Curried Lua

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Currying is defined by Wikipedia[1] as follows:

"In computer science, currying is the technique of transforming a function taking multiple arguments into a function that takes a single argument (the first of the arguments to the original function) and returns a new function that takes the remainder of the arguments and returns the result"

You can implement curried functions in all languages that support functions as first-class objects. For example, there's a little [tutorial about curried JavaScript].

Here is a small Lua example of a curried function:

function sum(number) 
  return function(anothernumber) 
    return number + anothernumber

local f = sum(5)
print(f(3)) --> 8

-- WalterCruz

Here is another, contributed by [GavinWraith], which takes a variable number of arguments terminated with a "()":

function addup(x)
  local sum = 0
  local function f(n)
    if type(n) == "number" then
      sum = sum + n
      return f
      return sum
  return f(x)

print(addup (1) (2) (3) ())  --> 6
print(addup (4) (5) (6) ())  --> 15

Although these pre-curried functions are useful, what we would really like to do is make a general-purpose function that can perform the curry operation on any other function. To do this, we need to realize that functions can be operated upon by a "Higher-order function" -- a function that takes functions as arguments. The following curry function is an example of this, and curries a 2-argument function:

function curry(f)
    return function (x) return function (y) return f(x,y) end end

powcurry = curry(math.pow)
powcurry (2) (4) --> 16
pow2 = powcurry(2)
pow2(3) --> 8
pow2(4) --> 16
pow2(8) --> 256

To go from currying 2 arguments to currying 'n' arguments is a bit more complicated. We need to store an indeterminate number of partial applications, and unfortunately there is no way for Lua to know how many arguments a function requires; Lua functions can successfully receive any number of arguments, whether too many or too few. So, it's necessary to tell the curry function how many single-argument calls to accept before applying those collected arguments to the original function.

(this code is freely available from and includes a full discussion of how to tackle this problem.)

-- curry(func, num_args) : take a function requiring a tuple for num_args arguments
--                         and turn it into a series of 1-argument functions
-- e.g.: you have a function dosomething(a, b, c)
-- curried_dosomething = curry(dosomething, 3) -- we want to curry 3 arguments
-- curried_dosomething (a1) (b1) (c1) -- returns the result of dosomething(a1, b1, c1)
-- partial_dosomething1 = curried_dosomething (a_value) -- returns a function
-- partial_dosomething2 = partial_dosomething1 (b_value) -- returns a function
-- partial_dosomething2 (c_value) -- returns the result of dosomething(a_value, b_value, c_value)
function curry(func, num_args)

   -- currying 2-argument functions seems to be the most popular application
   num_args = num_args or 2

   -- no sense currying for 1 arg or less
   if num_args <= 1 then return func end

   -- helper takes an argtrace function, and number of arguments remaining to be applied
   local function curry_h(argtrace, n)
      if 0 == n then
	 -- kick off argtrace, reverse argument list, and call the original function
         return func(reverse(argtrace()))
         -- "push" argument (by building a wrapper function) and decrement n
         return function (onearg)
                   return curry_h(function () return onearg, argtrace() end, n - 1)
   -- push the terminal case of argtrace into the function first
   return curry_h(function () return end, num_args)


-- reverse(...) : take some tuple and return a tuple of elements in reverse order
-- e.g. "reverse(1,2,3)" returns 3,2,1
function reverse(...)

   --reverse args by building a function to do it, similar to the unpack() example
   local function reverse_h(acc, v, ...)
      if 0 == select('#', ...) then
	 return v, acc()
         return reverse_h(function () return v, acc() end, ...)

   -- initial acc is the end of the list
   return reverse_h(function () return end, ...)

The above code is Lua 5.1 compatible.

Since Lua 5.2 (or LuaJIT 2.0) provides an advanced debug.getinfo function that let us know how many arguments a function desires, we can make a practical function which mixes currying and partial application techniques. Here's the code:

function curry(func, num_args)
  num_args = num_args or debug.getinfo(func, "u").nparams
  if num_args < 2 then return func end
  local function helper(argtrace, n)
    if n < 1 then
      return func(unpack(flatten(argtrace)))
      return function (...)
        return helper({argtrace, ...}, n - select("#", ...))
  return helper({}, num_args)

function flatten(t)
  local ret = {}
  for _, v in ipairs(t) do
    if type(v) == 'table' then
      for _, fv in ipairs(flatten(v)) do
        ret[#ret + 1] = fv
      ret[#ret + 1] = v
  return ret

function multiplyAndAdd (a, b, c) return a * b + c end

curried_multiplyAndAdd = curry(multiplyAndAdd)

multiplyBySevenAndAdd = curried_multiplyAndAdd(7)

multiplySevenByEightAndAdd_v1 = multiplyBySevenAndAdd(8)
multiplySevenByEightAndAdd_v2 = curried_multiplyAndAdd(7, 8)

assert(multiplyAndAdd(7, 8, 9) == multiplySevenByEightAndAdd_v1(9))
assert(multiplyAndAdd(7, 8, 9) == multiplySevenByEightAndAdd_v2(9))
assert(multiplyAndAdd(7, 8, 9) == multiplyBySevenAndAdd(8, 9))
assert(multiplyAndAdd(7, 8, 9) == curried_multiplyAndAdd(7, 8, 9))

See Also

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Last edited March 27, 2014 1:39 pm GMT (diff)