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This is called the expression problem.

http://homepages.inf.ed.ac.uk/wadler/papers/expression/expre...

http://stackoverflow.com/a/2079678 is a great SO answer on this topic.

The expression problem has a complete and rather elegant solution in mainstream OO languages with generics, invented in 2012 called object algebras:

Video: https://www.infoq.com/presentations/object-algebras

Paper: https://www.cs.utexas.edu/~wcook/Drafts/2012/ecoop2012.pdf

I understand that there is a comparable solution in FP languages called finally tagless interpreters: https://oleksandrmanzyuk.wordpress.com/2014/06/18/from-objec...

Vesa Karvonen posted a complete solution in SML here[1] (but LtU seems to be down so the link doesn't work), which I transliterated (directly, not idiomatically) to F# here[2].

[1] http://lambda-the-ultimate.org/node/2232#comment-31278

[2] http://fssnip.net/gn

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