I recently discovered a new way to trigger a stack overflow in Elm - chaining 10K random generators ðŸ™ˆ

Understanding why this happens and how to resolve it was quite the journey.
Along the way I had to bust out several different debugging techniques including
**proving myself wrong** and **reasoning by analogy**.

```
-- Fine with 1K, stack overflow for 10K
sprawlOut : Int -> Location -> Generator ( Location, Set Location )
sprawlOut depth loc =
List.foldl
(\_ acc -> R.andThen sprawl acc)
(R.constant ( loc, Set.empty ))
(List.range 1 depth)
sprawl : ( Location, Set Location ) -> Generator ( Location, Set Location )
sprawl ( loc, set ) =
R.uniform loc (neighborsOf loc)
|> R.map (\next -> ( next, Set.insert next set ))
```

See the full original problem in action

## Simplify the problem

That random generator is intimidating! ðŸ˜±ðŸ˜±ðŸ˜±

It’s doing two things: generating locations (via the `sprawl`

generator), and
accumulating them in a set.

It might be easier to figure out the answer if we work with a **simpler
problem**.

Let’s replace that `sprawl`

generator with one that generates random numbers.

```
dieRoll : Generator Int
dieRoll =
Random.int 1 6
```

We can extract the accumulation part to a separate function and use a plain old
list instead of a `Set`

. Also, it turns out all the rolls are independent so we
can use `map2`

instead of `andThen`

.

```
combine : List (Generator a) -> Generator (List a)
combine =
List.foldl (Random.map2 (::)) (Random.constant [])
```

Put those two together, our simplified problem looks like:

```
-- Stack overflow!
List.map (always dieRoll) (List.range 0 10000)
|> combine
```

We’re still getting a stack overflow. That’s good! If we didn’t that would mean
we’d *oversimplified*, and removed something essential to reproducing the bug
along the way. As it stands, if we can find a way to generate 10K random die
rolls, we’ll also be able to use the same solution to fix our original problem.

See the simplified problem in action.

## Construct experiments

Make a guess about why things are breaking. Then try to **prove yourself
wrong**!

Building up large lists of generators cause stack overflow

```
-- Works fine
List.map (always dieRoll) (List.range 0 10000)
```

This doesn’t stack overflow so that’s not the cause of our error.

## Process of elimination

Time to scale! List some of the possible reasons the code might be broken, then try to prove them all wrong. At each step you’ll learn something new.

We’ve already proven that building a large list of generators is fine. The error
must be in `combine`

.

Looking into the implementation, three possibilities jump to mind:

`::`

breaks on large lists`List.foldl`

breaks on large lists`Random.map2 (::)`

breaks on large lists

Lets try to prove all them wrong!

```
-- No problem!
0 :: (List.range 1 10000)
-- No problem!
List.foldl (::) [] (List.range 1 10000)
-- No problem!
Random.map2 (::)
(Random.constant 0)
(Random.constant <| List.range 1 10000)
```

Hmmm, all of the individual pieces work fine on their own. Maybe the problem lies with how they play together ðŸ¤”

## How are things the same?

`combine`

is a pretty common function that can be defined for many types. For
example, you could also define it for `Maybe`

:

```
combineMaybes : List (Maybe a) -> Maybe (List a)
combineMaybes =
List.foldl (Maybe.map2 (::)) (Just [])
```

and for `Result`

```
combineResults : List (Result e a) -> Result e (List a)
combineResults =
List.foldl (Result.map2 (::)) (Ok [])
```

Time for a new hypothesis:

There is a fundamental flaw in the algorithm for

`combine`

that breaks down at larger list sizes.

Let’s try to disprove it!

```
-- No problem!
List.map Just (List.range 1 10000)
|> combineMaybes
-- No problem!
List.map Ok (List.range 1 10000)
|> combineResults
```

Hmmm, combine seems to be working fine here. Let’s try with a more complicated type for good measure:

```
-- Stack overflow!
List.map Decode.succeed (List.range 1 10000)
|> combineDecoders
```

Huh, why does `combine`

fail for large lists of generators and decoders but not
for maybes and results? Or put differently, how are the `Generator`

and
`Decoder`

types **similar** to each other, but **different** from `Maybe`

and
`Result`

?

Looking at the source for `Random`

, we can see that `Generator`

is actually a
function under the hood:

```
type Generator a =
Generator (Seed -> (a, Seed))
```

and `Random.map2`

chains those functions under the hood to thread the `Seed`

to both generators.

The `Decoder`

type is implemented in JavaScript for efficiency, but if one were
to implement it in Elm it would also be a function under the hood:

```
-- What a pure Elm implementation could look like:
type Decoder a =
Decoder (Value -> Result Error a)
```

So it looks like `combine`

breaks on types that wrap a function. That’s
surprising. It would be like saying that composing a function 10K times doesn’t
work!

Just for thoroughness, let’s try to prove that last statement wrong:

```
increment n = n + 1
-- Stack overflow!
List.map (always increment) (List.range 1 10000)
|> List.foldl (<<) identity
```

ðŸ¤¯ðŸ¤¯ðŸ¤¯

This is HUGE! Not just because I made an incorrect assumption (it happens!), but
because this discovery is going to enable me to bring a powerful debugging
technique to bear - **reasoning by analogy**.

## Reasoning by analogy

Reasoning by analogy is a problem-solving technique that goes like this:

- You have a hard problem you don’t know how to solve
- Find an easy problem that’s similar
- Figure out the answer to the easy problem
- Use the same solution to solve the hard problem

We’ve *already* reached for a variation of this technique when we simplified our
generator right at the beginning! Our hard problem is “generating the complex
set of locations causes stack overflow for large sizes”. We simplified it to
“generating 10K random numbers causes stack overflow”. If we can solve that,
then we can retrofit the solution onto our original hard problem.

However, even our “easier problem” is proving difficult to solve. We’ve used some other debugging techniques to eliminate some possibilities and gain better understanding of what might be causing the problem.

We’ve also discovered an even easier problem that’s similar: “composing a large
number of functions causes a stack overflow”. This time however, it’s a problem
we already know the solution to! It’s definitely possible to `increment`

10K
times in a stack safe way.

We can do this as a recursion or via
`List.foldl`

:

```
-- Works fine!
List.range 1 10000
|> List.foldl (\_ acc -> increment acc) 0
```

So what’s the difference between this and folding `<<`

? Let’s look at each step
of the loop:

```
-- List.foldl (<<)
--
-- Each step composes `increment` and the
-- return of the previous step
(x -> increment x)
(x -> increment (increment x))
(x -> increment (increment (increment x))
(x -> increment (increment (increment (increment x))
...
-- stack overflow!
```

```
-- List.foldl (\_ x -> increment x)
--
-- Each step increments the return of the previous step
0
1
2
3
...
10000
```

When folding composition, we’re building a giant nested function but we never execute any of the steps. 10K nested function calls is enough to blow the stack on my machine.

When folding `increment`

directly, we’re *eagerly* evaluating each step. We
aren’t building deeper and deeper functions, instead we do the work immediately
at each step and increment the number.

Now that we have some facts, let’s do some reasoning! Given that:

- 10K chains of
`Random.map2`

causes a stack overflow - 10K compositions of
`increment`

causes a stack overflow - I can call
`increment`

10K times on itself if each step is*eagerly evaluated*.

**Therefore** (by analogy) I should also be able to accumulate the results of
10K random generators as long as each step is eagerly evaluated.

## Working our way back to the original problem

So how does one “eagerly” evaluate a random generator? If we have a seed we can
use `Random.step`

to manually evaluate the generator, giving us back a random
value immediately.

Let’s try those 10K random dice rolls from earlier, but now with an eager approach:

```
-- This works fine!
numbers : List Int
numbers =
List.range 0 10000
|> List.foldl numbersHelp ( [], Random.initialSeed 1234 )
|> Tuple.first -- don't need the seed anymore
numbersHelp : a -> ( List Int, Seed ) -> ( List Int, Seed )
numbersHelp _ ( acc, seed ) =
let
( newAcc, newSeed ) =
Random.step dieRoll seed
in
( newAcc :: acc, newSeed )
```

Oh look! That works! Looks like our reasoning by analogy pointed us to a working solution!

If we can solve our simplified 10K random dice rolls problem, we should also be able to use a similar solution for the original problem.

```
sprawlOut : Int -> Location -> R.Seed -> (( Location, Set Location ), R.Seed)
sprawlOut depth loc seed0 =
List.foldl
(\_ (acc, nextSeed) -> R.step (sprawl acc) nextSeed)
(( loc, Set.empty ), seed0)
(List.range 1 depth)
sprawl : ( Location, Set Location ) -> Generator ( Location, Set Location )
sprawl ( loc, set ) =
R.uniform loc (neighborsOf loc)
|> R.map (\next -> ( next, Set.insert next set ))
```

It’s not particularly nice, but it works! Success!

See the final solution in action

## Conclusion

Several debugging techniques were used in the course of solving this problem.
**Simplifying the problem** is always a good place to start. It’s a variation on
**reasoning by analogy**, although analogies are allowed to be more than just
simplified versions of your original problem.

When you’re debugging a problem, you will have a lot of assumptions. Test all of
them and **attempt to disprove them**.

Look at your code and try to **list the ways it could break**. Then go through
them all and try to see if they can trigger your bug. Use **process of
elimination** to narrow the focus of your search. Make sure to test all your
assumptions along the way though!

Once you have some data about some combinations that work and some that break,
ask yourself “how are these the **same**?” and “how are these **different**?”.

Discussion around stack overflow seen in this article and its solution led to a
PR against `Random.Extra`

to add some stack-safe helper functions.