Lifting binary operations, e.g. T+T → Option<T> + Option<T>

Buried in the lengthy thread about catching functions is a use case by @scottmcm that maybe should be discussed independently:

which is a shorter way to write

fn add_opt(a: Option<i32>, b: Option<i32>) -> Option<i32> {
    match (a, b) {
        (Some(x), Some(y)) => Some(x+y),
        _ => None

I read that, and I thought, hey, isn't this a job for a lifting combinator? If it was a unary operation, we could write it that way already:

fn add_five(a: Option<i32>) -> Option<i32> {|x| x+5) }

But we don't have combinators that let you write binary operations on Options or Results. Maybe we should.


You can use and_then for this I think?

fn add_opt(x: Option<i32>, y: Option<i32>) -> Option<i32> {
    x.and_then(|x||y| (x, y))).map(|(x, y)| x + y)

I was contemplating suggesting impl<T:Add<U>,U> Add<Option<U>> for Option<T>, but unfortunately (IMHO) the fact that Option was made Ord prevents that from being done consistently for the comparison operators, so I don't know if it's a good idea for the other operators.

Looks like nightly can apparently already make a lifting adapter:


fn main() {
    let f = OptionLift(std::ops::Add::add);
    assert_eq!(f(Some(2), Some(3)), Some(5));
    let g = OptionLift(std::ops::Neg::neg);
    assert_eq!(g(Some(2)), Some(-2));

struct OptionLift<F>(F);

impl<F:FnOnce<(T0,)>,T0> FnOnce<(Option<T0>,)> for OptionLift<F> {
    type Output = Option<F::Output>;
    extern "rust-call" fn call_once(self, (a0,): (Option<T0>,)) -> Self::Output {

impl<F:FnOnce<(T0,T1,)>,T0,T1> FnOnce<(Option<T0>,Option<T1>,)> for OptionLift<F> {
    type Output = Option<F::Output>;
    extern "rust-call" fn call_once(self, (a0,a1,): (Option<T0>,Option<T1>,)) -> Self::Output {

Hm, it could be simpler,

fn add_opt(x: Option<i32>, y: Option<i32>) -> Option<i32> {
    x.and_then(|x||y| x+y))

There is a certain lack of motivation in this construct, though. I have to think about it to understand why the outer combinator must be and_then and the inner must be map. Not nearly so tidy as ¿{ x? + y? }


Not nearly so tidy as ¿{ x? + y? }

If we aim for tidiness, I'd say that (currently working on stable) solution of Ok(x? + y?) is good enough.


Oh, neat, I did not know that already worked. (Modulo Ok versus Some.) Still haven’t fully grokked the expression-ness of the language.

I have the impression from the other thread that @scottmcm didn’t want to have to write Some, but I don’t think I would mind. Ok(()) bugs me because I want to be able to fall off the end of a -> Result<(),ErrorT> function, not because of the typing.

Can you elaborate about this? What's wrong with the way Ord is implemented for Option today?

That doesn't "capture" the errors, though, so only works if you want to use it in a method that returns an option where you want to return None if either is None.

Consider, for example, Chain::size_hint. The method doesn't return Option, so it can't use ? without a catch block, but still wants to combine the two Option<usize> upper-bound hints. The actual working on stable solution is (||{ Some(x? + y?) })(), but I loathe that syntax. (Assuming inference cooperates, since it doesn't always with ?-in-closures. And Chain needs checked_add to deal with overflow, but that's not important to the lifting discussion.)

Assuming a Lift like above, the problem is that, for example, Lift(u32::max) does something different from Option<u32>::max. (Both maxs in this case being instances of Ord::max.)

a b Option::max(a, b) Lift(Ord::max)(a, b)
None None None None
Some None Some None
None Some Some None
Some Some Some Some

And min doesn't have this difference, so the solutions to nearly-identical problems turn out to be very different depending whether you're looking for min or max, which can be quite confusing.

If Option were only PartialOrd instead, None could be neither before nor after the Somes, which is less arcane than the current totally-arbitrary choice. (And Option wouldn't get a min from Ord, so we could choose how to define it, or even just to not define it at all. All arguments here are also true with cmp::min/max; that's just less clean to write in the tables.)

I don't want to have to write ¿{} and Some(). One or the other is fine. I've elaborated on that in `catch` blocks are not `Ok`-wrapping their value · Issue #41414 · rust-lang/rust · GitHub

But what about just adding Add impls and so on? How is the current implementation of Ord for Option different from how the Add impls would be?

Well, the Add impl would be Lift(Add::add). So things would be perfect if PartialOrd for Option<T:Ord> were just Lift(Ord::cmp)—since that’s even directly the correct Option<Ordering> type—but it’s not.

Compare some other languages, where (None < Some) == false, unlike Rust:

It certainly doesn’t prevent adding Option<T:Add>: Add, but I think it’d be a footgun for Option<T> to, for example, be almost identical to diesel::sql_types::Nullable<T>, the only difference being in a subset of the comparisons, like None < Some or Some > None. With no operators lifted the comparison behaviour is a quirk of Option; with all operators lifted except the comparison ones, it feels more like a trap.

The comments about Lift seem like a misdirection: the real question is what should None + Some(_) return? (Thinking in terms of “lift” suggests a particular answer, but the question is whether or not we should.) I don’t know if we have a clear answer; I agree with you that None < Some(_) == true suggests intuitively that None + Some(x) = Some(x), but its not at all obvious thats the answer people want.


I think the biggest motivation for the Lift interpretation is heterogeneous operators.

Having None + Some(x) => Some(x) only naturally allows Option<T:Add<Output=T>>: Add<Output=Option<T>>. Allowing the most general Option<T:Add<U>>: Add<Option<U>> needs the None + Some(x) => None definition. The other definition would be possible with some extra bounds, maybe T: Into<T::Output>, U: Into<T::Output>, but that feels, subjectively, rather weird to me.

(So I think I agree with your last sentence, and I think I’m arguing the contrapositive: that people don’t want that + definition, so the < definition isn’t what they want either.)

I did not intend to suggest that we add implicit lifting of binary operations via impl Add and the like. I thought I was suggesting explicit binary lifters, along the lines of

fn add_opt(a: Option<i32>, b: Option<i32>) -> Option<i32> {
    (a, b).map_both(|a, b| a+b)

I’m not sure that’s better than Some(a? + b?) though.

No, C++ does this even worse than rust.

#include <optional>
#include <iostream>

int main(int argc, char **argv) {
    std::optional<int> a = std::nullopt;
    std::optional<int> b = 4;

    std::cout << "None < Some(4): " << (a < b) << std::endl;
    std::cout << "None > Some(4): " << (a > b) << std::endl;
    std::cout << "Some(4) < None: " << (b < a) << std::endl;
    std::cout << "Some(4) > None: " << (b > a) << std::endl;

    std::cout << std::endl;
    std::cout << "And you can even compare optional<int> to int..." << std::endl;
    std::cout << "      None < 4: " << (a < 4) << std::endl;
    std::cout << "      None > 4: " << (a > 4) << std::endl;
    std::cout << "      4 < None: " << (4 < a) << std::endl;
    std::cout << "      4 > None: " << (4 > a) << std::endl;
None < Some(4): 1
None > Some(4): 0
Some(4) < None: 0
Some(4) > None: 1

And you can even compare optional<int> to int...
      None < 4: 1
      None > 4: 0
      4 < None: 0
      4 > None: 1

That might work under a MonadPlus interpretation where + is seen as <|> (alternative), but under the (+) <$> Nothing <*> Just x == Nothing interpretation (applicative lifting), which I find most intuitive, it does not work.


I'd like to add that I find that Rust follows Haskell in doing the reasonable thing, that is: nothing is smaller than something.

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Did Haskell find some math to justify why Nothing < Just _ (as opposed to >), or is it just an arbitrary choice that someone made once and now people follow?

This is a hilarious sentence, since something is smaller than Just: Nothing :stuck_out_tongue:

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So I went and asked on #haskell @ freenode, and I got the following reply (verbatim.. I kid you not):

because nothing is less than anything

I asked about laws, but no one suggested any, so I think this was the rationale really.

Hmm… In various contexts you sometimes see this ‘first principles’ encoding of the natural numbers:

data Nat = Zero | Succ Nat

…which would be isomorphic to

type Nat = Maybe Nat

if that were valid - which it isn’t because type aliases can’t be recursive, but you get the idea.

So 0 would be represented by Nothing, 1 by Just Nothing, 2 by Just Just Nothing, etc.

Then at least in this special case, there’s a good reason for Nothing to compare as less than Just.


In actual Rust it would be more like struct Nat(Option<Box<Nat>>), but yes, it does make sense in a way that None < Some(_).

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My biggest concerns about this are twofold. First, the endless possibility of errors this can introduce. I have seen several bugs in my own code being prevented at compile time because (e.g.) two Option<usize>s or an Option<i32> and an i32 didn’t Add. Sure enough, in most of the cases handling a missing value required special logic which I would have erroneously omitted if the compiler hadn’t slapped on my wrist.

And this immediately leads to my second concern. It’s not at all obvious what these operations should yield. One choice is the monadic-style "if either operand is None, the result is also None". Another possibility that I’ve seen suggested somewhere in this thread is “treat None as the identity element”, i.e. "the result is None only if both operands are None". Both interpretations may be useful in different scenarios, along with a variety of others.

For these two reasons I don’t think it would be a good idea to hard-wire either interpretation into the stdlib and let implicit magic happen — it is more confusing than helpful. Neither one is clearly a natural + (etc.) operation on optionals, so code clarity would benefit more from a descriptively-named 2-ary free function that one would implement for oneself and that is specific to the problem being solved, instead of a single, rather ad-hoc choice of semantics for otherwise obviously-working operators being forced upon the entire ecosystem.