Are set operations needed in Perl6? No implementation of the perl6 set
specification yet exists (AFAIK).
The question occurred to me as I have been working my way through a new
book on foundational maths not based on sets
(http://homotopytypetheory.org/book/). Foundations of maths, until
recently, has been done in terms of set theory and first-order logic.
I wondered whether the desire to have sets in perl6 was driven by
mathematical fashion sensitivity (in some roundabout unconscious way)
and because sets are important to mathematical foundations. Given that
foundational maths may now be done (strictly the goal has not yet been
fully achieved) in homotopy type theory (HoTT), perhaps the imperative
to have sets in perl6 is no longer as strong?
An interesting thing about HoTT is that part of it, namely type theory,
has been driven by computer science. Indeed, part of the power of HoTT
is that it is possible to create computer-aided proof assistants. Sets
do not implement well on a computer.
In other words, perhaps sets, which have already been ring-fenced by
existing implementations, can be cut from the perl6 specification
altogether?
Richard Hainsworth
finanalyst
