numeric(Cool))
```

Coerces the invocant (or in sub form, its argument) to Numeric, and returns its arc-cosecans in radians.

## routine cotan

```
method cotan()
sub cotan(Numeric(Cool))
```

Coerces the invocant (or in sub form, its argument) to Numeric, interprets it as radians, returns its cotangens, that is, the reciprocal of its tangens.

## routine acotan

```
method acotan()
sub acotan(Numeric(Cool))
```

Coerces the invocant (or in method form, its argument) to Numeric, and returns its arc-cotangens in radians.

## routine sinh

```
method sinh()
sub sinh(Numeric(Cool))
```

Coerces the invocant (or in method form, its argument) to Numeric, and returns its Sine hyperbolicus.

## routine asinh

```
method asinh()
sub asinh(Numeric(Cool))
```

Coerces the invocant (or in method form, its argument) to Numeric, and returns its Inverse Sine hyperbolicus.

## routine cosh

```
method cosh()
sub cosh(Numeric(Cool))
```

Coerces the invocant (or in method form, its argument) to Numeric, and returns its Cosine hyperbolicus.

## routine acosh

```
method acosh()
sub acosh(Numeric(Cool))
```

Coerces the invocant (or in method form, its argument) to Numeric, and returns its Inverse Cosine hyperbolicus.

## routine tanh

```
method tanh()
sub tanh(Numeric(Cool))
```

Coerces the invocant (or in method form, its argument) to Numeric, and returns its Tangens hyperbolicus.

## routine atanh

```
method atanh()
sub atanh(Numeric(Cool))
```

Coerces the invocant (or in method form, its argument) to Numeric, and returns its Inverse tangens hyperbolicus.

## routine log

```
multi method log(Cool:D: Cool:D $base?)
multi sub log(Numeric(Cool) $number, Numeric(Cool) $base?)
```

Coerces the arguments (including the invocant in the method form) to Numeric, and returns its Logarithm to base `$base`

, or to base `e`

(Euler's Number) if no base was supplied (Natural logarithm.

```
say (e*e).log; # 2
```

## routine log10

```
multi method log10()
multi sub log10(Cool(Numeric))
```

Coerces the invocant (or in the sub form, the invocant) to Numeric, and returns its Logarithm to base 10, that is, a number that approximately produces the original number when raised to the power of 10.

```
say log10(1001); # 3.00043407747932
```

## method exp

```
multi method exp(Cool:D: Cool:D $base?)
multi sub exp(Cool:D $pow, Cool:D $base?)
```

Coerces the arguments (including the invocant in the method from) to Numeric, and returns `$base`

raised to the power of the first number. If no `$base`

is supplied, `e`

(Euler's Number) is used.

```
say 0.exp; # 1
say 1.exp; # 2.71828182845905
say 10.exp; # 22026.4657948067
```

## routine round

```
multi method round(Cool:D: $unit = 1)
multi sub round(Numeric(Cool))
```

Coerces the invocant (or in sub form, its argument) to Numeric, and rounds it to the unit of `$unit`

. If `$unit`

is 1, rounds to the nearest integer.

```
say 1.7.round; # 2
say 1.07.round(0.1); # 1.1
say 21.round(10); # 20
```

## routine floor

```
multi method floor
multi sub floor(Numeric(Cool))
```

Coerces the invocant (or in sub form, its argument) to Numeric, and rounds it downwards to the nearest integer.

```
say "1.99".floor; # 1
say "-1.9".floor; # -2
say 0.floor; # 0
```

## routine ceiling

```
multi method ceiling
multi sub ceiling(Numeric(Cool))
```

Coerces the invocant (or in sub form, its argument) to Numeric, and rounds it upwards to the nearest integer.

```
say "1".ceiling; # 1
say "-0.9".ceiling; # 0
say "42.1".ceiling; # 43
```

## routine truncate

```
multi method truncate()
multi sub truncate(Numeric(Cool))
```

Coerces the invocant (or in sub form, its argument) to Numeric, and rounds it towards zero.

```
say 1.2.truncate # 1
say truncate -1.2; # -1
```

## routine ord

```
method ord()
sub ord(Str(Cool))
```

Coerces the invocant (or in sub form, its argument) to Str, and returns the Unicode code point, number of the code point.

```
say 'a'.ord; # 65
```

The inverse operation is chr.

Mnemonic: returns an ordinal number

## routine chr

```
method chr()
sub chr(Int(Cool))
```

Coerces the invocant (or in sub form, its argument) to Int, interprets it as a Unicode code points, and returns a string made of that code point.

```
say '65'.chr; # A
```

The inverse operation is ord.

Mnemonic: turns an integer into a *char*acter.

## routine chars

```
method chars()
sub chars(Str(Cool))
```

Coerces the invocant (or in sub form, its argument) to Str, and returns the number of characters in the string. Characters should actually be grapheme clusters, though current implementations erroneously count codepoints instead.

```
say 'møp'.chars; # 3
```

## routine codes

```
method codes()
sub codes(Str(Cool))
```

Coerces the invocant (or in sub form, its argument) to Str, and returns the number of Unicode code points.

```
say 'møp'.codes; # 3
```

## routine flip

```
method flip()
sub flip(Str(Cool))
```

Coerces the invocant (or in sub form, its argument) to Str, and returns a reversed version.

```
say 421.flip; # 124
```

## routine trim

```
method trim()
sub trim(Str(Cool))
```

Coerces the invocant (or in sub form, its argument) to Str, and returns the string with both leading and trailing whitespace stripped.

```
my $stripped = ' abc '.trim;
say "<$stripped>"; # <abc>
```

## routine trim-leading

```
method trim-leading()
sub trim-leading(Str(Cool))
```

Coerces the invocant (or in sub form, its argument) to Str, and returns the string with leading whitespace stripped.

```
my $stripped = ' abc '.trim-leading;
say "<$stripped>"; # <abc >
```

## routine trim-trailing

```
method trim-trailing()
sub trim-trailing(Str(Cool))
```

Coerces the invocant (or in sub form, its argument) to Str, and returns the string with trailing whitespace stripped.

```
my $stripped = ' abc '.trim-trailing;
say "<$stripped>"; # < abc>
```

## routine lc

```
method lc()
sub lc(Str(Cool))
```

Coerces the invocant (or in sub form, its argument) to Str, and returns it case-folded to lower case.

```
say "ABC".lc; # abc
```

## routine uc

```
method uc()
sub uc(Str(Cool))
```

Coerces the invocant (or in sub form, its argument) to Str, and returns it case-folded to upper case (capital letters).

```
say "Abc".uc; # ABC
```

## routine tc

```
method tc()
sub tc(Str(Cool))
```

Coerces the invocant (or in sub form, its argument) to Str, and returns it with the first letter case-folded to title case (or where not available, upper case).

```
say "abC".tc; # AbC
```

## routine tclc

```
method tclc()
sub tclc(Str(Cool))
```

Coerces the invocant (or in sub form, its argument) to Str, and returns it with the first letter case-folded to title case (or where not available, upper case), and the rest of the string case-folded to lower case..

```
say 'abC'.tclc; # Abc
```

## routine wordcase

```
method wordcase(:&filter = &tclc, Mu :$where = True)
sub wordcase(Str(Cool) $input, :&filter = &tclc, Mu :$where = True)
```

Coerces the invocant (or in sub form, the first argument) to Str, and filters each word that smart-matches against `$where`

through the `&filter`

. With the default filter (first character to upper case, rest to lower) and matcher (which accepts everything), this title-cases each word:

```
say "perl 6 programming".wordcase; # Perl 6 Programming
```

With a matcher:

```
say "have fun working on perl".wordcase(:where({ .chars > 3 }));
# Have fun Working on Perl
```

With a customer filter too:

```
say "have fun working on perl".wordcase(:filter(&uc), :where({ .chars > 3 }));
# HAVE fun WORKING on PERL
```

## routine uniname

```
method uniname() returns Str
sub uniname(Str(Cool) returns Str
```

Interprets the invocant / first argument as a /type/Str, and returns the Unicode codepoint name of the first character.

## routine chop

```
method chop()
sub chop(Str(Cool))
```

Coerces the invocant (or in sub form, its argument) to Str, and returns it with the last character removed.

```
say 'perl'.chop; # per
```

## routine chomp

```
method chomp()
sub chomp(Str(Cool))
```

Coerces the invocant (or in sub form, its argument) to Str, and returns it with the last character removed, if it is a logical newline.

```
say 'ab'.chomp.chars; # 2
say "a\n".chomp.chars; # 1
```

## routine substr

```
method substr($from, $chars?)
sub substr(Str(Cool) $str, $from, $chars?)
```

Coerces the invocant (or in the sub form, the first argument) to Str, and returns the string starting from offset `$from`

. If `$chars`

is supplied, at most `$chars`

characters are returned.

```
say 'zenith'.substr(2); # nith
say 'zenith'.substr(0, 3); # zen
# works on non-strings too:
say 20151224.substr(6); # 24
# sub form:
say substr "zenith", 0, 3; # zen
```

If the `$from`

parameter is a Callable, it is called with the number of chars in the string as argument. This allows easy indexing relative to the end:

```
say 20151224.substr(*-2); # 24
```

## routine ords

```
method ords()
sub ords(Str(Cool) $str)
```

Coerces the invocant (or in the sub form, the first argument) to Str, and returns a list of Unicode codepoints for each character.

```
say "Perl 6".ords; # 80 101 114 108 32 54
say ords 10; # 49 48
```

This is the list-returning version of ord. The inverse operation in chrs.

## routine chrs

```
method chrs()
sub chrs(*@codepoints) return Str:D
```

Coerces the invocant (or in the sub form, the argument list) to a list of integers, and returns the string created by interpreting each integer as a Unicode codepoint, and joining the characters.

```
say <80 101 114 108 32 54>.chrs; # Perl 6
```

This is the list-input version of chr. The inverse operation is ords.

## routine split

```
multi method split( Str:D $delimiter, $limit = Inf, :$all)
multi method split(Regex:D $delimiter, $limit = Inf, :$all)
multi sub split( Str:D $delimiter, Str(Cool) $input, $limit = Inf, :$all)
multi sub split(Regex:D $delimiter, Str(Cool) $input, $limit = Inf, :$all)
```

Coerces the invocant (or in the sub form, the second argument) to Str, and splits it into pieces based on delimiters found in the string.

If `$delimiter`

is a string, it is searched for literally and not treated as a regex.

If the named parameter `:all`

is passed, the matches from `$delimiter`

are included in the result list.

Note that unlike in Perl 5, empty chunks are not removed from the result list. If you want that behavior, consider using comb instead.

```
say split(';', "a;b;c").perl; # ("a", "b", "c").list
say split(';', "a;b;c", :all).perl; # ("a", ";", "b", ";", "c").list
say split(';', "a;b;c", 2).perl; # ("a", "b;c").list
say split(';', "a;b;c", 2, :all).perl; #("a", ";", "b;c").list
say split(';', "a;b;c,d").perl; # ("a", "b", "c,d").list
say split(/\;/, "a;b;c,d").perl; # ("a", "b", "c,d").list
say split(/<[;,]>/, "a;b;c,d").perl; # ("a", "b", "c", "d").list
```

## routine lines

```
method lines()
sub lines(Str(Cool))
```

Coerces the invocant (and in sub form, the argument) to Str, decomposes it into lines (with the newline characters stripped), and returns the list of lines.

```
say lines("a\nb\n").join('|'); # a|b
say "some\nmore\nlines".lines.elems; # 3
```

This method can be used as part of an `IO::Path`

to process a file line-by-line, since `IO::Path`

objects inherit from `Cool`

, e.g.:

```
for 'huge-csv'.IO.lines -> $line {
# Do something with $line
}
# or if you'll be processing later
my @lines = 'huge-csv'.IO.lines;
```

## method words

```
method words(Int() $limit)
```

Coerces the invocant to Str, and returns a list of words that make up the string (and if `$limit`

is supplied, only the first `$limit`

words).

```
say 'The quick brown fox'.words.join('|'); # The|quick|brown|fox
say 'The quick brown fox'.words(2).join('|'); # The|quick
```

Only whitespace counts as word boundaries

```
say "isn't, can't".words.join('|'); # isn't,|can't
```

## routine comb

```
multi method comb(Regex $matcher, $limit = *) returns List:D
multi sub comb(Regex $matcher, Str(Cool) $input, $limit = *) returns List:D
```

Returns all (or if supplied, at most `$limit`

) matches of the invocant (method form) or the second argument (sub form) against the Regex as a list of strings.

```
say "6 or 12".comb(/\d+/).join(", "); # 6, 12
```

## routine index

```
multi sub index(Str(Cool) $s, Str:D $needle, Int(Cool) $startpos = 0) returns Int
multi method index(Str(Cool) $needle, Int(Cool) $startpos = 0) returns Int
```

Coerces the first two arguments (in method form, also counting the invocant) to Str, and searches for `$needle`

in the string starting from `$startpos`

. It returns the offset into the string where `$needle`

was found, and an undefined value if it was not found.

See the documentation in type Str for examples.

## routine rindex

```
multi sub rindex(Str(Cool) $haystack, Str(Cool) $needle, Int(Cool) $startpos = $haystack.chars)
multi method rindex(Str(Cool) $haystack: Str(Cool) $needle, Int(Cool) $startpos = $haystack.chars)
```

Coerces the first two arguments (including the invocant in method form) to Str and `$startpos`

to Int, and returns the last position of `$needle`

in `$haystack`

not after `$startpos`

. Returns an undefined value if `$needle`

wasn't found.

See the documentation in type Str for examples.

## routine roots

```
multi method roots(Int(Cool) $n)
multi sub roots(Numeric(Cool) $x, Int(Cool) $n)
```

Coerces the first argument (and in method form, the invocant) to Numeric and the second (`$n`

) to Int, and produces a list of `$n`

Complex `$n`

-roots, which means numbers that, raised to the `$n`

th power, approximately produce the original number.

For example

```
my $original = 16;
my @roots = $original.roots(4);
say @roots;
for @roots -> $r {
say abs($r ** 4 - $original);
}
```

produces this output:

```
2+0i 1.22464679914735e-16+2i -2+2.44929359829471e-16i -3.67394039744206e-16-2i
1.77635683940025e-15
4.30267170434156e-15
8.03651692704705e-15
1.04441561648202e-14
```

## method IO

```
method IO() returns IO::Path:D
```

Coerces the invocant to IO::Path.

```
.say for '.'.IO.dir; # gives a directory listing
```

# Routines supplied by class Any

Backtrace inherits from class Any, which provides the following methods:

## method ACCEPTS

```
multi method ACCEPTS(Any:D: Mu $other)
```

Returns `True`

if `$other === self`

(i.e. it checks object identity).

Many built-in types override this for more specific comparisons

## method any

```
method any() returns Junction:D
```

Interprets the invocant as a list and creates an `any`

-Junction from it.

```
say so 2 == <1 2 3>.any; # True
say so 5 == <1 2 3>.any; # False
```

## method all

```
method all() returns Junction:D
```

Interprets the invocant as a list and creates an `all`

-Junction from it.

```
say so 1 < <2 3 4>.all; # True
say so 3 < <2 3 4>.all; # False
```

## method one

```
method one() returns Junction:D
```

Interprets the invocant as a list and creates an `one`

-Junction from it.

```
say so 1 == (1, 2, 3).one; # True
say so 1 == (1, 2, 1).one; # False
```

## method none

```
method none() returns Junction:D
```

Interprets the invocant as a list and creates an `none`

-Junction from it.

```
say so 1 == (1, 2, 3).none; # False
say so 4 == (1, 2, 3).none; # True
```

## method list

Interprets the invocant as a list, and returns that List.

```
say so 42.list.^name; # List
say so 42.list.elems; # 1
```

## method flat

Interprets the invocant as a list, flattens it, and returns that list.

```
say ((1, 2), (3)).elems; # 2
say ((1, 2), (3)).flat.elems; # 3
```

## method eager

Interprets the invocant as a list, evaluates it eagerly, and returns that list.

```
say (1..10).eager; # 1 2 3 4 5 6 7 8 9 10
```

## method elems

Interprets the invocant as a list, and returns the number of elements in the list.

```
say 42.elems; # 1
say <a b c>.elems; # 3
```

## method end

Interprets the invocant as a list, and returns the last index of that list.

```
say 6.end; # 0
say <a b c>.end; # 2
```

## method pairup

```
method pairup() returns List
```

Interprets the invocant as a list, and constructs a list of pairs from it, in the same way that assignment to a Hash does. That is, it takes two consecutive elements and constructs a pair from them, unless the item in the key position already is a pair (in which case the pair is passed is passed through, and the next list item, if any, is considered to be a key again).

```
say (a => 1, 'b', 'c').pairup.perl; # ("a" => 1, "b" => "c").list
```

## sub exit

```
sub exit(Int() $status = 0)
```

Exits the current process with return code `$status`

.

# Routines supplied by class Mu

Backtrace inherits from class Mu, which provides the following methods:

## routine defined

```
multi sub defined(Mu) returns Bool:D
multi method defined() returns Bool:D
```

Returns `False`

on the type object, and `True`

otherwise.

```
say Int.defined; # False
say 42.defined; # True
```

Very few types (like Failure) override `defined`

to return `False`

even for instances:

```
sub fails() { fail 'oh noe' };
say fails().defined; # False
```

## routine Bool

```
multi sub Bool(Mu) returns Bool:D
multi method Bool() returns Bool:D
```

Returns `False`

on the type object, and `True`

otherwise.

Many built-in types override this to be `False`

for empty collections, the empty string or numerical zeros

```
say Mu.Bool; # False
say Mu.new.Bool; # True
say [1, 2, 3].Bool; # True
say [].Bool; # False
say { 'hash' => 'full'}.Bool; # True
say {}.Bool; # False
```

## method Str

```
multi method Str() returns Str
```

Returns a string representation of the invocant, intended to be machine readable. Method `Str`

warns on type objects, and produces the empty string.

```
say Mu.Str; #!> use of uninitialized value of type Mu in string context
```

## routine gist

```
multi sub gist(Mu) returns Str
multi method gist() returns Str
```

Returns a string representation of the invocant, optimized for fast recognition by humans.

The default `gist`

method in `Mu`

re-dispatches to the perl method for defined invocants, and returns the type name in parenthesis for type object invocants. Many built-in classes override the case of instances to something more specific.

`gist`

is the method that say calls implicitly, so `say $something`

and `say $something.gist`

generally produce the same output.

```
say Mu.gist; # (Mu)
say Mu.new.gist; # Mu.new()
```

## routine perl

```
multi sub perl(Mu) returns Str
multi method perl() returns Str
```

Returns a Perlish representation of the object (i.e., can usually be re-evaluated with EVAL to regenerate the object). The exact output of `perl`

is implementation specific, since there are generally many ways to write a Perl expression that produces a particular value

## method clone

```
method clone(*%twiddles)
```

Creates a shallow clone of the invocant. If named arguments are passed to it, their values are used in every place where an attribute name matches the name of a named argument.

```
class Point2D {
has ($.x, $.y);
multi method gist(Point2D:D:) {
"Point($.x, $.y)";
}
}
my $p = Point2D.new(x => 2, y => 3);
say $p; # Point(2, 3)
say $p.clone(y => -5); # Point(2, -5)
```

## method new

```
multi method new(*%attrinit)
```

Default method for constructing (create + initialize) new objects of a class. This method expects only named arguments which are then used to initialize attributes with accessors of the same name.

Classes may provide their own `new`

method to override this default.

`new`

triggers an object construction mechanism that calls submethods named `BUILD`

in each class of an inheritance hierarchy, if they exist. See the documentation on object construction for more information.

## method bless

```
method bless(*%attrinit) returns Mu:D
```

Lower-level object construction method than `new`

.

Creates a new object of the same type as the invocant, uses the named arguments to initialize attributes, and returns the created object.

You can use this method when writing custom constructors:

```
class Point {
has $.x;
has $.y;
multi method new($x, $y) {
self.bless(:$x, :$y);
}
}
my $p = Point.new(-1, 1);
```

(Though each time you write a custom constructor, remember that it makes subclassing harder).

## method CREATE

```
method CREATE() returns Mu:D
```

Allocates a new object of the same type as the invocant, without initializing any attributes.

```
say Mu.CREATE.defined; # True
```

## method print

```
multi method print() returns Bool:D
```

Prints value to `$*OUT`

after stringification using `.Str`

method without adding a newline at end.

```
"abc\n".print; # abc
```

## method say

```
multi method say() returns Bool:D
```

Prints value to `$*OUT`

after stringification using `.gist`

method with newline at end.

```
say 42; # 42
```

## method ACCEPTS

```
multi method ACCEPTS(Mu:U: $other)
```

`ACCEPTS`

is the method that smart matching with the infix ~~ operator and given/when invokes on the right-hand side (the matcher).

The `Mu:U`

multi performs a type check. Returns `True`

if `$other`

conforms to the invocant (which is always a type object or failure).

```
say 42 ~~ Mu; # True
say 42 ~~ Int; # True
say 42 ~~ Str; # False
```

Note that there is no multi for defined invocants; this is to allow autothreading of junctions, which happens as a fallback mechanism when no direct candidate is available to dispatch to.

## method WHICH

```
multi method WHICH() returns ObjAt:D
```

Returns an object of type ObjAt which uniquely identifies the object. Value types override this method which makes sure that two equivalent objects return the same return value from `WHICH`

.

```
say 42.WHICH eq 42.WHICH; # True
```

## method WHERE

```
method WHERE() returns Int
```

Returns an `Int`

representing the memory address of the object.

## method WHY

```
multi method WHY()
```

Returns the attached Pod value. For instance,

```
sub cast(Spell $s)
#= Initiate a specified spell normally
#= (do not use for class 7 spells)
{
do-raw-magic($s);
}
say &cast.WHY;
```

prints

```
Initiate a specified spell normally (do not use for class 7 spells)
```

See the documentation specification for details about attaching Pod to variables, classes, functions, methods, etc.

## trait is export

```
multi sub trait_mod:<is>(Mu:U \type, :$export!)
```

Marks a type as being exported, that is, available to external users.

```
my class SomeClass is export { }
```

A user of a module or class automatically gets all the symbols imported that are marked as `is export`

.

## method take

```
method take()
```

Takes the given item and passes it to the enclosing `gather`

block.

```
#| randomly select numbers for lotto
my $num-selected-numbers = 6;
my $max-lotto-numbers = 49;
gather for ^$num-selected-numbers {
take (1 .. $max-lotto-numbers).pick(1);
}.say; #-> 32 22 1 17 32 9 (for example)
```

## method so

```
method so()
```

Returns a `Bool`

value representing the logical non-negation of an expression. One can use this method similarly to the English sentence: "If that is **so**, then do this thing". For instance,

```
my @args = <-a -e -b -v>;
my $verbose-selected = any(@args) eq '-v' | '-V';
if $verbose-selected.so {
say "Verbose option detected in arguments";
} #-> Verbose option detected in arguments
```

## method not

```
method not()
```

Returns a `Bool`

value representing the logical negation of an expression. Thus it is the opposite of `so`

.

```
my @args = <-a -e -b>;
my $verbose-selected = any(@args) eq '-v' | '-V';
if $verbose-selected.not {
say "Verbose option not present in arguments";
} #-> Verbose option not present in arguments
```

Since there is also a prefix version of `not`

, the above code reads better like so:

```
my @args = <-a -e -b>;
my $verbose-selected = any(@args) eq '-v' | '-V';
if not $verbose-selected {
say "Verbose option not present in arguments";
} #-> Verbose option not present in arguments
```