From language/operators

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multi sub infix:<cmp>(Any,       Any)
multi sub infix:<cmp>(Real:D,    Real:D)
multi sub infix:<cmp>(Str:D,     Str:D)
multi sub infix:<cmp>(Version:D, Version:D)

Generic, "smart" three-way comparator.

Compares strings with string semantics, numbers with number semantics, Pair objects first by key and then by value etc.

if $a eqv $b, then $a cmp $b always returns Order::Same.

say (a => 3) cmp (a => 4);   # OUTPUT: «Less␤» 
say 4        cmp 4.0;        # OUTPUT: «Same␤» 
say 'b'      cmp 'a';        # OUTPUT: «More␤»

Strings are compared codepoint by codepoint; if leading codepoints are the same, the result of comparing the first differing codepoint is returned or the longer string if their lengths differ.

"abcd" cmp "abcde";    # OUTPUT: «Less␤» 
"abcd " cmp "abcde";   # OUTPUT: «Less␤» 
'A' cmp 'Ẳ';           # OUTPUT: «Less␤»

From type/Allomorph

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multi sub infix:<cmp>(Allomorph:D $a, Allomorph:D $b)

Compare two Allomorph objects. The comparison is done on the Numeric value first and then on the Str value. If you want to compare in a different order then you would coerce to an Numeric or Str value first:

my $f = IntStr.new(42, "smaller");
my $g = IntStr.new(43, "larger");
say $f cmp $g;          # OUTPUT: «Less␤» 
say $f.Str cmp $g.Str;  # OUTPUT: «More␤»

From type/Pair

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multi sub infix:<cmp>(Pair:D, Pair:D)

The type-agnostic comparator; compares two Pairs. Compares first their key parts, and then compares the value parts if the keys are equal.

my $a = (Apple => 1);
my $b = (Apple => 2);
say $a cmp $b; # OUTPUT: «Less␤»

From type/List

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multi sub infix:<cmp>(List @a, List @b)

Evaluates Lists by comparing element @a[$i] with @b[$i] (for some Int $i, beginning at 0) and returning Order::Less, Order::Same, or Order::More depending on if and how the values differ. If the operation evaluates to Order::Same, @a[$i + 1] is compared with @b[$i + 1]. This is repeated until one is greater than the other or all elements are exhausted.

If the Lists are of different lengths, at most only $n comparisons will be made (where $n = @a.elems min @b.elems). If all of those comparisons evaluate to Order::Same, the final value is selected based upon which List is longer.

say (1, 2, 3) cmp (1, 2, 3);   # OUTPUT: «Same␤» 
say (4, 5, 6) cmp (4, 5, 7);   # OUTPUT: «Less␤» 
say (7, 8, 9) cmp (7, 8, 8);   # OUTPUT: «More␤» 
 
say (1, 2)    cmp (1, 2, 3);   # OUTPUT: «Less␤» 
say (1, 2, 3) cmp (1, 2);      # OUTPUT: «More␤» 
say (9).List  cmp (^10).List;  # OUTPUT: «More␤»

From type/Order

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multi sub infix:<cmp>(\a, \b --> Order:D)

cmp will first try to compare operands as strings (via coercion to Stringy), and, failing that, will try to compare numerically via the <=> operator or any other type-appropriate comparison operator. See also the documentation for the cmp operator.