Have you gone through The Little Schemer?

More on topic:

> No comparable primitive has been known for continuous mathematics: computing elementary functions such as sin, cos, sqrt, and log has always required multiple distinct operations.

I was taught that these were all hypergeometric functions. What distinction is being drawn here?

▲

adrian_b 38 minutes ago | parent [-]

Hypergeometric functions are functions with 4 parameters.

When you have a function with many parameters it becomes rather trivial to express simpler functions with it.

You could find a lot of functions with 4 parameters that can express all elementary functions.

Finding a binary operation that can do this, like in TFA, is far more difficult, which is why it has not been done before.

A function with 4 parameters can actually express not only any elementary function, but an infinity of functions with 3 parameters, e.g. by using the 4th parameter to encode an identifier for the function that must be computed.

	▲	thaumasiotes a few seconds ago \| parent [-]
		> Hypergeometric functions are functions with 4 parameters. Granted, but the claim in the abstract says: >> computing elementary functions such as sin, cos, sqrt, and log has always required multiple distinct operations And I don't see how this is true as to hypergeometric functions in a way that isn't shared by the approach in the paper. > Finding a binary operation that can do this, like in TFA, is far more difficult, which is why it has not been done before. > A function with 4 parameters can actually express not only any elementary function, but an infinity of functions with 3 parameters, e.g. by using the 4th parameter to encode an identifier for the function that must be computed. These statements seem to be in direct conflict with each other; you can use the second parameter of a binary function to identify a unary function just as you can use the fourth parameter of a quaternary function to identify a trinary one.