🚀 go-pugleaf

In article <BvFvEz.7A@dcs.ed.ac.uk> alti@dcs.ed.ac.uk (Thorsten Altenkirch) writes:

   However, I find it quite hard to come up with useful examples of 3rd
   order functions (e.g. which have types like ((A->B)->C)->D).

   Sure, it is not hard to come up with constructed examples like:

	   \lambda f:(A->A)->B . f (\lambda  x:A . x) : ((A->A)->B)->B

   but I am rather looking for examples motivated by programming
   problems. 

   Any ideas?

Check out microwave and analog engineering.  Information is passed as
"signals", or functions from time (or frequency) to some other
physical quantity, such as voltage, current, or power.  The function
of various devices is expressed as a function on these signals; for
example, in the simple case, a mixer will take two functions and
produce a function which is their sum.

As this gets more complex (for example, writing a general description
which produces behaviors based upon parameters such as gain and power
consumption), third order functions appear frequently.

					Dave Barton
					dlb@hudson.wash.inmet.com