How would I write an higher-order function of sum(f,n) in Lua?

Question

First of all, I am of course aware that strictly speaking Lua does not support higher order functions, but only first-class functions.

However, I would like to try to implement some kind of function which, for a given function and a number n >= 0, returns the sum 0 + f 1 + ... + f n. My way of attempting this, looks like this:

function sum(f,n)
    if n < 1 
then 
    return 0
else
    return sum(f, n-1) + f(n)
    end
end

I'm not sure though if it really does what it should do when I try to call it:

print(sum(function(x) return x*x end, 2),3)

Answer 1

First of all, I am of course aware that strictly speaking Lua does not support higher order functions, but only first-class functions.

This is wrong. Lua's functions being "first-class" allows higher-order functions: You can simply pass functions as parameters.

I'm not sure though if it really does what it should do when I try to call it: print(sum(function(x) return x*x end, 2),3)

Calling this in the Lua REPL, I get the desired result of 5 = 1^2 + 2^2:

$ lua
Lua 5.3.4  Copyright (C) 1994-2017 Lua.org, PUC-Rio
> function sum(f,n)
>>     if n < 1 
>> then 
>>     return 0
>> else
>>     return sum(f, n-1) + f(n)
>>     end
>> end
> 
> print(sum(function(x) return x*x end, 2),3)
5   3

I don't see the purpose of the , 3 (which ends up as an extra argument to print) though.

A more efficient implementation would use a for-loop instead of recursion:

function sum(f, n)
    local sum = 0
    for i = 1, n do
        sum = sum + f(i)
    end
    return sum
end