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zipper_algebra: Add XOR#42

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zipper_xor
Open

zipper_algebra: Add XOR#42
marcin-rzeznicki wants to merge 1 commit into
dnffrom
zipper_xor

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@marcin-rzeznicki

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This change introduces an n-way XOR operation implemented on top of the
existing ordered zipper traversal framework.

The implementation treats tries as sparse path→value mappings, with missing
paths interpreted as the lattice bottom element. XOR is therefore computed
pointwise on values rather than on path presence:

result(p) = xor(v₁(p), ..., vₙ(p))

A deliberate design choice is that traversal follows join semantics: a child
edge is explored whenever it is present in at least one input. Although XOR is
often described in terms of parity, cancelling values at a path does not imply
that all descendants cancel as well. Stopping traversal based solely on path
parity would therefore miss surviving values in deeper subtries.

As a result, XOR shares the same traversal skeleton as join and differs only in
the algebra used to combine coincident values.

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