If you have been trained in the use of formal methods (FM) for programming:

  • How useful have you found it?
  • What did your FM training involve (e.g. a course, a book)?
  • What FM tools do you use?
  • What advantages in speed/quality has it given you compared to not using FM?
  • What kind of software do you create with FM?
  • And if you don't directly use FM now, was it at least worth learning??

I'm curious to hear as many experiences/opinions on FM as can be found in this community; I'm starting to read up on it and want to know more.


Programming and software development/engineering are some of the newest human skills/professions on Earth, so not surprisingly, the field is immature — that shows in our field's main output, as code that is typically late and error-prone. Industry immaturity is also shown by the wide margin (at least 10:1) in productivity between average and top coders. Such dismal facts are well covered in the literature, and introduced by books like Steve McConnell's Code Complete.

The use of formal methods (FM) has been proposed by major figures in software/CS (e.g. the late E. Dijkstra) to address (one of) the root causes of errors: the lack of mathematical rigour in programming. Dijkstra, for instance, advocated for students developing a program and its proof together.

FM seems to be much more prevalent in CS curricula in Europe compared to the US. But in the past few years, new "lightweight" FM approaches and tools like Alloy have attracted some attention. Still, FM is far from common usage in industry, and I'm hoping for some feedback here on why.


As of now (10/14/2010), of the 6 answers below, no one has clearly argued for the usage of FM in "real world" work. I'm really curious if someone can and will; or perhaps FM really does illustrate the divide between academia (FM is the future!) and industry (FM is mostly useless).

  • Regarding your update, maybe no one has argued for the usage of FM in "real world" work because there are very few use cases for them in real world work
    – Richard
    Nov 3, 2011 at 12:42

8 Answers 8


Absolutely useless for anything nontrivial.

I had a course called, aptly, "Formal Methods" that focused on Alloy- I can't possibly see using that anywhere. Had another class that focused on concurrency modeling with LTSA- equally useless.

The problem is that most bugs and problems in software (at least in my experience) arise from complexity that occurs below the level of abstraction of those tools.

  • Thanks for sharing; Would you say the training in FM was at least helpful to your later work, e.g. helped you think more clearly? Or not?
    – limist
    Oct 7, 2010 at 23:34
  • @limist: I really don't think so. I mean, I kinda liked Alloy, but I don't think it was useful even just to expanding how I think. Oct 8, 2010 at 4:08
  • 2
    This is exactly the answer I would have given. The most totally redundant class I took at university and not something I have ever looked back on and been glad I learned it. I think the root of the problem is that the Formal Specification must be more complex than the code in order to model it correctly, so for any remotely complex code it's a massively arduous task creating a formal model of it, to the point that I can't imagine anyone outside hardware design or similarly irrevocable work wanting or being able to do it.
    – glenatron
    Oct 14, 2010 at 21:39
  • 1
    That's disappointing. I was imagining it might be useful for testing that you had a reasonably complete model; while the actual bugs would most often be below the model (screwing up the mutexes or whatever), I assumed it would be useful to use Alloy to find flaws in the model itself. (Intuitively it seems less likely to be useful to try to use a proof assistant; I'd expect counterexamples to be more useful, and that seems more in the domain of things like Alloy (though ideally I guess it would be good to be able to approach both in the same system).) Dec 20, 2012 at 16:04

I have a background in CSP (Communicating Sequential Processes). Not to toot my own horn but I wrote my Master's thesis on Timed CSP, particularly "compiling" specifications written in formal methods into executable C++. I can say I have some experience with formal methods. Once I completed my degree and got a job in the industry, I have not been using formal methods at all. Formal methods is still too theoretical to be applied in the industry. Formal methods have found some practical application in the area of embedded systems. For example, NASA uses formal methods in their projects. I would speculate that formal methods are very far from being widely adopted in the industry. It simply does not make sense to write software specifications in formal methods and then "human interpret" them to your framework of choice. Plain English and diagrams work better for that, while unit and integration tests have been doing a pretty good job of "verifying" the correctness of code. I think formal methods will remain in the world of academia for some time.

  • Thanks for sharing, I'll ask a follow-up repeated often on this Q: Would you say the training in FM was at least helpful to your later work, e.g. helped you think more clearly? Or not?
    – limist
    Oct 7, 2010 at 23:35
  • Congrats on your masters!
    – Chris
    Oct 8, 2010 at 0:13
  • @limist: I would say it was a very good theoretical experience, but I found very little practical application in the industry.
    – ysolik
    Oct 8, 2010 at 3:24

State diagrams and Petri nets are useful for modelling and analyzing protocols and realtime systems. First they help design a solution. Second they help find test cases for exciting software in very specific situations.


I've read a few books about formal methods, and applied some. My immediate reaction was, "Gee, these books tell me how to be a good programmer, as long as I'm a perfect mathematician." Another weakness is that you can only prove equivalence with another formal description. Writing up a formal specification for a program is tantamount to writing a program in a higher-level language, and there's no way you can avoid introducing bugs in a reasonably large spec.

I've never made formal methods work on a large scale. They can be useful in getting something small and tricky correct, and in convincing me that they're correct. In that way, I can work with slightly larger building blocks and sometimes get a little more done.

One thing I did pick up that is more generally useful is the concept of an invariant, a statement about a program and its state that is always true. Anything you can reason from is good.

As alluded to above, I'm not a perfect mathematician, and so my proofs sometimes contain errors. However, in my experience these tend to be big dumb mistakes that are easy to catch and fix.


I took a graduate course in formal program analysis, where we focused on operational semantics. I did my final paper on the seL4 effort, reviewing the formal methods they used. My primary take-away in terms of practicality was that it's of marginal value. Not only do you have to write the program, you have to write the proof. Wow. Two sources of bugs. Not just one. Further, there was an enormous amount of restrictions placed on the actual code. It's very hard to formally describe a physical computer, including I/O.

  • I once saw a stab at describing tape-style I/O. The author had no solutions for formally describing random access files, and contented himself with badmouthing them. Oct 8, 2010 at 17:43
  • 1
    @David: Those random-access files. Bad news. You don't want to use them. =) Oct 8, 2010 at 20:19

Self-taught myself TLA+ last year, have been using it ever since. It's one of the first tools I reach for whenever I start a project. The mistake most people make is they assume that formal methods is an all-or-nothing thing: either you're not using formal methods or you have complete verification. However, there's something between them: formal specification, where you check that an abstract specification of your project doesn't break your invariants. Unlike verification, specification is practical enough to use in industry.

Specification languages are more expressive than programming languages. For example, here's a (very) simple PlusCal spec for a distributed data store:

process node \in 1..5 \* Nodes
variables online = TRUE,
          stored \in SUBSET data; \* Some set
      with node \in Nodes, datum \in stored do
        node.stored := node.stored \union {datum};
    or \* crash
      online := FALSE;
    end either;
end process;

This snippet specifies five nodes running simultaneously, running transfers in an arbitrary order, where every transfer is an arbitrary piece of data to an arbitrary node. Additionally, we've specified that any given transfer may fail and cause the node to crash. And we can simulate all of these behaviors in the TLA+ model checker! That way we can test that regardless of order, failure rates, etc, our requirements still hold. Speaking of which, let's add a couple of requirements. First, that we never transfer data to an offline node:

[][\A node \in Nodes: ~online => UNCHANGED node.stored]_vars

In our simplified version, the model checker will find a failure state. We can also specify "any given piece of data is in at least one online node":

\A d \in data: \E n \in Nodes: n.online /\ d \in n.stored

Which will also fail. Good luck checking these with a unit test!

The main limitation of specification is it exists independently of your actual code. It can only tell you that your design is correct, not that you implemented it right. But it's faster to specify than verify and it catches bugs that are too subtle for testing, so I find it worth the effort. Pretty much any code involving concurrency or multiple systems is a good place for a formal spec.


I used to work in a department at ICL, before they were bought up by Fujitsu. They had some large government-type contracts that required proof that the software worked as advertised, so they built a machine that would take the formal specification written in Z and validate the code as it ran, with a big green or red light for pass/fail.

It was an amazing thing, but, as the esteemed @FishToaster points out, it was useless for anything non-trivial.

  1. "How useful have you found it?"

The application of Petri Nets to computer programming is very useful. I created “Net Elements and Annotations”, a method based on Petri Nets (Chionglo, 2014). I have been applying the method since 2014 to write JavaScript programs that use the Acrobat/JavaScript API for PDF form applications.

  1. What did your FM training involve (e.g. a course, a book)?

I “trained” on Petri Nets through self-study. I read the chapters on Petri Nets from the textbook “Petri Nets and Grafcet: Tools for Modelling Discrete Event Systems” (David and Alla, 1992). I have also been reading research papers on Petri Nets. After creating and documenting “Net Elements and Annotations” I practiced on applying the method for several weeks.

  1. What FM tools do you use?

I draw Petri Net diagrams using PowerPoint. I create the form view of annotations using Word. I create token games as PDF form applications using Acrobat and Notepad too. After adding the entries into the form the translation of these entries into JavaScript code is systematic. Thus it should be possible to automate the translation. If the “entries” were added to the graphics objects in PowerPoint then it should also be possible to systematically translate them into JavaScript code and to automate this translation as well. I also use a set of work-in-progress tools that performs these translations and for creating additional resources for creating PDF form applications (Chionglo, 2018; 2017).

  1. What advantages in speed/quality has it given you compared to not using FM?

I can write JavaScript programs using “Net Elements and Annotations” faster than I can write a JavaScript program without using “Net Elements and Annotations”. And for large programs I can stop coding and return to coding later (or much later) without wondering where to continue (Chionglo, 2019). In some cases I can write JavaScript programs using “Net Elements and Annotations” but cannot write the JavaScript programs without using “Net Elements and Annotations”. For example I could not have created non-recursive implementations of recursive functions without the use of “Net Elements and Annotations” (Chionglo, 2019b; 2018b; 2016). These are true with or without the work-in-progress tools.

  1. "What kind of software do you create with FM?"

I use “Net Elements and Annotations” to create JavaScript programs that use the Acrobat/JavaScript API for PDF form applications. I can also apply the method to create JavaScript programs for HTML documents and to create Arduino Sketches (Chionglo, 2019c; 2019d).

  1. "And if you don't directly use FM now, was it at least worth learning?" Not applicable.


Chionglo, J. F. (2019b). Computing the N-th Term of a Recursive Relation: Using a Non-Recursive Function – A Reply to a Question at Mathematics Stack Exchange. < https://www.academia.edu/38496025/Computing_the_N-th_Term_of_a_Recursive_Relation_Using_a_Non-Recursive_Function_A_Reply_to_a_Question_at_Mathematics_Stack_Exchange>.

Chionglo, J. F. (2019c). Flame Effect Control Logic, Simulation and Sketch: A Reply to a Request at the Arduino Community Forum. https://www.academia.edu/40342956/Flame_Effect_Control_Logic_Simulation_and_Sketch_A_Reply_to_a_Request_at_the_Arduino_Community_Forum.

Chionglo, J. F. (2019). How I Continue Coding an Application after a Long Break? Reply to “How do you know where you stopped in your codes after a 2-week break?” – Software Engineering Stack Exchange. https://www.academia.edu/39705042/How_I_Continue_Coding_an_Application_after_a_Long_Break_Reply_to_How_do_you_know_where_you_stopped_in_your_codes_after_a_2-week_break_Software_Engineering_Stack_Exchange.

Chionglo, J. F. (2019d). Show-and-Hide Control Logic: Inspired by a Question at Stack Overflow. < https://www.academia.edu/40283015/Show-and-Hide_Control_Logic_Inspired_by_a_Question_at_Stack_Overflow>.

Chionglo, J. F. (2018b). A Petri Net Model for the Factorial of a Number: And a Non-Recursive JavaScript Function to Compute It. <>.

Chionglo, J. F. (2018). Create Hyper Form™ - A Workflow in Progress: Update on the Net Programming Research. https://www.academia.edu/37697498/Create_Hyper_Form_-A_Workflow_in_Progress_Update_on_the_Net_Programming_Research.

Chionglo, J. F. (2017). Net Programming: A Research Proposal: For Developing PDF Form Applications with PowerPoint and Acrobat. https://www.academia.edu/33374809/Net_Programming_A_Research_Proposal_For_Developing_PDF_Form_Applications_with_PowerPoint_and_Acrobat..

Chionglo, J. F. (2016). A Petri Net Model for Computing the Fibonacci Number. https://www.academia.edu/31748108/A_Petri_Net_Model_for_Computing_the_Fibonacci_Number.

Chionglo, J. F. (2014). Net Elements and Annotations for Computer Programming: Computations and Interactions in PDF. https://www.academia.edu/26906314/Net_Elements_and_Annotations_for_Computer_Programming_Computations_and_Interactions_in_PDF.

David, R. and H. Alla. (1992). Petri Nets and Grafcet: Tools for Modeling Discrete-Event Systems. Upper Saddle, NJ: Prentice Hall.

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