CASCADE endtest template startvalue			(library procedure)
(CASCADE endtest tmp1 sv1 tmp2 sv2 ...)
(CASCADE endtest tmp1 sv1 tmp2 sv2 ... finaltemplate)

	outputs the result of applying a template (or several templates,
	as explained below) repeatedly, with a given value filling the
	slot the first time, and the result of each application filling
	the slot for the following application.

	In the simplest case, CASCADE has three inputs.  The second input
	is a one-slot expression template.  That template is evaluated
	some number of times (perhaps zero).  On the first evaluation,
	the slot is filled with the third input; on subsequent evaluations,
	the slot is filled with the result of the previous evaluation.
	The number of evaluations is determined by the first input.  This
	can be either a nonnegative integer, in which case the template is
	evaluated that many times, or a predicate expression template, in
	which case it is evaluated (with the same slot filler that will be
	used for the evaluation of the second input) repeatedly, and the
	CASCADE evaluation continues as long as the predicate value is
	FALSE.  (In other words, the predicate template indicates the
	condition for stopping.)

	If the template is evaluated zero times, the output from CASCADE
	is the third (startvalue) input.  Otherwise, the output is the
	value produced by the last template evaluation.

	CASCADE templates may include the symbol # to represent the number
	of times the template has been evaluated.  This slot is filled with
	1 for the first evaluation, 2 for the second, and so on.

		? show cascade 5 [lput # ?] []
		[1 2 3 4 5]
		? show cascade [vowelp first ?] [bf ?] "spring
		ing
		? show cascade 5 [# * ?] 1
		120
		?

	Several cascaded results can be computed in parallel by providing
	additional template-startvalue pairs as inputs to CASCADE.  In this
	case, all templates (including the endtest template, if used) are
	multi-slot, with the number of slots equal to the number of pairs of
	inputs.  In each round of evaluations, ?2, for example, represents the
	result of evaluating the second template in the previous round.  If
	the total number of inputs (including the first endtest input) is odd,
	then the output from CASCADE is the final value of the first template.
	If the total number of inputs is even, then the last input is a
	template that is evaluated once, after the end test is satisfied, to
	determine the output from CASCADE.

		to fibonacci :n
		output (cascade :n [?1 + ?2] 1 [?1] 0)
		end

		to piglatin :word
		output (cascade [vowelp first ?] ~
				[word bf ? first ?] ~
				:word ~
				[word ? "ay])
		end

