[ruby-core:52574] [ruby-trunk - Feature #7738] Deprecate Set#+ as an alias of Set#|, use it for symmetric difference. Introduce Hash#| for Hash#reverse_merge in Rails.

Issue #7738 has been updated by alexeymuranov (Alexey Muranov).


In fact, sets (or rather subsets of a given set) form a Boolean ring ( http://en.wikipedia.org/wiki/Boolean_ring ) under the following two operations:
 - the product is the set intersection and
 - the sum is the set symmetric difference.
However, according to the Wikipedia article, it is accepted to use `+` for the union (which is not the ring addition) in this case, contrary to what i thought.

So maybe it is alright to have it this way in Ruby, except that there are two symbols for the same operation.
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Feature #7738: Deprecate Set#+ as an alias of Set#|, use it for symmetric difference.  Introduce Hash#| for Hash#reverse_merge in Rails.
https://bugs.ruby-lang.org/issues/7738#change-36669

Author: alexeymuranov (Alexey Muranov)
Status: Open
Priority: Normal
Assignee: 
Category: 
Target version: Next Major


=begin
I am almost sure this will be rejected, but i want to try anyway.  My goal is to propose a more efficient and consistent use of binary operator symbols for some classes, in this case for (({Set})) and (({Hash})).

I propose to deprecate (({Set#+})) as an alias of (({Set#|})), and use (({Set#+})) later for the ((*symmetric difference*)) of sets.  I think that operator symbols like (({+})) and (({|})) are too precious to alias one another.

Currently (({Set#+})) is probably the only use of (({#+})) for an operation which is not ((*injective*)) in each of the arguments: for sets (({a})), (({b})), (({c})), the equality

  a + b == a + c

does not currently imply

  b == c

The natural binary operation on sets that is injective in each argument is the ((*symmetric difference*)), it corresponds to the bitwise XOR.  I have also noticed that the "(({+}))" for sets is used in "Lectures on ergodic theory " by P. Halmos to denote the symmetric difference.

I also suggest for to define (({Hash#|})) as Hash#reverse_merge in Rails, in my opinion this would correspond nicely to (({Set#|})).
=end



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