Recursion

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TODO: This article is about tail calls

- introduction/overview

- 'magic of recursion'?

- lua

Recursion

As a quick refresher, recursion is when code calls itself.

Here's a textbook example:

function fac(n)
  if n < 1 then
    return 1
  else
    return n * fac(n - 1)
  end
end

print(fac(20))
-- prints 2432902008176640000

This code has a function 'fac' that takes a number and:

  • Returns 1 if the number is less than 1
  • Calls fac with the number minus 1
  • Multiplies the result of fac by the number
  • Returns the multiplied result

Unfortunately there's a problem with this. When we call fac we need to save our current number to the 'stack' so we can multiply it with the result of fac. If we recurse too many times we run out of memory on the stack to save our numbers.

Because of this tendency to overflow the stack recursion isn't seen much in mainstream programming.

Tail calls

What if we didn't need to save anything? We could recurse forever without any stack overflows.

Let's say we rewrite our factorial code to this:

function fac(n, acc)
  if n < 1 then
    return acc
  else
    return fac(n - 1, acc * n)
  end
end

print(fac(20, 1))
-- prints 2432902008176640000

This new code has a function 'fac' that takes a number and accumulator:

  • Returns the accumulator if the number is less than 1
  • Multiplies the accumulator by the number
  • Calls fac with the number minus 1 and new accumulator value
  • Returns result of fac

Instead of storing numbers on the stack and multiplying them afterwards, we now accumulate them as we go.

TODO: explain tail calls

Tail call elimination

We still have a problem. I didn't mention it earlier, but when we call functions in programming languages we also put a return address on the stack. We don't store any numbers on the stack but we still store a return address every time we call fac. If we recurse too many times we still run out of memory.

What if we

- we've been writing code as there's no stack

- tail call elimination

- NOT an optimization, how many optimizations decide which way you can program?

- hints deeper at function calls vs jumps

- structured programming, goto wars

Loops

- recursion can implement loops!

- implementing a for loop

- implementing a while loop

- implementing a do while loop

- each loop iteration only shares global and function args

State machines

- implementing a stateful algorithm

- some kind of menu system

- the code makes sense to read

- this is mutual recursion

- very hard to do in a traditional structured language

Lambdas

- lambdas to actually replace looping constructs/switch statements

- most mainstream languages support lambas

- recursion-based control flow

Mainstream support

- functional programming languages

- lua

- clang mustcall

- webassembly