(* --------------------------------------------------------------------
   This program defines and evaluates a polynomial -- with integer
   coefficients and an integer solution, of course -- using Horner's
   Rule. The main program's argument is the value at which to evaluate
   the polynomial.  The polynomial's coefficients are defined using
   an array indexed 0 through n, where n is the degree of the polynomial
   and coefficient[i] is the coefficient on the ith-power term.
   The array is simulated by a function, which gives one example
   of how to represent more complex data types using Klein's built
   in types of boolean, integer, and function.

   Based on code written by Doug Baldwin for his MinimL language.
   -------------------------------------------------------------------- *)

(* --------------------------------------------------------------------
   This main hard-codes the degree of the polynomial with the second
   arg it passes to horner, and by the selection in coefficients.
   -------------------------------------------------------------------- *)

function main( x : integer ) : integer
    horner( x, 3, 0 )


(*
   before
*)

function horner(x: integer, n: integer, value: integer): integer
    if GE(n, 0) then
       horner( x, n - 1, (value * x) + coefficient(n) )
    else
       value


(*
   after
*)

function horner(x: integer, n: integer, value: integer): integer
    if n < 0 then
       value
    else
       horner( x, n - 1, (value * x) + coefficient(n) )







(* --------------------------------------------------------------------
   This function defines the polynomial x^3 - 4x^2 + 2x + 9.
   -------------------------------------------------------------------- *)

function coefficient( i : integer ) : integer
    if i < 1 then
	9
    else if i < 2 then
	2
    else if i < 3 then
	-4
    else
	1