Indeed if having an execution of O(1) is switch's primary benefit, that will not be present in Perl6's switch, except perhaps in primitive uses. C's switches must have constant case labels to facilitate the chicanery it uses for producing O(1) behavior. Perl6 will not enforce constants as the "labels". From what I understand, you'll be able to use any Perl expression you wish as a label. Therefore, each one will need to be evaluated, at runtime, to find the correct one. I think in this case, the benefit to the switch statement for Perl would be its conciseness over using chained if/elses.
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