class Mix

Immutable collection of distinct objects with Real weights

class Mix does Mixy { }

A Mix is an immutable collection of distinct elements in no particular order that each have a real-number weight assigned to them. (For mutable mixes, see MixHash instead.)

Mixes are often used for performing weighted random selections - see .roll.

Objects/values of any type are allowed as mix elements. Within a Mix, items that would compare positively with the === operator are considered the same element, with a combined weight.

my $recipe = (butter => 0.22, sugar => 0.1,
              flour => 0.275, sugar => 0.02).Mix;
 
say $recipe.elems;      # OUTPUT: «3␤» 
say $recipe.keys.sort;  # OUTPUT: «butter flour sugar␤» 
say $recipe.pairs.sort; # OUTPUT: «"butter" => 0.22 "flour" => 0.275 "sugar" => 0.12␤» 
say $recipe.total;      # OUTPUT: «0.615␤» 

Mixes can be treated as object hashes using the { } postcircumfix operator, which returns the corresponding numeric weight for keys that are elements of the mix, and 0 for keys that aren't:

my $recipe = (butter => 0.22, sugar => 0.1,
              flour => 0.275, sugar => 0.02).Mix;
say $recipe<butter>;     # OUTPUT: «0.22␤» 
say $recipe<sugar>;      # OUTPUT: «0.12␤» 
say $recipe<chocolate>;  # OUTPUT: «0␤»

Creating Mix objects

Mixes can be composed using the mix subroutine (or Mix.new, for which it is a shorthand). Any positional parameters, regardless of their type, become elements of the mix - with a weight of 1 for each time the parameter occurred:

my $n = mix "a", "a", "b" => 0, 3.14, π, π; # The Pair is a single element 
say $n.keys.map: *.^name; # OUTPUT: «(Rat Pair Num Str)␤» 
say $n.pairs;
# OUTPUT: «(3.14 => 1 (b => 0) => 1 3.141592653589793 => 2 a => 2)␤»

Alternatively, the .Mix coercer (or its functional form, Mix()) can be called on an existing object to coerce it to a Mix. Its semantics depend on the type and contents of the object. In general it evaluates the object in list context and creates a mix with the resulting items as elements, although for Hash-like objects or Pair items, only the keys become elements of the mix, and the (cumulative) values become the associated numeric weights:

my $n = ("a", "a", "b" => 0, "c" => 3.14).Mix;
say $n.keys.map(&WHAT);  # OUTPUT: «((Str) (Str))␤» 
say $n.pairs;            # OUTPUT: «(a => 2 c => 3.14)␤»

Elements with a 0 value, as b above, are simply eliminated from the Mix.

Alternatively, since Mixes are Associative, we can use the % sigil to declare them; in that case, we can employ is to declare their type:

my %n is Mix = ("a", "a", "b" => 0, "c" => 3.14);
say %n.^name; # OUTPUT: «Mix␤» 
say %n;       # OUTPUT: «Mix(a(2), c(3.14))␤»

Since 6.d (2019.03 and later) it is also possible to specify the type of values you would like to allow in a Mix. This can either be done when calling .new:

# only allow strings 
my $n = Mix[Str].new: <a b b c c c>;

or using the masquerading syntax:

# only allow strings 
my %m is Mix[Str] = <a b b c c c>;
say %m<b>;  # 2 
say %m<d>;  # 0 
 
# only allow whole numbers 
my %m is Mix[Int] = <a b b c c c>;
# Type check failed in binding; expected Int but got Str ("a")

Operators

Mixes can use all kind of set operators returning either Bool or other Mixes:

my $this-mix = (sugar => ⅓, spice => ¼, all-things-nice => ¾);
my $that-mix = ( sugar => 1, spice => 2);
 
say $that-mix (<) $this-mix;     # OUTPUT: «True␤» 
say $that-mix (^) $this-mix;     # OUTPUT: «set(all-things-nice)␤» 
say $that-mix (+) $this-mix;     # OUTPUT: «Bag(spice(2), sugar)␤» 

With their equivalent Unicode operators:

say $that-mix ⊂ $this-mix;     # OUTPUT: «True␤» 
say $that-mix ⊖ $this-mix;     # OUTPUT: «set(all-things-nice)␤» 
say $that-mix ⊎ $this-mix;     # OUTPUT: «Bag(spice(2), sugar)␤» 

See Set/Bag Operators for a complete list of set and bag operators with detailed explanations.

sub mix

sub mix(*@args --> Mix)

Creates a new Mix from @args.

Methods

method Bag

Defined as:

method Bag (--> Bag:D)

Coerces the Mix to a Bag. The weights are convert to Int, which means the number of keys in the resulting Bag can be fewer than in the original Mix, if any of the weights are negative or truncate to zero.

method BagHash

Defined as:

method BagHash (--> BagHash:D)

Coerces the Mix to a BagHash. The weights are convert to Int, which means the number of keys in the resulting BagHash can be fewer than in the original Mix, if any of the weights are negative or truncate to zero.

method reverse

Note: This method is inherited from Any, however, Mixes do not have an inherent order and you should not trust it returning a consistent output.

Note on order

Same as the other elements in the Bag/Mix suite, order is not guaranteed or consistent and you shouldn't rely on methods like reverse above returning always the same result.

See Also

Sets, Bags, and Mixes

Type Graph

Type relations for Mix
perl6-type-graph Mix Mix Any Any Mix->Any Mixy Mixy Mix->Mixy Mu Mu Any->Mu Associative Associative QuantHash QuantHash QuantHash->Associative Baggy Baggy Baggy->QuantHash Mixy->Baggy

Expand above chart

Routines supplied by role Mixy

Mix does role Mixy, which provides the following routines:

(Mixy) method total

method total(--> Real)

Returns the sum of all the weights

say mix('a', 'b', 'c', 'a', 'a', 'd').total == 6;  # OUTPUT: «True␤» 
say %(a => 5.6, b => 2.4).Mix.total == 8;          # OUTPUT: «True␤»

(Mixy) method roll

method roll($count = 1)

Similar to a Bag.roll, but with Real weights rather than integral ones.

Routines supplied by role Baggy

Mix does role Baggy, which provides the following routines:

(Baggy) method new-from-pairs

Defined as:

method new-from-pairs(*@pairs --> Baggy:D)

Constructs a Baggy objects from a list of Pair objects given as positional arguments:

say Mix.new-from-pairs: 'butter' => 0.22, 'sugar' => 0.1, 'sugar' => 0.02;
# OUTPUT: «mix(butter(0.22), sugar(0.12))␤»

Note: be sure you aren't accidentally passing the Pairs as positional arguments; the quotes around the keys in the above example are significant.

(Baggy) method grab

Defined as:

multi method grab(Baggy:D: --> Any)
multi method grab(Baggy:D: $count --> Seq:D)

Like pick, a grab returns a random selection of elements, weighted by the values corresponding to each key. Unlike pick, it works only on mutable structures, e.g. BagHash. Use of grab on an immutable structure results in an X::Immutable exception. If * is passed as $count, or $count is greater than or equal to the total of the invocant, then total elements from the invocant are returned in a random sequence; i.e. they are returned shuffled.

Grabbing decrements the grabbed key's weight by one (deleting the key when it reaches 0). By definition, the total of the invocant also decreases by one, so the probabilities stay consistent through subsequent grab operations.

my $cars = ('Ford' => 2, 'Rover' => 3).BagHash;
say $cars.grab;                                   # OUTPUT: «Ford␤» 
say $cars.grab(2);                                # OUTPUT: «(Rover Rover)␤» 
say $cars.grab(*);                                # OUTPUT: «(Rover Ford)␤» 
 
my $breakfast = ('eggs' => 2, 'bacon' => 3).Bag;
say $breakfast.grab;
CATCH { default { put .^name, ': ', .Str } };
# OUTPUT: «X::Immutable: Cannot call 'grab' on an immutable 'Bag'␤»

(Baggy) method grabpairs

Defined as:

multi method grabpairs(Baggy:D: --> Any)
multi method grabpairs(Baggy:D: $count --> Seq:D)

Returns a Pair or a Seq of Pairs depending on the version of the method being invoked. Each Pair returned has an element of the invocant as its key and the elements weight as its value. Unlike pickpairs, it works only on mutable structures, e.g. BagHash. Use of grabpairs on 'an immutable structure results in an X::Immutable exception. If * is passed as $count, or $count is greater than or equal to the number of elements of the invocant, then all element/weight Pairs from the invocant are returned in a random sequence.

What makes grabpairs different from pickpairs is that the 'grabbed' elements are in fact removed from the invocant.

my $breakfast = (eggs => 2, bacon => 3).BagHash;
say $breakfast.grabpairs;                         # OUTPUT: «bacon => 3␤» 
say $breakfast;                                   # OUTPUT: «BagHash.new(eggs(2))␤» 
say $breakfast.grabpairs(1);                      # OUTPUT: «(eggs => 2)␤» 
say $breakfast.grabpairs(*);                      # OUTPUT: «()␤» 
 
my $diet = ('eggs' => 2, 'bacon' => 3).Bag;
say $diet.grabpairs;
CATCH { default { put .^name, ': ', .Str } };
# OUTPUT: «X::Immutable: Cannot call 'grabpairs' on an immutable 'Bag'␤»

(Baggy) method pick

Defined as:

multi method pick(Baggy:D: --> Any)
multi method pick(Baggy:D: $count --> Seq:D)

Like an ordinary list pick, but returns keys of the invocant weighted by their values, as if the keys were replicated the number of times indicated by the corresponding value and then list pick used. The underlying metaphor for picking is that you're pulling colored marbles out a bag. (For "picking with replacement" see roll instead). If * is passed as $count, or $count is greater than or equal to the total of the invocant, then total elements from the invocant are returned in a random sequence.

Note that each pick invocation maintains its own private state and has no effect on subsequent pick invocations.

my $breakfast = bag <eggs bacon bacon bacon>;
say $breakfast.pick;                              # OUTPUT: «eggs␤» 
say $breakfast.pick(2);                           # OUTPUT: «(eggs bacon)␤» 
 
say $breakfast.total;                             # OUTPUT: «4␤» 
say $breakfast.pick(*);                           # OUTPUT: «(bacon bacon bacon eggs)␤»

(Baggy) method pickpairs

Defined as:

multi method pickpairs(Baggy:D: --> Pair:D)
multi method pickpairs(Baggy:D: $count --> Seq:D)

Returns a Pair or a Seq of Pairs depending on the version of the method being invoked. Each Pair returned has an element of the invocant as its key and the elements weight as its value. The elements are 'picked' without replacement. If * is passed as $count, or $count is greater than or equal to the number of elements of the invocant, then all element/weight Pairs from the invocant are returned in a random sequence.

Note that each pickpairs invocation maintains its own private state and has no effect on subsequent pickpairs invocations.

my $breakfast = bag <eggs bacon bacon bacon>;
say $breakfast.pickpairs;                         # OUTPUT: «eggs => 1␤» 
say $breakfast.pickpairs(1);                      # OUTPUT: «(bacon => 3)␤» 
say $breakfast.pickpairs(*);                      # OUTPUT: «(eggs => 1 bacon => 3)␤»

(Baggy) method roll

Defined as:

multi method roll(Baggy:D: --> Any:D)
multi method roll(Baggy:D: $count --> Seq:D)

Like an ordinary list roll, but returns keys of the invocant weighted by their values, as if the keys were replicated the number of times indicated by the corresponding value and then list roll used. The underlying metaphor for rolling is that you're throwing $count dice that are independent of each other, which (in bag terms) is equivalent to picking a colored marble out your bag and then putting it back, and doing this $count times. In dice terms, the number of marbles corresponds to the number of sides, and the number of marbles of the same color corresponds to the number of sides with the same color. (For "picking without replacement" see pick instead).

If * is passed to $count, returns a lazy, infinite sequence of randomly chosen elements from the invocant.

my $breakfast = bag <eggs bacon bacon bacon>;
say $breakfast.roll;                                  # OUTPUT: «bacon␤» 
say $breakfast.roll(3);                               # OUTPUT: «(bacon eggs bacon)␤» 
 
my $random_dishes := $breakfast.roll(*);
say $random_dishes[^5];                               # OUTPUT: «(bacon eggs bacon bacon bacon)␤»

(Baggy) method pairs

Defined as:

method pairs(Baggy:D: --> Seq:D)

Returns all elements and their respective weights as a Seq of Pairs where the key is the element itself and the value is the weight of that element.

my $breakfast = bag <bacon eggs bacon>;
my $seq = $breakfast.pairs;
say $seq.sort;                                    # OUTPUT: «(bacon => 2 eggs => 1)␤»

(Baggy) method antipairs

Defined as:

method antipairs(Baggy:D: --> Seq:D)

Returns all elements and their respective weights as a Seq of Pairs, where the element itself is the value and the weight of that element is the key, i.e. the opposite of method pairs.

my $breakfast = bag <bacon eggs bacon>;
my $seq = $breakfast.antipairs;
say $seq.sort;                                    # OUTPUT: «(1 => eggs 2 => bacon)␤»

(Baggy) method invert

Defined as:

method invert(Baggy:D: --> Seq:D)

Returns all elements and their respective weights as a Seq of Pairs, where the element itself is the value and the weight of that element is the key, i.e. the opposite of method pairs. Except for some esoteric cases invert on a Baggy type returns the same result as antipairs.

my $breakfast = bag <bacon eggs bacon>;
my $seq = $breakfast.invert;
say $seq.sort;                                    # OUTPUT: «(1 => eggs 2 => bacon)␤»

(Baggy) method classify-list

Defined as:

multi method classify-list(&mapper, *@list --> Baggy:D)
multi method classify-list(%mapper, *@list --> Baggy:D)
multi method classify-list(@mapper, *@list --> Baggy:D)

Populates a mutable Baggy by classifying the possibly-empty @list of values using the given mapper. The @list cannot be lazy.

say BagHash.new.classify-list: { $_ %% 2 ?? 'even' !! 'odd' }, ^10;
# OUTPUT: BagHash.new(even(5), odd(5)) 
 
my @mapper = <zero one two three four five>;
say MixHash.new.classify-list: @mapper, 1, 2, 3, 4, 4, 6;
# OUTPUT: MixHash.new((Any), two, three, four(2), one)

The mapper can be a Callable that takes a single argument, an Associative, or an Iterable. With Associative and an Iterable mappers, the values in the @list represent the key and index of the mapper's value respectively. A Callable mapper will be executed once per each item in the @list, with that item as the argument and its return value will be used as the mapper's value.

The mapper's value is used as the key of the Baggy that will be incremented by 1. See .categorize-list if you wish to classify an item into multiple categories at once.

Note: unlike the Hash's .classify-list, returning an Iterable mapper's value will throw, as Baggy types do not support nested classification. For the same reason, Baggy's .classify-list does not accept :&as parameter.

(Baggy) method categorize-list

Defined as:

multi method categorize-list(&mapper, *@list --> Baggy:D)
multi method categorize-list(%mapper, *@list --> Baggy:D)
multi method categorize-list(@mapper, *@list --> Baggy:D)

Populates a mutable Baggy by categorizing the possibly-empty @list of values using the given mapper. The @list cannot be lazy.

say BagHash.new.categorize-list: {
    gather {
        take 'largish' if $_ > 5;
        take .is-prime ?? 'prime' !! 'non-prime';
        take $_ %% 2   ?? 'even'  !! 'odd';
    }
}, ^10;
# OUTPUT: BagHash.new(largish(4), even(5), non-prime(6), prime(4), odd(5)) 
 
my %mapper = :sugar<sweet white>, :lemon<sour>, :cake('sweet', 'is a lie');
say MixHash.new.categorize-list: %mapper, <sugar lemon cake>;
# OUTPUT: MixHash.new(is a lie, sour, white, sweet(2))

The mapper can be a Callable that takes a single argument, an Associative, or an Iterable. With Associative and an Iterable mappers, the values in the @list represent the key and index of the mapper's value respectively. A Callable mapper will be executed once per each item in the @list, with that item as the argument and its return value will be used as the mapper's value.

The mapper's value is used as a possibly-empty list of keys of the Baggy that will be incremented by 1.

Note: unlike the Hash's .categorize-list, returning a list of Iterables as mapper's value will throw, as Baggy types do not support nested categorization. For the same reason, Baggy's .categorize-list does not accept :&as parameter.

(Baggy) method keys

Defined as:

method keys(Baggy:D: --> Seq:D)

Returns a Seq of all keys in the Baggy object without taking their individual weights into account as opposed to kxxv.

my $breakfast = bag <eggs spam spam spam>;
say $breakfast.keys.sort;                        # OUTPUT: «(eggs spam)␤» 
 
my $n = ("a" => 5, "b" => 2).BagHash;
say $n.keys.sort;                                # OUTPUT: «(a b)␤»

(Baggy) method values

Defined as:

method values(Baggy:D: --> Seq:D)

Returns a Seq of all values, i.e. weights, in the Baggy object.

my $breakfast = bag <eggs spam spam spam>;
say $breakfast.values.sort;                      # OUTPUT: «(1 3)␤» 
 
my $n = ("a" => 5, "b" => 2, "a" => 1).BagHash;
say $n.values.sort;                              # OUTPUT: «(2 6)␤»

(Baggy) method kv

Defined as:

method kv(Baggy:D: --> Seq:D)

Returns a Seq of keys and values interleaved.

my $breakfast = bag <eggs spam spam spam>;
say $breakfast.kv;                                # OUTPUT: «(spam 3 eggs 1)␤» 
 
my $n = ("a" => 5, "b" => 2, "a" => 1).BagHash;
say $n.kv;                                        # OUTPUT: «(a 6 b 2)␤»

(Baggy) method kxxv

Defined as:

method kxxv(Baggy:D: --> Seq:D)

Returns a Seq of the keys of the invocant, with each key multiplied by its weight. Note that kxxv only works for Baggy types which have integer weights, i.e. Bag and BagHash.

my $breakfast = bag <spam eggs spam spam bacon>;
say $breakfast.kxxv.sort;                         # OUTPUT: «(bacon eggs spam spam spam)␤» 
 
my $n = ("a" => 0, "b" => 1, "b" => 2).BagHash;
say $n.kxxv;                                      # OUTPUT: «(b b b)␤»

(Baggy) method elems

Defined as:

method elems(Baggy:D: --> Int:D)

Returns the number of elements in the Baggy object without taking the individual elements weight into account.

my $breakfast = bag <eggs spam spam spam>;
say $breakfast.elems;                             # OUTPUT: «2␤» 
 
my $n = ("b" => 9.4, "b" => 2).MixHash;
say $n.elems;                                     # OUTPUT: «1␤»

(Baggy) method total

Defined as:

method total(Baggy:D:)

Returns the sum of weights for all elements in the Baggy object.

my $breakfast = bag <eggs spam spam bacon>;
say $breakfast.total;                             # OUTPUT: «4␤» 
 
my $n = ("a" => 5, "b" => 1, "b" => 2).BagHash;
say $n.total;                                     # OUTPUT: «8␤»

(Baggy) method default

Defined as:

method default(Baggy:D: --> Int:D)

Returns zero.

my $breakfast = bag <eggs bacon>;
say $breakfast.default;                           # OUTPUT: «0␤»

(Baggy) method hash

Defined as:

method hash(Baggy:D: --> Hash:D)

Returns a Hash where the elements of the invocant are the keys and their respective weights the values.

my $breakfast = bag <eggs bacon bacon>;
my $h = $breakfast.hash;
say $h.^name;                    # OUTPUT: «Hash[Any,Any]␤» 
say $h;                          # OUTPUT: «{bacon => 2, eggs => 1}␤»

(Baggy) method Bool

Defined as:

method Bool(Baggy:D: --> Bool:D)

Returns True if the invocant contains at least one element.

my $breakfast = ('eggs' => 1).BagHash;
say $breakfast.Bool;                              # OUTPUT: «True   (since we have one element)␤» 
$breakfast<eggs> = 0;                             # weight == 0 will lead to element removal 
say $breakfast.Bool;                              # OUTPUT: «False␤»

(Baggy) method Set

Defined as:

method Set(--> Set:D)

Returns a Set whose elements are the keys of the invocant.

my $breakfast = (eggs => 2, bacon => 3).BagHash;
say $breakfast.Set;                               # OUTPUT: «set(bacon, eggs)␤»

(Baggy) method SetHash

Defined as:

method SetHash(--> SetHash:D)

Returns a SetHash whose elements are the keys of the invocant.

my $breakfast = (eggs => 2, bacon => 3).BagHash;
my $sh = $breakfast.SetHash;
say $sh.^name;                            # OUTPUT: «SetHash␤» 
say $sh.elems;                            # OUTPUT: «2␤»

(Baggy) method ACCEPTS

Defined as:

method ACCEPTS($other --> Bool:D)

Used in smartmatching if the right-hand side is a Baggy.

If the right-hand side is the type object, i.e. Baggy, the method returns True if $other does Baggy otherwise False is returned.

If the right-hand side is a Baggy object, True is returned only if $other has the same elements, with the same weights, as the invocant.

my $breakfast = bag <eggs bacon>;
say $breakfast ~~ Baggy;                            # OUTPUT: «True␤» 
say $breakfast.does(Baggy);                         # OUTPUT: «True␤» 
 
my $second-breakfast = (eggs => 1, bacon => 1).Mix;
say $breakfast ~~ $second-breakfast;                # OUTPUT: «True␤» 
 
my $third-breakfast = (eggs => 1, bacon => 2).Bag;
say $second-breakfast ~~ $third-breakfast;          # OUTPUT: «False␤»

Routines supplied by role QuantHash

Mix does role QuantHash, which provides the following routines:

(QuantHash) method hash

method hash()

Coerces the QuantHash object to a Hash (by stringifying the objects for the keys) with the values of the hash limited to the same limitation as QuantHash, and returns that.

(QuantHash) method Hash

method Hash()

Coerces the QuantHash object to a Hash (by stringifying the objects for the keys) without any limitations on the values, and returns that.

(QuantHash) method of

method of()

Returns the type of value a value of this QuantHash may have. This is typically Bool for Setty, UInt for Baggy or Real for Mixy roles.

(QuantHash) method keyof

method keyof()

Returns the type of value a key of this QuantHash may have. This is typically Mu.

(QuantHash) method Setty

method Setty(--> Setty:D)

Coerce the QuantHash object to the equivalent object that uses the Setty role. Note that for Mixy type coercion items with negative values will be skipped.

my %b is Bag = one => 1, two => 2;
say %b.Setty; # OUTPUT: «set(one two)␤» 
my %m is Mix = one => 1, minus => -1;
say %m.Setty; # OUTPUT: «set(one)␤»

(QuantHash) method Baggy

method Baggy(--> Baggy:D)

Coerce the QuantHash object to the equivalent object that uses the Baggy role. Note that for Mixy type coercion items with negative values will be skipped.

my %s is Set = <one two>;
say %s.Baggy; # OUTPUT: «Bag(one, two)␤» 
my %m is Mix = one => 1, minus => -1;
say %m.Baggy; # OUTPUT: «Bag(one)␤»

(QuantHash) method Mixy

method Mixy(--> Mixy:D)

Coerce the QuantHash object to the equivalent object that uses the Mixy role.

my %s is Set = <one two>;
say %s.Mixy; # OUTPUT: «Mix(one, two)␤» 
my %b is Bag = one => 1, two => 2;
say %b.Mixy; # OUTPUT: «Mix(one, two)␤»

Routines supplied by role Associative

Mix does role Associative, which provides the following routines:

(Associative) method of

Defined as:

method of()

Associative is actually a parameterized role which can use different classes for keys and values. As seen at the top of the document, by default it coerces to Str for the key and uses a very generic Mu for value.

my %any-hash;
say %any-hash.of;#  OUTPUT: «(Mu)␤»

The value is the first parameter you use when instantiating Associative with particular classes:

class DateHash is Hash does Associative[Cool,DateTime] {};
my %date-hash := DateHash.new;
say %date-hash.of; # OUTPUT: «(Cool)␤»

(Associative) method keyof

Defined as:

method keyof()

Returns the parameterized key used for the Associative role, which is Any coerced to Str by default. This is the class used as second parameter when you use the parameterized version of Associative.

my %any-hash;
%any-hash.keyof; #OUTPUT: «(Str(Any))␤»

(Associative) method AT-KEY

method AT-KEY(\key)

Should return the value / container at the given key.

(Associative) method EXISTS-KEY

method EXISTS-KEY(\key)

Should return a Bool indicating whether the given key actually has a value.

(Associative) method STORE

method STORE(\values, :$initialize)

This method should only be supplied if you want to support the:

my %h is Foo = a => 42, b => 666;

syntax for binding your implementation of the Associative role.

Should accept the values to (re-)initialize the object with, which either could consist of Pairs, or separate key/value pairs. The optional named parameter will contain a True value when the method is called on the object for the first time. Should return the invocant.