Posts tagged "toy problems"

Einstein's problem December 24, 2009

Phantom Types in Java June 19, 2010

Phantom Types in Java, Revisted July 5, 2010

Monads and regular expressions August 8, 2010

Variations on the theme of monadic regular expressions: Abstraction September 6, 2010

Variations on the theme of monadic regular expressions: Records September 13, 2010

Variations on the theme of monadic regular expressions: Back references September 14, 2010

"(How to write a (Lisp) interpreter (in C++) (or make Peter Norvig cry, whichever comes first))" October 11, 2010

Knights, knaves, and Program Construction November 11, 2010

More Phantom Types in Java December 9, 2010

A paean to the pulldown resistor March 6, 2011

Tony Morris on static types May 9, 2011

Snakes! On a Yeti! July 4, 2011

Mad science, abstract data types, and objects December 12, 2011

State space search: the basics January 15, 2012

State space search: heuristics January 22, 2012

Nth Fibonacci number in Emacs Lisp January 29, 2012

State space search: A* February 1, 2012

Update to "Mad science, abstract data types, and objects" July 13, 2012

Letterpress cheating in Rust 0.7 July 6, 2013

Letterpress cheating in Rust 0.8 October 6, 2013

Letterpress cheating in Rust 0.11.0, part 1 July 19, 2014

Letterpress cheating in Rust 0.11.0, part 2 August 9, 2014

Abstracted Algebra in Rust July 19, 2015

More Abstracted Algebra in Rust July 28, 2015

Letterpress cheating in Rust 1.6: How long has it been?!? January 27, 2016

Push-parsing and Pony July 2, 2016

Hey, let’s write a quick parser! A simple one, for the simple version of hoc from The Unix Programming Environment. The chapter on hoc is used to demonstrate the use of the yacc parser; it’s a dandy example to play with parsing.

I haven’t hand written a parser in a long time, so that’s what I want to do now. But there is a bit of a catch: it reads from stdin in Pony. And the interface for that is:

interface StdinNotify
  """
  Notification for data arriving via stdin.
  """
  fun ref apply(data: Array[U8] iso) =>
    """
    Called when data is available on stdin.
    """
    None

  fun ref dispose() =>
    """
    Called when no more data will arrive on stdin.
    """
    None
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Applied Formal Logic: Brute Force String Search June 19, 2017

Need is there, but tools are not.

– zzz95

Let’s play with Frama-C.

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Applied Formal Logic: The bug in Quick Search June 23, 2017

In my last post, I presented a brief introduction to Frama-C and to the process of verifying properties about a very simple C function, a brute force string search. This time around, I intended to do roughly the same thing, using a slightly more complicated function, a faster string searching algorithm. Unfortunately, in doing so, I found a bug in the algorithm. Admittedly, the bug is rather minor and should not affect the actual behavior of an implementation in practice, but still, it is doing something it shouldn’t ought to be doing.

The string searching algorithm I am looking at this time is Quick Search, so named by Daniel M. Sunday in 1990 because it “is a simple, fast, practical algorithm [and] because it can be both coded and debugged quickly” (“A Very Fast Substring Search Algorithm” [PDF]. It is my personal favorite string search because it is, indeed, simple, fast, and practical. Let me quickly show why.

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Applied Formal Logic: Correctness of Quick Search July 16, 2017

When last I left, I had verified that the implementation of Quick Search was safe: the modified algorithm didn’t access memory it shouldn’t, it didn’t have numeric overflows, and it didn’t modify anything outside of its own implementation. And, using Frama-C, the process hadn’t hardly been torturous or even particularly unpleasant at all. The most important tasks were describing the requirements for calling the two functions. Those requirements are…detailed…but nothing more than what an experienced C programmer would have in mind while writing or calling the functions. A final set of shiny set of annotations ensured that the loops and the variable modifications needed by them behaved themselves.

But I hadn’t done anything about proving that the function actually did what it claimed it was supposed to do. It’s not hard to understand (one of the reasons I like Quick Search), but the ANSI/ISO C Specification Language is unfamiliar and I didn’t know how to express what went on, where. Fortunately, Yannick Moy, a software engineer at AdaCore, came to my assistance with an excellent introduction to doing the same thing with SPARK, and Loïc Correnson, one of the creators of Frama-C, popped in with some excellent suggestions (and very flattering comments).

So now, for your software verification pleasure, here is my essay at proving the correctness of Quick Search. It pretty much follows the same pattern as Yannick’s, but I did come up with a slightly different postcondition for make_bad_shift.

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Applied Formal Logic: Verifying Quicksort August 9, 2017

Have you ever tried to solve a problem, gotten stuck, backed off, tried again, changed approaches, failed, and then suddenly, with some approach that you’d already abandoned, solved the problem as sweetly as Penelope Doglington begging for part of your sandwich? I’ve had one of those weeks, and now I honestly don’t know what the problem was. Everything seems to be all better now.

So, here it is: my proof of Quicksort. The proof, which is mine, is mine. And therefore, my proof, which belongs to me, is as follows.

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