I recently came across a use case where formal methods were incredibly helpful. I've been rewriting Postgres in Rust and am currently focusing on correctness. The biggest challenge is that there's so much surface area to cover. Postgres has over 3000 user-facing functions, ranging from regular expression matching to JSON iteration to computing the gamma function. About half of these functions are simple pure functions.
Of the 3000 functions, I've been able to formally verify that the Rust behavior is identical to the Postgres C behavior for over 1000 of them. In the process, I found 4 different Postgres bugs. All of them would not be triggered under ordinary usage, but one, if triggered, would corrupt your database.
I think why formal methods works well for this is I'm testing a large number of small to medium self-contained pieces of code. For each of them the specification is simple: does postgres_fn(args) == pgrust_fn(args). I've been using Kani[0] which works across both Rust and C code so the proofs are based off the actual code and not a translation of the code to another language.
If you want to check out what all the verification look like, you can see them here[1]
Yep, I did submit bug reports. This was on Tuesday. I don't see a public copy of the mailing list that has my bug reports yet. The four bugs were:
0) When parsing a macaddr[0], Postgres uses sscanf with %x. %x can wraparound. This means SELECT '10000000aa:bb:cc:dd:ee:ff'::macaddr; will return aa:bb:cc:dd:ee:ff.
1) When parsing a tid[1], Postgres uses strtoul. The return value of strtoul is different across platform for the empty string. This means on some platforms Postgres SELECT '(,5)'::tid; will error and others will accept it.
2) Postgres missed an overflow check in it's cash type[2]. When running SELECT '-92233720368547758.08'::money / (-1)::int8; some platforms will error and other's will return the MIN value. Postgres does check for this for some of the other cash related functions, but it missed it for one of them.
3) When hashing the "char" type Postgres will cast a char to an integer[3]. On some platforms char is signed and on others it's unsigned. This means the hash of a char can be different depending on the platform. If you are using a hash index or hash partitioning on a char and move your DB from x86 to arm, the hashes will differ and your index/partitioned tables become corrupted. Note that this is special char type that you have to refer to by "char" that is separate from the typically used CHAR(n) type which is what you typically use, hence this would never come up under real usage.
The common pattern with all of these is they rely on C behavior that differs across platform (integer overflow, char signedness, strtoul). Rust is better about having more consistent behavior across platforms so these cases get flagged when the Rust code and the C code differ.
To me, "this returns sorted lists" illustrates the crux.
You may know exactly what you want, and you may have a reasonably fast and cheap way to verify your code against a formal specification. But the formal specification needs to come from somewhere and for any non-trivial program its complexity is going to be in the same order of magnitude as the code implementing it. So we are back to writing "code" (which is what a formal specification is) that needs to be checked against what we actually want. And that "code" needs .. a test? Hard thinking? A formal verification itself?
Don't believe me that this is hard? Back to "this returns sorted lists". The promise of formal verification is that whatever implementation I throw at the verifier, as long as it passes the check, I'm happy (assuming that I can also encode things like running time and resource use). Now imagine a program that always returns the empty list. It satisfies "this returns sorted lists" trivially but is not at all what we want. The formal spec has a bug. Such issues can be subtle in larger projects and no amount of model checking or SMT solvers can guard you against a bug in that "code".
Don't get me wrong, it can be incredibly useful. But it's not the silver bullet that some proponents make it out to be. It's another tool next to testing, not instead of it. (The whole "testing can only prove the existence of bugs, not their absence, that's why we should use formal verification instead" is just misguided at best and propaganda at worst.)
I think every formal methods phd student who's interested in adoption of their techniques/tools has a short bout of doubt/depression upon realizing just how large of a surface area for bugs lives in a sufficiently useful specification.
This is deeply related to the conceptual error a lot of executives are currently making around automation in/of their software engineering orgs.
It has always been true that learning some formal methods probably makes you a better programmer in certain ways, even if you never use them. I think it's increasingly also true that learning some formal methods probably makes you a better manager of people/processes that product software.
I have a deeper problem. When I'm calling sort() it is useful that it returns a sorted list. However my program rarely has sorted lists of any sort in any requirement. My requirements are around the features my users care about. Sure the list of employees that I need to display needs to be sorted (sometimes by hire date, sometimes by title, sometimes by name - and often combinations of the above), but there are a lot of things I'm doing with that list that are not sorting.
I mean, just for this particular example, you could certainly also add a check that the sorted list is the same length as the input list.
That said, your broader point is more or less correct. I think the advantage of something like TLA+ is that the specs can generally be more abstract and as such the checks can be more exhaustive than you would likely get with regular "code".
With concurrent code, in particular, it can be difficult to know if your algorithm is correct, especially without the confounding variables that you get with a "real" programming language. Is my program broken because of some memory allocation quirk? Is it broken because of some peculiarity with how pthreads are dispatched? Or is my design wrong? Being able to work at an abstract level at least can check the last part.
Of course, though, you are correct that formal methods aren't silver bullets.
The promise of formal verification (and testing) is essentially the same promise as double-entry accounting. It assumes that if you do the same thing twice that it is unlikely you will screw it up in the exact same way twice. When there is disagreement it tells you that something went wrong, but you still need to look at both sides to determine which one is wrong. There is no such thing as a panacea, of course.
> It's another tool next to testing, not instead of it.
Theoretically it is instead of. They both are trying to solve the exact same problem. The real world with real constraints, of course, isn't so neat and tidy, so they don't end up perfectly overlapping.
We do. It's called a type checker. Every "formally verified" system is going to be partially verified. e.g. you might prove your sort procedure sorts, but did you prove its complexity? Under a cost model for integer compares or a cost model for page fetches? Or both? Multi-layer cache page fetch costs? How well you verify just depends on how well you decide to model the problem. Different type checkers have different modeling features.
This is a more useful perspective; it's not "we do/don't use formal methods," but instead "how can I more precisely model my domain?" Helpfully, if you model your domain well, code tends to be obvious/write itself.
Thankfully this is no longer strictly true. So, I think the quote needs a slight adjustment, "Type systems and $THING are just ...", but $THING is not very well defined yet. Between "linters", and other relatively fast AST-based rule enforcers, some of which looking at higher order behavior, I think we now have an amalgamation of formally verified concepts that we can consider fast enough and sufficient exercised in practice that we are ever closer to widespread formally and dependably verified software.
Still, it's a long journey, and academic formal verification would always be, by design, a few steps ahead of what the industry can do efficiently in practice.
In most industries that need software made for them it's hard enough to get people to care about spending enough time on informal methods let alone formal ones. I simply don't think most of the industry has had the breathing room and respect for engineering for this pattern to develop.
I think its also about tolerance for failure. For software that must not fail or where reliability commands a premium you would be wise to invest in formal methods. Core systems at aws for example. For throwaway CRUD code its just easier to try iterations on the problem and call it a day. Its not about respect just RoI.
I think programmers in general do not give much thought to the level of engineering required for a task.
Mostly, there's too little, but there are many cases when there's too much. I see people writing tons of tests for corporate software that will be used by a couple of people and will have to be updated regularly anyway.
Building a hut is not the same as building a skyscraper, but we don't really have guidelines for different software projects. No methodology I've ever seen distinguishes types of projects by complexity.
I've been a big nerd for formal methods for quite awhile, and have been broadly unsuccessful in getting employers onboard.
I have pretty cynical opinions as to the "why" of this, largely involving the fact that the vast majority of software engineers refuse to learn anything that they weren't explicitly taught in college, but regardless of the reason whenever I have tried proposing TLA+ in the past, people will nod along and wait for me to stop talking. I've had several managers say "they'll look into it", which was such an obvious lie that I don't know why they even bothered.
I've "snuck in" TLA+ usage a few times. I gave up on getting anyone else to use TLA+, but as I've gotten more senior-level, I have been given a fair bit more leeway on how I approach projects and as such I have been able to budget myself a day or two to model some of the less-obvious bits of concurrency.
All that said, I have had some luck with designing stuff with TLA+, then feeding the spec into Claude and getting that to implement the actual executable code. Maybe I'll be able to convince an employer that's a good use of time now.
> I have pretty cynical opinions as to the "why" of this, largely involving the fact that the vast majority of software engineers refuse to learn anything that they weren't explicitly taught in college, but regardless of the reason
I think it's not only SWEs, but general persons that goe to college primarily to get a job, without having a natural curiosity for things.
This blog is actually very useful... There's also the flip side, possibly due to the expense (technically, intellectually, and emotionally), where "IT'S FORMALLY VERIFIED!!" has become some marketing code for "it's safe, secure, and PFAS free..." - just because something is formally verified, doesn't mean it's secure or fit for purpose. It usually just means it conforms to a given spec "and that's that..."
Pretty much every job I've had has involved integrating with highly imperfect, changeable, and inaccurately implemented (and barely documented) third party APIs. That's where most of the work went and I don't see formal methods improving the situation any time soon.
My 2c I don't understand any of the material I've read describing them. What I do understand makes them sound like it will be a load of work for questionable benefits. If I end up writing safety-critical code. (Aerospace firmware, big robots etc), I will get over this hump and learn them. If not, I am not yet compelled; rather intimidated.
Maybe this is like Quaternions, that are actually very easy and useful, but suffer from confusing descriptions. Or maybe more like Monads, which are actually very abstract, and may not be suitable unless your the sort who understands Mathematician style mathematics.
More to the point: I'm not even sure how I would get started and evaluate them tacitly.
Of particular confusion: Does formal verification lead to a strange-loop style or "It's verification all the way down" scenario, where you are shifting the correctness from the original code to the verification? Then must verify the verification ad-infinitum? (This is almost certainly wrong, but I don't grasp why)
The big question I ask: "Would I rather have a code base with formal verification, or one in which all the time and effort used by add that were spent using and testing the software in a practical way; or code reviewing it"
Speaking for myself (and I bought Hillel's recently published Logic for Programmers): It's not clear to me which formal method I should use. I'm certain the answer is "there's a different best one for each situation", but I don't want to know one for each problem I'll face. I'd rather have a definitive answer to what is the second best for all situations, similar to how we can answer "python" to that question when the question is about general programming
Most programs don't need to be rigorously perfect. If they did, LLMs wouldn't be as popular as they are right now.
If you're dealing with medical equipment or space flight, maybe there's a need. But usually the goal is to make errors _inexpensive_ to find and fix, not theoretically impossible.
The ironic thing is that LLMs are what will make formal methods feasible.
First: LLMs find so many bugs and security holes in software right now. So you pretty much have to prove your stuff correct, if you don't want to get hacked into.
Second: LLMs make it much easier to apply formal methods. Just ask Claude to prove your stuff in Lean or whatever, no PhD required anymore.
I think everyone knows the answer already - it's too hard to be worth it for most problems. The article doesn't disagree with that and was a good read anyway. Don't skip it because you already know the answer.
IMO the reason is way more on the "it's too hard" side than "it isn't worth the effort". Formal verification is extremely common in the silicon hardware design world, despite its extreme cost (the tool licenses cost on the order of $100k per seat, as far as I can tell). And in this domain bugs are really expensive. But I think it would be used in spite of that simply because it is an order of magnitude easier than software formal verification.
I don't know if there is any solution to that. Software itself is an order of magnitude (or more) more complex than hardware... I think the author's suggestion of partial verification is the way to you. You're not going to formally verify your GUI but you could formally verify your LZ4 decoder. Maybe.
Formal verification is also extremely common in the software design world, to be fair. Most programming languages in use have at least a primitive type system and even those that historically didn't are gaining them (e.g. Typescript, Python gradual typing, etc.)
The question is, as always, to what degree do the returns start to diminish. The Rust crowd laughs at Go's level of formal verification and says that their level of formal verification is the right level, but then the Lean crowd laughs at Rust's level of verification and says that their level of formal verification is the right level. For crowds so concerned about mathematical proofs, it is funny that they end up right back at gut feeling.
For me, I wish the systems languages I am interested in could couple with legible verification systems, but alas, the world of formal methods seems disjoint. The only way to get a satisfactory development experience seems to be to learn Lean.
I recently came across a use case where formal methods were incredibly helpful. I've been rewriting Postgres in Rust and am currently focusing on correctness. The biggest challenge is that there's so much surface area to cover. Postgres has over 3000 user-facing functions, ranging from regular expression matching to JSON iteration to computing the gamma function. About half of these functions are simple pure functions.
Of the 3000 functions, I've been able to formally verify that the Rust behavior is identical to the Postgres C behavior for over 1000 of them. In the process, I found 4 different Postgres bugs. All of them would not be triggered under ordinary usage, but one, if triggered, would corrupt your database.
I think why formal methods works well for this is I'm testing a large number of small to medium self-contained pieces of code. For each of them the specification is simple: does postgres_fn(args) == pgrust_fn(args). I've been using Kani[0] which works across both Rust and C code so the proofs are based off the actual code and not a translation of the code to another language.
If you want to check out what all the verification look like, you can see them here[1]
[0] https://github.com/model-checking/kani
[1] https://github.com/malisper/pgrust/tree/main/proofs
> I found 4 different Postgres bugs.
Bugs in the upstream Postgres C implementations? Did you report them or submit patches? I'm curious to see what you found!
Yep, I did submit bug reports. This was on Tuesday. I don't see a public copy of the mailing list that has my bug reports yet. The four bugs were:
0) When parsing a macaddr[0], Postgres uses sscanf with %x. %x can wraparound. This means SELECT '10000000aa:bb:cc:dd:ee:ff'::macaddr; will return aa:bb:cc:dd:ee:ff.
1) When parsing a tid[1], Postgres uses strtoul. The return value of strtoul is different across platform for the empty string. This means on some platforms Postgres SELECT '(,5)'::tid; will error and others will accept it.
2) Postgres missed an overflow check in it's cash type[2]. When running SELECT '-92233720368547758.08'::money / (-1)::int8; some platforms will error and other's will return the MIN value. Postgres does check for this for some of the other cash related functions, but it missed it for one of them.
3) When hashing the "char" type Postgres will cast a char to an integer[3]. On some platforms char is signed and on others it's unsigned. This means the hash of a char can be different depending on the platform. If you are using a hash index or hash partitioning on a char and move your DB from x86 to arm, the hashes will differ and your index/partitioned tables become corrupted. Note that this is special char type that you have to refer to by "char" that is separate from the typically used CHAR(n) type which is what you typically use, hence this would never come up under real usage.
The common pattern with all of these is they rely on C behavior that differs across platform (integer overflow, char signedness, strtoul). Rust is better about having more consistent behavior across platforms so these cases get flagged when the Rust code and the C code differ.
[0] https://github.com/postgres/postgres/blob/REL_18_3/src/backe...
[1] https://github.com/postgres/postgres/blob/REL_18_3/src/backe...
[2] https://github.com/postgres/postgres/blob/REL_18_3/src/backe...
[3] https://github.com/postgres/postgres/blob/REL_18_3/src/backe...
To me, "this returns sorted lists" illustrates the crux.
You may know exactly what you want, and you may have a reasonably fast and cheap way to verify your code against a formal specification. But the formal specification needs to come from somewhere and for any non-trivial program its complexity is going to be in the same order of magnitude as the code implementing it. So we are back to writing "code" (which is what a formal specification is) that needs to be checked against what we actually want. And that "code" needs .. a test? Hard thinking? A formal verification itself?
Don't believe me that this is hard? Back to "this returns sorted lists". The promise of formal verification is that whatever implementation I throw at the verifier, as long as it passes the check, I'm happy (assuming that I can also encode things like running time and resource use). Now imagine a program that always returns the empty list. It satisfies "this returns sorted lists" trivially but is not at all what we want. The formal spec has a bug. Such issues can be subtle in larger projects and no amount of model checking or SMT solvers can guard you against a bug in that "code".
Don't get me wrong, it can be incredibly useful. But it's not the silver bullet that some proponents make it out to be. It's another tool next to testing, not instead of it. (The whole "testing can only prove the existence of bugs, not their absence, that's why we should use formal verification instead" is just misguided at best and propaganda at worst.)
I think every formal methods phd student who's interested in adoption of their techniques/tools has a short bout of doubt/depression upon realizing just how large of a surface area for bugs lives in a sufficiently useful specification.
This is deeply related to the conceptual error a lot of executives are currently making around automation in/of their software engineering orgs.
It has always been true that learning some formal methods probably makes you a better programmer in certain ways, even if you never use them. I think it's increasingly also true that learning some formal methods probably makes you a better manager of people/processes that product software.
I have a deeper problem. When I'm calling sort() it is useful that it returns a sorted list. However my program rarely has sorted lists of any sort in any requirement. My requirements are around the features my users care about. Sure the list of employees that I need to display needs to be sorted (sometimes by hire date, sometimes by title, sometimes by name - and often combinations of the above), but there are a lot of things I'm doing with that list that are not sorting.
I mean, just for this particular example, you could certainly also add a check that the sorted list is the same length as the input list.
That said, your broader point is more or less correct. I think the advantage of something like TLA+ is that the specs can generally be more abstract and as such the checks can be more exhaustive than you would likely get with regular "code".
With concurrent code, in particular, it can be difficult to know if your algorithm is correct, especially without the confounding variables that you get with a "real" programming language. Is my program broken because of some memory allocation quirk? Is it broken because of some peculiarity with how pthreads are dispatched? Or is my design wrong? Being able to work at an abstract level at least can check the last part.
Of course, though, you are correct that formal methods aren't silver bullets.
I think you'd want to specify that every element in the original list is present in the sorted list (and in the same number, in case of ties).
And of course, that raises the issue of what do you want to do about ties....
> The promise of formal verification
The promise of formal verification (and testing) is essentially the same promise as double-entry accounting. It assumes that if you do the same thing twice that it is unlikely you will screw it up in the exact same way twice. When there is disagreement it tells you that something went wrong, but you still need to look at both sides to determine which one is wrong. There is no such thing as a panacea, of course.
> It's another tool next to testing, not instead of it.
Theoretically it is instead of. They both are trying to solve the exact same problem. The real world with real constraints, of course, isn't so neat and tidy, so they don't end up perfectly overlapping.
We do. It's called a type checker. Every "formally verified" system is going to be partially verified. e.g. you might prove your sort procedure sorts, but did you prove its complexity? Under a cost model for integer compares or a cost model for page fetches? Or both? Multi-layer cache page fetch costs? How well you verify just depends on how well you decide to model the problem. Different type checkers have different modeling features.
This is a more useful perspective; it's not "we do/don't use formal methods," but instead "how can I more precisely model my domain?" Helpfully, if you model your domain well, code tends to be obvious/write itself.
One of my favorite quotes on this topic is:
"Type systems are just the parts of formal verification we've figured out how to make fast."
Thankfully this is no longer strictly true. So, I think the quote needs a slight adjustment, "Type systems and $THING are just ...", but $THING is not very well defined yet. Between "linters", and other relatively fast AST-based rule enforcers, some of which looking at higher order behavior, I think we now have an amalgamation of formally verified concepts that we can consider fast enough and sufficient exercised in practice that we are ever closer to widespread formally and dependably verified software.
Still, it's a long journey, and academic formal verification would always be, by design, a few steps ahead of what the industry can do efficiently in practice.
In most industries that need software made for them it's hard enough to get people to care about spending enough time on informal methods let alone formal ones. I simply don't think most of the industry has had the breathing room and respect for engineering for this pattern to develop.
I think its also about tolerance for failure. For software that must not fail or where reliability commands a premium you would be wise to invest in formal methods. Core systems at aws for example. For throwaway CRUD code its just easier to try iterations on the problem and call it a day. Its not about respect just RoI.
I think programmers in general do not give much thought to the level of engineering required for a task.
Mostly, there's too little, but there are many cases when there's too much. I see people writing tons of tests for corporate software that will be used by a couple of people and will have to be updated regularly anyway.
Building a hut is not the same as building a skyscraper, but we don't really have guidelines for different software projects. No methodology I've ever seen distinguishes types of projects by complexity.
I've been a big nerd for formal methods for quite awhile, and have been broadly unsuccessful in getting employers onboard.
I have pretty cynical opinions as to the "why" of this, largely involving the fact that the vast majority of software engineers refuse to learn anything that they weren't explicitly taught in college, but regardless of the reason whenever I have tried proposing TLA+ in the past, people will nod along and wait for me to stop talking. I've had several managers say "they'll look into it", which was such an obvious lie that I don't know why they even bothered.
I've "snuck in" TLA+ usage a few times. I gave up on getting anyone else to use TLA+, but as I've gotten more senior-level, I have been given a fair bit more leeway on how I approach projects and as such I have been able to budget myself a day or two to model some of the less-obvious bits of concurrency.
All that said, I have had some luck with designing stuff with TLA+, then feeding the spec into Claude and getting that to implement the actual executable code. Maybe I'll be able to convince an employer that's a good use of time now.
> I have pretty cynical opinions as to the "why" of this, largely involving the fact that the vast majority of software engineers refuse to learn anything that they weren't explicitly taught in college, but regardless of the reason
I think it's not only SWEs, but general persons that goe to college primarily to get a job, without having a natural curiosity for things.
Probably true, I've just only ever worked in the software engineering world so I cannot speak about anything else.
https://blog.janestreet.com/formal-methods-at-jane-street-in...
I thought this article from Jane Street makes a nice complimentary pairing.
This blog is actually very useful... There's also the flip side, possibly due to the expense (technically, intellectually, and emotionally), where "IT'S FORMALLY VERIFIED!!" has become some marketing code for "it's safe, secure, and PFAS free..." - just because something is formally verified, doesn't mean it's secure or fit for purpose. It usually just means it conforms to a given spec "and that's that..."
Pretty much every job I've had has involved integrating with highly imperfect, changeable, and inaccurately implemented (and barely documented) third party APIs. That's where most of the work went and I don't see formal methods improving the situation any time soon.
My 2c I don't understand any of the material I've read describing them. What I do understand makes them sound like it will be a load of work for questionable benefits. If I end up writing safety-critical code. (Aerospace firmware, big robots etc), I will get over this hump and learn them. If not, I am not yet compelled; rather intimidated.
Maybe this is like Quaternions, that are actually very easy and useful, but suffer from confusing descriptions. Or maybe more like Monads, which are actually very abstract, and may not be suitable unless your the sort who understands Mathematician style mathematics.
More to the point: I'm not even sure how I would get started and evaluate them tacitly.
Of particular confusion: Does formal verification lead to a strange-loop style or "It's verification all the way down" scenario, where you are shifting the correctness from the original code to the verification? Then must verify the verification ad-infinitum? (This is almost certainly wrong, but I don't grasp why)
The big question I ask: "Would I rather have a code base with formal verification, or one in which all the time and effort used by add that were spent using and testing the software in a practical way; or code reviewing it"
I think it's the culture is software engineering.
In a good delivery app/social network it seems like a waste of time to use formal methods.
When designing software for aircraft, pacemakers, fintechs, cryptography and DeFi protocols there is a bit of value for formal methods.
The problem is the often people with the food app/social network culture are hired to build DeFi protocols.
Which explains why so much money is being stolen form DeFi protocols of late.
So why people don't use formal methods.
- 95% of the time, the stakes are low
- 5% of the time, the engineers don't understand the value of formal methods.
Leslie Lamport once joked that if software developers were architects, they would first build a skyscraper and then later draw the blue print.
Also you can write a perfect specification get into implementation and have to step back and redesign.
Software is fast to iterate and test that a lot assumptions can be proven by actually writing the code.
Software is closer to gardening or painting. We discover a lot through practice and writing code. Then we can often write more formal specifications.
But formal method is impractical for most software upfront, and instead is likely used for more serious runtime failures or cost of life.
That's just my two cents.
I enjoyed this quote from the article, which concisely summarizes the first part of the above comment:
> “website isn’t airplane!!!”
Speaking for myself (and I bought Hillel's recently published Logic for Programmers): It's not clear to me which formal method I should use. I'm certain the answer is "there's a different best one for each situation", but I don't want to know one for each problem I'll face. I'd rather have a definitive answer to what is the second best for all situations, similar to how we can answer "python" to that question when the question is about general programming
> similar to how we can answer "python" to that question when the question is about general programming
An ironic claim in the context of formal methods.
Out of curiosity, why’s that? I don’t know formal methods nor it’s relationship to python.
Isn't the problem with formal methods that it isn't clear whether or not most of the useful code we use are actually formally verifiable?
The article mentions NP-complete, but is it actually a solvable problem in general?
> For extremely restricted cases, like propositional logic or HM type-checking, it’s “only” NP-complete.
Because there is almost never a business need?
Most programs don't need to be rigorously perfect. If they did, LLMs wouldn't be as popular as they are right now.
If you're dealing with medical equipment or space flight, maybe there's a need. But usually the goal is to make errors _inexpensive_ to find and fix, not theoretically impossible.
The ironic thing is that LLMs are what will make formal methods feasible.
First: LLMs find so many bugs and security holes in software right now. So you pretty much have to prove your stuff correct, if you don't want to get hacked into.
Second: LLMs make it much easier to apply formal methods. Just ask Claude to prove your stuff in Lean or whatever, no PhD required anymore.
I would say the tooling plays a part. Where are the go-to open source solution that a beginner can turn to without too much research?
I think everyone knows the answer already - it's too hard to be worth it for most problems. The article doesn't disagree with that and was a good read anyway. Don't skip it because you already know the answer.
IMO the reason is way more on the "it's too hard" side than "it isn't worth the effort". Formal verification is extremely common in the silicon hardware design world, despite its extreme cost (the tool licenses cost on the order of $100k per seat, as far as I can tell). And in this domain bugs are really expensive. But I think it would be used in spite of that simply because it is an order of magnitude easier than software formal verification.
I don't know if there is any solution to that. Software itself is an order of magnitude (or more) more complex than hardware... I think the author's suggestion of partial verification is the way to you. You're not going to formally verify your GUI but you could formally verify your LZ4 decoder. Maybe.
Formal verification is also extremely common in the software design world, to be fair. Most programming languages in use have at least a primitive type system and even those that historically didn't are gaining them (e.g. Typescript, Python gradual typing, etc.)
The question is, as always, to what degree do the returns start to diminish. The Rust crowd laughs at Go's level of formal verification and says that their level of formal verification is the right level, but then the Lean crowd laughs at Rust's level of verification and says that their level of formal verification is the right level. For crowds so concerned about mathematical proofs, it is funny that they end up right back at gut feeling.
For me, I wish the systems languages I am interested in could couple with legible verification systems, but alas, the world of formal methods seems disjoint. The only way to get a satisfactory development experience seems to be to learn Lean.