--[[ Rational Arithmetic Data Representation Module (Closure)
     H. Conrad Cunningham, Professor
     Computer and Information Science
     University of Mississippi

Developed for CSci 450/503, Organization of Programming Languages,
Fall 2016

This version of the data representation module uses a closure 
instead of an array to represent a rational number but defers 
computing the GCD until numer or denom is called.

1234567890123456789012345678901234567890123456789012345678901234567890

2016-09-11: Adapted from Lua modules rationalCore & rationalDeferGCD
2016-09-14: Removed misleading Haskell code

This is a new Lua version. It benefits from from section 2.1 and other
sections of Abelson and Sussman's _Structure and 
Interpretation of Computer Programs_ (http://mitpress.mit.edu/sicp/).

--]]

-- UTILITY FUNCTIONS (not exported)

-- Assumes n is numeric
local function signum(n)
   if n == 0 then
      return 0 
   elseif n > 0 then
      return 1
   else
      return -1
   end
end

-- Assumes arguments are integers
local function gcd(x,y)
   local function gcdaux(x,y)
      if y == 0 then
	 return x
      else
	 return gcdaux(y, x % y) -- tail recursive
      end
   end
   
   return gcdaux(math.abs(x), math.abs(y))
end

-- RATIONAL ARITHMETIC OPERATORS

-- Creates a new rational number, but does not
-- check whether x and y are integers and y nonzero
local function newRat(x,y)
   if x == 0 then
      return function() return 0, 1 end
   else
      return -- return thunk (closure)
	 function()
            local xx = signum(y) * x
            local yy = math.abs(y)
            local d  = gcd(xx,yy)
            return xx/d, yy/d
	 end
   end
end

-- Checks whether arguments are integers in Lua <= 5.2
local function makeRat(x,y)
   if type(x) == "number" and type(y) == "number" and 
         x == math.floor(x) and y == math.floor(y) and y ~= 0 then
      return newRat(x,y)
   else
      error("Cannot construct rational number " ..
	    tostring(x) .. "/" .. tostring(y)     )
   end
end

-- Assumes r is created by makeRat
local function numer(r)
   local x, _ = r() -- force thunk (closure)
   return x
end

-- Assumes r is created by makeRat
local function denom(r)
   local _, y = r() -- force thunk (closure)
   return y
end

-- Should newRat also be exported?
return { makeRat = makeRat, numer = numer, denom = denom }