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
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
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
Applied Formal Logic: Brute Force String Search June 19, 2017
Need is there, but tools are not.
Let’s play with Frama-C.Read more…
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.Read more…
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
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.Read more…
Software Foundations, Volume 1: Logical Foundations December 8, 2017
There is a certain amount of celebration going on at Maniagnosis’ underground lair at the moment. (Underground lair? There’s nothing underground or lair-ish about this place. It’s not even spectacularly office-like. –Ed) I have (Insert lame drum-roll here.) completed all of the exercises in Software Foundations, Vol. 1: Logical Foundations by Benjamin Pierce, et al. (Very much al.)
(Cue fireworks!) Pop!Read more…