True Sums of Products
Edsko de Vries, Andres Löh

We introduce the sum-of-products (SOP) view for datatype-generic programming (in Haskell). While many of the libraries that are commonly in use today represent datatypes as arbitrary combinations of binary sums and products, SOP reflects the structure of datatypes more faithfully: each datatype is a single n-ary sum, where each component of the sum is a single n-ary product. This representation turns out to be expressible accurately in GHC with today's extensions. The resulting list-like structure of datatypes allows for the definition of powerful high-level traversal combinators, which in turn encourage the definition of generic functions in a compositional and concise style. A major plus of the SOP view is that it allows to separate function-specific metadata from the main structural representation and recombining this information later.

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ACM DL Author-ize serviceTrue sums of products
Edsko de Vries, Andres Löh
WGP '14 Proceedings of the 10th ACM SIGPLAN workshop on Generic programming, 2014
Talk slides, presented at WGP 2014
Library on Hackage
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Andres Löh, 2016-02-04