The approach is so simple and trivial that it must have occurred to people a hundred times over. Yet I do not find any other examples of this. Whenever I google for church encoding the examples don't go beyond church numerals.

Am I googling for the wrong keywords?

You might find "Typing Record Concatenation for Free"
interesting:

   http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.49.401

Claus

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