Indeed, maps and sets cannot be constructed from sums, products and recursion. They can be approximated if you throw exponentials in there. Instead, you can ex

Indeed, maps and sets cannot be constructed from sums, products and recursion. They can be approximated if you throw exponentials in there. Instead, you can extend algebraic data types to combinatorial species, which do allow exactly the kind of quotienting you speak of. While they're unexplored in programming, they are believed to be programmable similarly to ADTs. https://repository.upenn.edu/cgi/viewcontent.cgi?article=1774&context=cis_papers https://repository.upenn.edu/cgi/viewcontent.cgi?article=177... I must take issue with the "objects are products" characterization you implied. Structures are products; objects need existential types: http://www.cis.upenn.edu/~bcpierce/papers/compobj.ps http://www.cis.upenn.edu/~bcpierce/papers/compobj.ps