perl-diddler:

From the docs:

The "=>" operator is a synonym for the comma except that it causes its left operand to be interpreted as a string if it begins with a letter or underscore and is composed only of letters, digits and underscores. This includes operands that might otherwise be interpreted as operators, constants, single number v-strings or function calls. If in doubt about this behaviour, the left operand can be quoted explicitly.

So I'd suggest just using a comma:

my %map = (
  Page, 'mypage',
  Index, 'myindex',
);
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Notes: (1) Untested, as I don't recall ever using the constant module before, and (2) Yes, it looks strange to me, too!

...roboticus