🚀 go-pugleaf

I enjoyed your "loud thinking".  When I read

  Ok, so now I want to write a procedure that could solve any problem of
  this form.  What specifics do I have to give it to tell it which
  problem of this form to solve?  Well, I could give it the numbers to
  multiply together. ...  No, that's silly, there could be arbitrarily
  many of them.  I certainly don't want to say that the way to compute
  100!  is by multiplying together 100 times 99 times ... all day.

I thought that it wasn't so "silly".  To my way of thinking it is perhaps the
most natural of the bunch.  Namely, write or use something that will generate
a list of numbers and then multiply them together.  This is the APL-style of
doing factorial.  I think there is something to be said for programming by
combining generic components.  In this case routines to "generate a list from
1 to n [by inc]" and "apply function to each element in the list" are good
candidates.  I think the primary reason this style of programming (combining
generic elements) is not wide-spread is that, without very sophisticated
compilers, it leads to slow programs.

 -ken