Feb  8 22:25 2015 derivative.ex Page 1


# Derivative Function with Function Return
# Functional Programming Example -- Higher Order
# H. Conrad Cunningham, Professor
# Computer and Information Science
# University of Mississippi

# Developed for CSci 556, Multiparadigm Programming, Spring 2015

# 34567890123456789012345678901234567890123456789012345678901234567890

# 2015-02-08: Developed from 2013 Lua version

defmodule Derivative do

  @moduledoc """ 
  This higher-order differentiation function is adapted from a Lua
  version, which itself is adapted from a Scheme version in section
  1.3.4 of Abelson and Sussman's Structure and Interpretation of
  Computer Programs (SICP) textbook.
  """

  @doc """
  Function "deriv" takes a single-argument function "f" and a small
  delta "dx" and returns a single-argument function (closure) that
  computes an approximation of the value of the derivative at the
  value of its argument.

  Definition of derivative: lim(dx->0) (f(x+dx) - f(x)) / dx
  """
  def deriv(f,dx) when is_function(f) and is_number(dx) do
    (fn x -> (f.(x+dx) - f.(x)) / dx end)
  end

end