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In some sports certain techniques or elements are named after the athlete who invented or first performed them—for example, Biellmann spin.
Is their widespread use of such names for programming techniques and idioms? What are they? To be clear, I am explicitly not asking about algorithms, which are quite often named after their creators.
For example, one is Schwartzian transform, but I can't recall any more.
The functional programming technique currying is named after its (re)-inventor, Haskell Curry.
Boolean logic is named after George Boole
Duff's device is pretty famous and seems to me to qualify as technique/idiom.
I used to do a "Carmack" which was referring to the "fast inverse square root" but according to the Wikipedia entry the technique was probably found by the smarties at SGI in 1990 or so.
Even if it doesn't fit your description, it's still a pretty amazing read :)
Kleene closure: it's the * operator in regular expressions. It means "0 or more of what precedes it".
At one point in time, the Karnaugh Map could have been considered a technique to facilitate programming (albeit at a low level).
Markov Chains are named after Andrey Markov and used in programming to generate:
Google PageRank
Generating Spam-Mail Texts
Mnemonic Codewords to replace IDs/Hashvalues
The graphics world is full of eponymous techniques:
Bresenham's line algorithm
Bézier curve
Gouraud shading
Phong shading
Fisher-Yates shuffle, the standard way to implement an in-place random shuffle on an array.
Please edit to add more if found...
In Standard ML and other functional programming languages which use tuple and record literals, I sometimes see literals written thus:
( first
, second
, third
)
or
{ name = "Atwood"
, age = 37
, position = "founder"
, reports_to = NONE
}
This highly idiomatic layout, as opposed to layout where the commas or semicolons appear at the end of the line, is something that I have always heard referred to as MacQueen style, after Dave MacQueen (formerly of Bell Labs, now at the University of Chicago).
K&R (Kernighan and Ritchie) and Allman indentation styles.
I think timsort would qualify. It's used in python and open jdk 7
How about anything related to Bayes: Bayesian filtering, Bayesian inference, Bayesian classification. While rooted in statistics, these techniques have found their ways into plenty of programming-related applications.
Carmack's Reverse:
Depth fail
Around 2000, several people discovered that Heidmann's method can be made to work for all camera positions by reversing the depth. Instead of counting the shadow surfaces in front of the object's surface, the surfaces behind it can be counted just as easily, with the same end result. This solves the problem of the eye being in shadow, since shadow volumes between the eye and the object are not counted, but introduces the condition that the rear end of the shadow volume must be capped, or shadows will end up missing where the volume points backward to infinity.
Disable writes to the depth and colour buffers.
Use front-face culling.
Set the stencil operation to increment on depth fail (only count shadows behind the object).
Render the shadow volumes.
Use back-face culling.
Set the stencil operation to decrement on depth fail.
Render the shadow volumes.
The depth fail method has the same considerations regarding the stencil buffer's precision as the depth pass method. Also, similar to depth pass, it is sometimes referred to as the z-fail method.
William Bilodeau and Michael Songy discovered this technique in October 1998, and presented the technique at Creativity, a Creative Labs developer's conference, in 19991. Sim Dietrich presented this technique at a Creative Labs developer's forum in 1999 [2]. A few months later, William Bilodeau and Michael Songy filed a US patent application for the technique the same year, US patent 6384822, entitled "Method for rendering shadows using a shadow volume and a stencil buffer" issued in 2002. John Carmack of id Software independently discovered the algorithm in 2000 during the development of Doom 3 [3]. Since he advertised the technique to the larger public, it is often known as Carmack's Reverse.
ADL - Argument Dependent Lookup is also known as Koenig lookup (after Andrew Koenig although I don't think he appreciates it, as it didn't turn out the way he originally planned it)
Exception guarantees are often called Abrahams guarantees (Dave Abrahams) see (http://en.wikipedia.org/wiki/Abrahams_guarantees)
Liskov substitution principle http://en.wikipedia.org/wiki/Liskov_substitution_principle - Barabara Liskov
I am shocked that no one has mentioned Backus–Naur Form (BNF), named after John Backus and Peter Naur.
The method of constructing programs by computing weakest preconditions, as expounded in Edsger Dijkstra's book A Discipline of Programming, is usually referred to as Dijkstra's Method. It's more of a programming methodology than a technique, but it might qualify.
Several hard to fix or unusual software bugs has been categorized after famous scientists. Heisenbug could be the most known example.
Boyer-Moore string search algorithm: it can find a string inside a string of length N with fewer than N operations.
Seriously shocked to see that no one yet has mentioned Hindley Milner Type Inference.
In C++, the Barton-Nackman trick.
The BWT (Burroughs Wheeler Transform) is pretty important in data compression.
Jensen's Device
How about: Ada named after Ada Lovelace the first computer programmer??
Perhaps Hungarian notation might qualify? It was invented by Charles Simonyi (who was Hungarian).
In C++, the Schwartz counter (aka Nifty Counter) idiom is used to prevent multiple, static initialization of shared resources. It's named after Jerry Schwartz, original creator of the C++ iostreams at AT&T.
Related
Native support for differential programming has been added to Swift for the Swift for Tensorflow project. Julia has similar with Zygote.
What exactly is differentiable programming?
what does it enable? Wikipedia says
the programs can be differentiated throughout
but what does that mean?
how would one use it (e.g. a simple example)?
and how does it relate to automatic differentiation (the two seem conflated a lot of the time)?
I like to think about this question in terms of user-facing features (differentiable programming) vs implementation details (automatic differentiation).
From a user's perspective:
"Differentiable programming" is APIs for differentiation. An example is a def gradient(f) higher-order function for computing the gradient of f. These APIs may be first-class language features, or implemented in and provided by libraries.
"Automatic differentiation" is an implementation detail for automatically computing derivative functions. There are many techniques (e.g. source code transformation, operator overloading) and multiple modes (e.g. forward-mode, reverse-mode).
Explained in code:
def f(x):
return x * x * x
∇f = gradient(f)
print(∇f(4)) # 48.0
# Using the `gradient` API:
# ▶ differentiable programming.
# How `gradient` works to compute the gradient of `f`:
# ▶ automatic differentiation.
I never heard the term "differentiable programming" before reading your question, but having used the concepts noted in your references, both from the side of creating code to solve a derivative with Symbolic differentiation and with Automatic differentiation and having written interpreters and compilers, to me this just means that they have made the ability to calculate the numeric value of the derivative of a function easier. I don't know if they made it a First-class citizen, but the new way doesn't require the use of a function/method call; it is done with syntax and the compiler/interpreter hides the translation into calls.
If you look at the Zygote example it clearly shows the use of prime notation
julia> f(10), f'(10)
Most seasoned programmers would guess what I just noted because there was not a research paper explaining it. In other words it is just that obvious.
Another way to think about it is that if you have ever tried to calculate a derivative in a programming language you know how hard it can be at times and then ask yourself why don't they (the language designers and programmers) just add it into the language. In these cases they did.
What surprises me is how long it to took before derivatives became available via syntax instead of calls, but if you have ever worked with scientific code or coded neural networks at at that level then you will understand why this is a concept that is being touted as something of value.
Also I would not view this as another programming paradigm, but I am sure it will be added to the list.
How does it relate to automatic differentiation (the two seem conflated a lot of the time)?
In both cases that you referenced, they use automatic differentiation to calculate the derivative instead of using symbolic differentiation. I do not view differentiable programming and automatic differentiation as being two distinct sets, but instead that differentiable programming has a means of being implemented and the way they chose was to use automatic differentiation, they could have chose symbolic differentiation or some other means.
It seems you are trying to read more into what differential programming is than it really is. It is not a new way of programming, but just a nice feature added for doing derivatives.
Perhaps if they named it differentiable syntax it might have been more clear. The use of the word programming gives it more panache than I think it deserves.
EDIT
After skimming Swift Differentiable Programming Mega-Proposal and trying to compare that with the Julia example using Zygote, I would have to modify the answer into parts that talk about Zygote and then switch gears to talk about Swift. They each took a different path, but the commonality and bottom line is that the languages know something about differentiation which makes the job of coding them easier and hopefully produces less errors.
About the Wikipedia quote that
the programs can be differentiated throughout
At first reading it seems nonsense or at least lacks enough detail to understand it in context which is why I am sure you asked.
In having many years of digging into what others are trying to communicate, one learns that unless the source has been peer reviewed to take it with a grain of salt, and unless it is absolutely necessary to understand, then just ignore it. In this case if you ignore the sentence most of what your reference makes sense. However I take it that you want an answer, so let's try and figure out what it means.
The key word that has me perplexed is throughout, but since you note the statement came from Wikipedia and in Wikipedia they give three references for the statement, a search of the word throughout appears only in one
∂P: A Differentiable Programming System to Bridge Machine Learning and Scientific Computing
Thus, since our ∂P system does not require primitives to handle new
types, this means that almost all functions and types defined
throughout the language are automatically supported by Zygote, and
users can easily accelerate specific functions as they deem necessary.
So my take on this is that by going back to the source, e.g. the paper, you can better understand how that percolated up into Wikipedia, but it seems that the meaning was lost along the way.
In this case if you really want to know the meaning of that statement you should ask on the Wikipedia talk page and ask the author of the statement directly.
Also note that the paper referenced is not peer reviewed, so the statements in there may not have any meaning amongst peers at present. As I said, I would just ignore it and get on with writing wonderful code.
You can guess its definition by application of differentiability.
It's been used for optimization i.e. to calculate minimum value or maximum value
Many of these problems can be solved by finding the appropriate function and then using techniques to find the maximum or the minimum value required.
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A pure function is one that has no side effects -- it cannot do any kind of I/O and it cannot modify the state of anything -- and it is referentially transparent -- when called multiple times with the same inputs, it always gives the same outputs.
Why is the word "pure" used to describe functions with those properties? Who first used the word "pure" in that way, and when? Are there other words that mean roughly the same thing?
To answer your first question, mathematical functions have often been described as "pure" in terms of some specified variables. e.g.:
the first term is a pure function of x and the second term is a pure function of y
Because of this, I don't think you'll find a true "first" occurrence.
For programming languages, a little searching shows that Ada 95 (pragma Pure), High Performance Fortran (1993) (PURE) and VHDL-93 (pure) all contain formal notions of 'pure functions'.
Haskell (1990) is fairly obvious, but purity isn't explicit. GCC's C has various function attributes for various differing levels of 'pure'.
A couple of books: Rationale for the C programming language (1990) uses the term, as does Programming Languages and their Definitions (1984). However, both apparently only use it once! Programming the IBM Personal Computer, Pascal (also 1984) uses the term, but it isn't clear from Google's restricted view whether or not the Pascal compiler had support for it. (I suspect not.)
An interesting note is that Green, the predecessor to Ada, actually had a fairly strict 'function' definition - even memory allocation was disallowed. However, this was dropped before it became Ada, where functions can have side-effects (I/O or global variables), but can't modify their arguments.
C28-6571-3 (the first PL/I reference manual, written before the compiler) shows that PL/I had support for pure functions, in the form of the REDUCIBLE (= pure) attribute, as far back as 1966 - when the compiler was first released. (This also answers your third question.)
This last document specifically notes that it includes REDUCIBLE as a new change since document C28-6571-2. So REDUCIBLE, which is possibly the first incarnation of formal pure functions in programming languages, appeared somewhere between January and July 1966.
Update: The earliest instance of "pure function" on Google Groups in this sense is from 1988, which easily postdates the book references.
A couple of myths:
The term "pure functional" doesn't come from mathematics, where all functions are by nature "pure" and, so, there was never any need to call anything a "pure function".
The term doesn't come from imperative programming. The early imperative programming languages, Fortran, Algol 60, Pascal etc., always had two kinds of abstractions: "functions" that produced results based on their inputs and "procedures" which took some inputs and did an action. It was considered good programming practice for "functions" not to have side effects. There was no need for them to have side effects because one could always use procedures instead.
So, where else could the term "pure functional" have come from? The answer is - sort of- obvious. It came from impure functional programming languages, the foremost among them being Lisp. Lisp was designed sometime between 1958 and 1960 (between the first and second reports of Algol 60, whose design McCarthy was involved in, but didn't feel satisfied with). Lisp's design was based fundamentally on functional programming. However, it also allowed side-effects as a pragmatic choice. It did not have a notion of a command or a procedure. So, in Lisp, one mostly wrote "pure functions", but occasionally, one wrote "impure functions," i.e., functions with side-effects, to get something done. The terms "pure Lisp" or "purely functional subset of Lisp" have been in use for a long time. Slowly, by osmosis, this idea of "purity" has come to invade all our space.
The imperative programming languages could have resisted the trend. But, once C decided to abolish the idea of "procedures" and call them "void functions" instead, they didn't have much of a leg to stand on.
It comes from the mathematical definition of "function", where it is not possible for functions to have side effects.
Why is the word "pure" used to describe functions with those properties?
From Wiktionary > pure # adjective
free of flaws or imperfections; unsullied
free of foreign material or pollutants
free of immoral behavior or qualities; clean
of a branch of science, done for its own sake instead of serving another branch of science.
It should be obvious that the behavior of interacting functions is easiest to reason about when they are influenced only by their inputs, and they themselves influence only their outputs. Therefore it is inevitable that these kinds of functions will be noticed and classified. Now what word could we use to describe a function with such properties? "free of foreign material or pollutants" and "free of immoral behavior or qualities" seem to describe this rather well.
Who first used the word "pure" in that way, and when?
I am much too young to answer this with any degree of confidence. I argue, however, that it was inevitable that the word pure (or some very close synonym) would be used to describe functions that behave in this way.
Are there other words that mean roughly the same thing?
You said it yourself: "referentially transparent". However, you seem to suggest that "referential transparency" encompasses only part of the meaning of the phrase "pure function". I disagree; I feel it is entirely synonymous. From Wikipedia > Referential Transparency:
An expression is said to be referentially transparent if it can be replaced with its value without changing the behavior of a program. (emphasis mine)
The Haskell community sometimes uses the adjective "safe" in a similar manner. (See the Safe library, made to avoid throwing exceptions. Contrast with unsafePerformIO)
I can't think of any other synonyms right now.
The concept of a function originated in mathematics. The mathematical concept of a function is more-or-less a mapping from one set onto another. In this sense it's impossible for functions to have side effects; not because they're "better" that way or because they're specifically defined as to not have side effects, but because the concept of "having side effects" doesn't make any sense with this definition of a function. Mathematical functions aren't a series of steps that execute, so how could any of those steps somehow "affect" other mathematical objects you're talking about?
When people started studying computation, they became interested in machine-implementable algorithms for computing the values of mathematical functions given their inputs. People started talking about computable functions. But functions as implemented in a computer (in imperative languages at least, which are what programmers first worked with) are a series of executable steps, which obviously can have side effects.
So it became natural for programmers to think about functions as algorithms, not as mathematical functions. So then a pure function is one that is purely a mathematical function, to which all the hundreds of years of theory about functions applies, as opposed to the generalised programmer's function, which can't be reasoned about that way.
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When all you have is a pair of bolt cutters and a bottle of vodka, everything looks like the lock on the door of Wolf Blitzer's boathouse. (Replace that with a hammer and a nail if you don't read xkcd)
I currently program Clojure, Python, Java and PHP, so I am familiar with the C and LISP syntax as well as the whitespace thing. I know imperative, functional, immutable, OOP and a couple type systems and other things. Now I want more!
What are languages that take a different approach and would be useful for either practical tool choosing or theoretical understanding?
I don't feel like learning another functional language(Haskell) or another imperative OOP language(Ruby), nor do I want to practice impractical fun languages like Brainfuck.
One very interesting thing I found myself are monoiconic stack based languages like Factor.
Only when I feel I understand most concepts and have answers to all my questions, I want to start thinking about my own toy language to contain all my personal preferences.
Matters of practicality are highly subjective, so I will simply say that learning different language paradigms will only serve to make you a better programmer. What is more practical than that?
Functional, Haskell - I know you said that you didn't want to, but you should really really reconsider. You've gotten some functional exposure with Clojure and even Python, but you've not experienced it to its fullest without Haskell. If you're really against Haskell then good compromises are either ML or OCaml.
Declarative, Datalog - Many people would recommend Prolog in this slot, but I think Datalog is a cleaner example of a declarative language.
Array, J - I've only just discovered J, but I find it to be a stunning language. It will twist your mind into a pretzel. You will thank J for that.
Stack, Factor/Forth - Factor is very powerful and I plan to dig into it ASAP. Forth is the grand-daddy of the Stack languages, and as an added bonus it's simple to implement yourself. There is something to be said about learning through implementation.
Dataflow, Oz - I think the influence of Oz is on the upswing and will only continue to grow in the future.
Prototype-based, JavaScript / Io / Self - Self is the grand-daddy and highly influential on every prototype-based language. This is not the same as class-based OOP and shouldn't be treated as such. Many people come to a prototype language and create an ad-hoc class system, but if your goal is to expand your mind, then I think that is a mistake. Use the language to its full capacity. Read Organizing Programs without Classes for ideas.
Expert System, CLIPS - I always recommend this. If you know Prolog then you will likely have the upper-hand in getting up to speed, but it's a very different language.
Frink - Frink is a general purpose language, but it's famous for its system of unit conversions. I find this language to be very inspiring in its unrelenting drive to be the best at what it does. Plus... it's really fun!
Functional+Optional Types, Qi - You say you've experience with some type systems, but do you have experience with "skinnable* type systems? No one has... but they should. Qi is like Lisp in many ways, but its type system will blow your mind.
Actors+Fault-tolerance, Erlang - Erlang's process model gets a lot of the buzz, but its fault-tolerance and hot-code-swapping mechanisms are game-changing. You will not learn much about FP that you wouldn't learn with Clojure, but its FT features will make you wonder why more languages can't seem to get this right.
Enjoy!
What about Prolog (for unification/backtracking etc), Smalltalk (for "everything's a message"), Forth (reverse polish, threaded interpreters etc), Scheme (continuations)?
Not a language, but the Art of the Metaobject Protocol is mind-bending stuff
I second Haskell. Don't think "I know a Lisp, so I know functional programming". Ever heard of type classes? Algebraic data types? Monads? "Modern" (more or less - at least not 50 years old ;) ) functional languages, especially Haskell, have explored a plethora of very powerful useful new concepts. Type classes add ad-hoc polymorphism, but type inference (yet another thing the languages you already know don't have) works like a charm. Algebraic data types are simply awesome, especially for modelling trees-like data structures, but work fine for enums or simple records, too. And monads... well, let's just say people use them to make exceptions, I/O, parsers, list comprehensions and much more - in purely functional ways!
Also, the whole topic is deep enough to keep one busy for years ;)
I currently program Clojure, Python, Java and PHP [...] What are languages that take a different approach and would be useful for either practical tool choosing or theoretical understanding?
C
There's a lot of C code lying around---it's definitely practical. If you learn C++ too, there's a big lot of more code around (and the leap is short once you know C and Java).
It also gives you (or forces you to have) a great understanding of some theoretical issues; for instance, each running program lives in a 4 GB byte array, in some sense. Pointers in C are really just indices into this array---they're just a different kind of integer. No different in Java, Python, PHP, except hidden beneath a surface layer.
Also, you can write object-oriented code in C, you just have to be a bit manual about vtables and such. Simon Tatham's Portable Puzzle Collection is a great example of fairly accessible object-oriented C code; it's also fairly well designed and well worth a read to a beginner/intermediate C programmer. This is what happens in Haskell too---type classes are in some sense "just another vtable".
Another great thing about C: engaging in Q&A with skilled C programmers will get you a lot of answers that explain C in terms of lower-level constructs, which builds your closer-to-the-iron knowledge base.
I may be missing OP's point---I think I am, judging by the other answers---but I think it might be a useful answer to other people who have a similar question and read this thread.
From Peter Norvig's site:
"Learn at least a half dozen programming languages. Include one language that supports class abstractions (like Java or C++), one that supports functional abstraction (like Lisp or ML), one that supports syntactic abstraction (like Lisp), one that supports declarative specifications (like Prolog or C++ templates), one that supports coroutines (like Icon or Scheme), and one that supports parallelism (like Sisal). "
http://norvig.com/21-days.html
I'm amazed that after 6 months and hundreds of votes, noone has mentioned SQL ...
In the types as theorems / advanced type systems: Coq ( I think Agda comes in this category too).
Coq is a proof assistant embedded into a functional programing language.
You can write mathematical proofs and Coq helps to build a solution.
You can write functions and prove properties about it.
It has dependent types, that alone blew my mind. A simple example:
concatenate: forall (A:Set)(n m:nat), (array A m)->(array A n)->(array A (n+m))
is the signature of a function that concatenates two arrays of size n and m of elements of A and returns an array of size (n+m). It won't compile if the function doesn't return that!
Is based on the calculus of inductive constructions, and it has a solid theory behind it.
I'm not smart enough to understand it all, but I think is worth taking a look, specially if you trend towards type theory.
EDIT: I need to mention: you write a function in Coq and then you can PROVE it is correct for any input, that is amazing!
One of the languages which i am interested for have a very different point of view (including a new vocabulary to define the language elements and a radical diff syntax) is J. Haskell would be the obvious choice for me, although it is a functional lang, cause its type system and other unique features open your mind and makes you rethink you previous knowledge in (functional) programming.
Just like fogus has suggested it to you in his list, I advise you too to look at the language OzML/Mozart
Many paradigms, mainly targetted at concurrency/multi agent programming.
Concerning concurrency, and distributed calculus, the equivalent of Lambda calculus (which is behind functionnal programming) is called the Pi Calculus.
I have only started begining to look at some implementation of the Pi calculus. But they already have enlarged my conceptions of computing.
Pict
Nomadic Pict
FunLoft. (this one is pretty recent, conceived at INRIA)
Dataflow programming, aka flow-based programming is a good step ahead on the road. Some buzzwords: paralell processing, rapid prototyping, visual programming (not as bad as sounds first).
Wikipedia's articles are good:
In computer science, flow-based
programming (FBP) is a programming
paradigm that defines applications as
networks of "black box" processes,
which exchange data across predefined
connections by message passing, where
the connections are specified
externally to the processes. These
black box processes can be reconnected
endlessly to form different
applications without having to be
changed internally. FBP is thus
naturally component-oriented.
http://en.wikipedia.org/wiki/Flow-based_programming
http://en.wikipedia.org/wiki/Dataflow_programming
http://en.wikipedia.org/wiki/Actor_model
Read JPM's book: http://jpaulmorrison.com/fbp/
(We've written a simple implementation in C++ for home automation purposes, and we're very happy with it. Documentation is under construction.)
You've learned a lot of languages. Now is the time to focus on one language, and master it.
perhaps you might want to try LabView for it's visual programming, although it's for engineering purposes.
nevertheless, you seem pretty interested in all that's out there, hence the suggestion
also, you could try the android appinventor for visually building stuff
Bruce A. Tate, taking a page from The Pragmatic Programmer wrote a book on exactly that:
Seven Languages in Seven Weeks: A Pragmatic Guide to Learning Programming Languages
In the book, he covers Clojure, Haskell, Io, Prolog, Scala, Erlang, and Ruby.
Mercury: http://www.mercury.csse.unimelb.edu.au/
It's a typed Prolog, with uniqueness types and modes (i.e. specifying that the predicate append(X,Y,Z) meaning X appended to Y is Z yields one Z given an X and Y, but can yield multiple X/Ys for a given Z). Also, no cut or other extra-logical predicates.
If you will, it's to Prolog as Haskell is to Lisp.
Programming does not cover the task of programmers.
New things are always interesting, but there are some very cool old stuff.
The first database system was dBaseIII for me, I was spending about a month to write small examples (dBase/FoxPro/Clipper is a table-based db with indexes). Then, at my first workplace, I met MUMPS, and I got headache. I was young and fresh-brained, but it took 2 weeks to understand the MUMPS database model. There was a moment, like in comics: after 2 weeks, a button has been switched on, and the bulb has just lighten up in my mind. MUMPS is natural, low level, and very-very fast. (It's an unbalanced, unformalized btree without types.) Today's trends shows the way back to it: NoSQL, key-value db, multidimensional db - so there are only some steps left, and we reach Mumps.
Here's a presentation about MUMPS's advantages: http://www.slideshare.net/george.james/mumps-the-internet-scale-database-presentation
A short doc on hierarchical db: http://www.cs.pitt.edu/~chang/156/14hier.html
An introduction to MUMPS globals (in MUMPS, local variables, short: locals are the memory variables, and the global variables, short: globals are the "db variables", setting a global variable goes to the disk immediatelly):
http://gradvs1.mgateway.com/download/extreme1.pdf (PDF)
Say you want to write a love poem...
Instead of using a hammer just because there's one already in your hand, learn the proper tools for the task: learn to speak French.
Once you've reached near-native speaking level, you're ready to start your poem.
While learning new languages on an academical level is an interesting hobby, IMHO you can't really learn to use one until you try to apply it to a real world problem. So, rather than looking for a new language to learn, I'd in your place first look for a new things to build, and only then I'd look for the right language to use for that one specific project. First pick the problem, then the tool, not the other way around..
For anyone who hasn't been around since the mid 80's, I'd suggest learning 8-bit BASIC. It's very low-level, very primitive and it's an interesting exercise to program around its holes.
On the same line, I'd pick an HP-41C series calculator (or emulator, although nothing beats real hardware). It's hard to wrap your brain around it, but well worth it. A TI-57 will do, but will be a completely different experience. If you manage to solve second degree equations on a TI-55, you'll be considered a master (it had no conditionals and no branches except a RST, that jumped the program back to step 0).
And last, I'd pick FORTH (it was mentioned before). It has a nice "build your language" Lisp-ish thing, but is much more bare metal. It will teach you why Rails is interesting and when DSLs make sense and you'll have a glipse on what your non-RPN calculator is thinking while you type.
PostScript. It is a rather interesting language as it's stack based, and it's quite practical once you want to put things on paper and you want either to get it done or troubleshoot why isn't it getting done.
Erlang. The intrinsic parallelism gives it a rather unusual feel and you can again learn useful things from that. I'm not so sure about practicality, but it can be useful for some fast prototyping tasks and highly redundant systems.
Try programming GPUs - either CUDA or OpenCL. It's just C/C++ extensions, but the mental model of the architecture is again completely different from the classic approach, and it definitely gets practical once you need to get some real number crunching done.
Erlang, Forth and some embedded work with assembly language. Really; buy an Arduino kit or something similar, and create a polyphonic beep in assembly. You'll really learn something.
There's also anic:
https://code.google.com/p/anic/
From its site:
Faster than C, Safer than Java, Simpler than *sh
anic is the reference implementation compiler for the experimental, high-performance, implicitly parallel, deadlock-free general-purpose dataflow programming language ANI.
It doesn't seem to be under active development anymore, but it seems to have some interesting concepts (and that, after all, is what you seem to be after).
While not meeting your requirement of "different" - I'd wager that Fantom is a language that a professional programmer should look at. By their own admission, the authors of fantom call it a boring language. It merely shores up the most common use cases of Java and C#, with some borrowed closure syntax from ruby and similar newer languages.
And yet it manages to have its own bootstrapped compiler, provide a platform that has a drop in install with no external dependencies, gets packages right - and works on Java, C# and now the Web (via js).
It may not widen your horizons in terms of new ways of programming, but it will certainly show you better ways of programming.
One thing that I see missing from the other answers: languages based on term-rewriting.
You could take a look at Pure - http://code.google.com/p/pure-lang/ .
Mathematica is also rewriting based, although it's not so easy to figure out what's going on, as it's rather closed.
APL, Forth and Assembly.
Have some fun. Pick up a Lego Mindstorm robot kit and CMU's RobotC and write some robotics code. Things happen when you write code that has to "get dirty" and interact with the real world that you cannot possibly learn in any other way. Yes, same language, but a very different perspective.
People like Alexander Stepanov and Sean Parent vote for a formal and abstract approach on software design.
The idea is to break complex systems down into a directed acyclic graph and hide cyclic behaviour in nodes representing that behaviour.
Parent gave presentations at boost-con and google (sheets from boost-con, p.24 introduces the approach, there is also a video of the google talk).
While i like the approach and think its a neccessary development, i have a problem with imagining how to handle subsystems with amorphous behaviour.
Imagine for example a common pattern for state-machines: using an interface which all states support and having different behaviour in concrete implementations for the states.
How would one solve that?
Note that i am just looking for an abstract approach.
I can think of hiding that behaviour behind a node and defining different sub-DAGs for the states, but that complicates the design considerately if you want to influence the behaviour of the main DAG from a sub-DAG.
Your question is not clear. Define amorphous subsystems.
You are "just looking for an abstract approach" but then you seem to want details about an implementation in a conventional programming language ("common pattern for state-machines"). So, what are you asking for? How to implement nested finite state-machines?
Some more detail will help the conversation.
For a real abstract approach, look at something like Stream X-Machines:
... The X-machine model is structurally the
same as the finite state machine, except
that the symbols used to label the machine's
transitions denote relations of type X→X. ...
The Stream X-Machine differs from Eilenberg's
model, in that the fundamental data type
X = Out* × Mem × In*,
where In* is an input sequence,
Out* is an output sequence, and Mem is the
(rest of the) memory.
The advantage of this model is that it
allows a system to be driven, one step
at a time, through its states and
transitions, while observing the
outputs at each step. These are
witness values, that guarantee that
particular functions were executed on
each step. As a result, complex
software systems may be decomposed
into a hierarchy of Stream
X-Machines, designed in a top-down
way and tested in a bottom-up way.
This divide-and-conquer approach to
design and testing is backed by
Florentin Ipate's proof of correct
integration, which proves how testing
the layered machines independently is
equivalent to testing the composed
system. ...
But I don't see how the presentation is related to this. He seems to speak about a quite mainstream approach to programming, nothing similar to X-Machines. Anyway, the presentation is quite confusing and I have no time to see the video right now.
First impression of the talk, reading the slides only
The author touches haphazardly on numerous fields/problems/solutions, apparently without recognizing it: from Peopleware (for example Psychology of programming), to Software Engineering (for example software product lines), to various programming techniques.
How the various parts are linked and what exactly he is advocating is not clear at all (I'm accustomed to just reading slides and they are usually consequential):
Dataflow programming?
Constraints solving for User Interfaces? For practical implementations, see Garnet for Common Lisp, Amulet/OpenAmulet for C++.
What advantages gives us this "new" concept-based generic programming with respect to well-known approaches (for example, tools based on Hoare logic pre/post conditions and invariants or, better, Hoare's Communicating Sequential Processes (CSP) or Hehner's Practical Theory of Programming or some programming language with a sophisticated type-system like ATS, Qi or Epigram and so on)? It seems to me that introducing "concepts" - which, as-is, are specific to C++ - is not more simple than using the alternatives. Is it just about jargon and "politics"? (Finally formal methods... but disguised).
Why organizing program modules as a DAG and not as a tree, like David Parnas advocated decades ago in Designing software for ease of extension and contraction? (here a directly accessible .pdf and here slides from a lecture). The work on X-Machines probably is an answer to this question (going even beyond DAGs), but, again, the author seems to speak about a quite conventional program development regime in which Parnas' approach is the only sensible.
If/when I will see the video I will update this answer.
I took a glimpse on Hoare Logic in college. What we did was really simple. Most of what I did was proving the correctness of simple programs consisting of while loops, if statements, and sequence of instructions, but nothing more. These methods seem very useful!
Are formal methods used in industry widely?
Are these methods used to prove mission-critical software?
Well, Sir Tony Hoare joined Microsoft Research about 10 years ago, and one of the things he started was a formal verification of the Windows NT kernel. Indeed, this was one of the reasons for the long delay of Windows Vista: starting with Vista, large parts of the kernel are actually formally verified wrt. to certain properties like absence of deadlocks, absence of information leaks etc.
This is certainly not typical, but it is probably the single most important application of formal program verification, in terms of its impact (after all, almost every human being is in some way, shape or form affected by a computer running Windows).
This is a question close to my heart (I'm a researcher in Software Verification using formal logics), so you'll probably not be surprised when I say I think these techniques have a useful place, and are not yet used enough in the industry.
There are many levels of "formal methods", so I'll assume you mean those resting on a rigourous mathematical basis (as opposed to, say, following some 6-Sigma style process). Some types of formal methods have had great success - type systems being one example. Static analysis tools based on data flow analysis are also popular, model checking is almost ubiquitous in hardware design, and computational models like Pi-Calculus and CCS seem to be inspiring some real change in practical language design for concurrency. Termination analysis is one that's had a lot of press recently - The SDV project at Microsoft and work by Byron Cook are recent examples of research/practice crossover in formal methods.
Hoare Reasoning has not, so far, made great inroads in the industry - this is for more reasons than I can list, but I suspect is mostly around the complexity of writing then proving specifications for real programs (they tend to get big, and fail to express properties of many real world environments). Various sub-fields in this type of reasoning are now making big inroads into these problems - Separation Logic being one.
This is partially the nature of ongoing (hard) research. But I must confess that we, as theorists, have entirely failed to educate the industry on why our techniques are useful, to keep them relevant to industry needs, and to make them approachable to software developers. At some level, that's not our problem - we're researchers, often mathematicians, and practical usage is not foremost in our minds. Also, the techniques being developed are often too embryonic for use in large scale systems - we work on small programs, on simplified systems, get the math working, and move on. I don't much buy these excuses though - we should be more active in pushing our ideas, and getting a feedback loop between the industry and our work (one of the main reasons I went back to research).
It's probably a good idea for me to resurrect my weblog, and make some more posts on this stuff...
I cannot comment much on mission-critical software, although I know that the avionics industry uses a wide variety of techniques to validate software, including Hoare-style methods.
Formal methods have suffered because early advocates like Edsger Dijkstra insisted that they ought to be used everywhere. Neither the formalisms nor the software support were up to the job. More sensible advocates believe that these methods should be used on problems that are hard. They are not widely used in industry, but adoption is increasing. Probably the greatest inroads have been in the use of formal methods to check safety properties of software. Some of my favorite examples are the SPIN model checker and George Necula's proof-carrying code.
Moving away from practice and into research, Microsoft's Singularity operating-system project is about using formal methods to provide safety guarantees that ordinarily require hardware support. This in turn leads to faster performance and stronger guarantees. For example, in singularity they have proved that if a third-party device driver is allowed into the system (which means basic verification conditions have been proved), then it cannot possibly bring down that whole OS–he worst it can do is hose its own device.
Formal methods are not yet widely used in industry, but they are more widely used than they were 20 years ago, and 20 years from now they will be more widely used still. So you are future-proofed :-)
Yes, they are used, but not widely in all areas. There are more methods than just hoare logic, some are used more, some less, depending on suitability for given task. The common problem is that sofware is biiiiiiig and verifying that all of it is correct is still too hard a problem.
For example the theorem-prover (a software that aids humans in proving program correctness) ACL2 has been used to prove that a certain floating-point processing unit does not have a certain type of bug. It was a big task, so this technique is not too common.
Model checking, another kind of formal verification, is used rather widely nowadays, for example Microsoft provides a type of model checker in the driver development kit and it can be used to verify the driver for a set of common bugs. Model checkers are also often used in verifying hardware circuits.
Rigorous testing can be also thought of as formal verification - there are some formal specifications of which paths of program should be tested and so on.
"Are formal methods used in industry?"
Yes.
The assert statement in many programming languages is related to formal methods for verifying a program.
"Are formal methods used in industry widely ?"
No.
"Are these methods used to prove mission-critical software ?"
Sometimes. More often, they're used to prove that the software is secure. More formally, they're used to prove certain security-related assertions about the software.
There are two different approaches to formal methods in the industry.
One approach is to change the development process completely. The Z notation and the B method that were mentioned are in this first category. B was applied to the development of the driverless subway line 14 in Paris (if you get a chance, climb in the front wagon. It's not often that you get a chance to see the rails in front of you).
Another, more incremental, approach is to preserve the existing development and verification processes and to replace only one of the verification tasks at a time by a new method. This is very attractive but it means developing static analysis tools for exiting, used languages that are often not easy to analyse (because they were not designed to be).
If you go to (for instance)
http://dblp.uni-trier.de/db/indices/a-tree/d/Delmas:David.html
(sorry, only one hyperlink allowed for new users :( )
you will find instances of practical applications of formal methods to the verification of C programs (with static analyzers Astrée, Caveat, Fluctuat, Frama-C) and binary code (with tools from AbsInt GmbH).
By the way, since you mentioned Hoare Logic, in the above list of tools, only Caveat is based on Hoare logic (and Frama-C has a Hoare logic plug-in). The others rely on abstract interpretation, a different technique with a more automatic approach.
My area of expertise is the use of formal methods for static code analysis to show that software is free of run-time errors. This is implemented using a formal methods technique known "abstract interpretation". The technique essentially enables you to prove certain atributes of a s/w program. E.g. prove that a+b will not overflow or x/(x-y) will not result in a divide by zero. An example static analysis tool that uses this technique is Polyspace.
With respect to your question: "Are formal methods used in industry widely?" and "Are these methods used to prove mission-critical software?"
The answer is yes. This opinion is based on my experience and supporting the Polyspace tool for industries that rely on the use of embedded software to control safety critical systems such as electronic throttle in an automobile, braking system for a train, jet engine controller, drug delivery infusion pump, etc. These industries do indeed use these types of formal methods tools.
I don't believe all 100% of these industry segments are using these tools, but the use is increasing. My opinion is that the Aerospace and Automotive industries lead with the Medical Device industry quickly ramping up use.
Polyspace is a a (hideously expensive, but very good) commercial product based on program verification. It's fairly pragmatic, in that it scales up from 'enhanced unit testing that will probably find some bugs' to 'the next three years of your life will be spent showing these 10 files have zero defects'.
It is based more on negative verification ('this program won't corrupt your stack') instead positive verification ('this program will do precisely what these 50 pages of equations say it will').
To add to Jorg's answer, here's an interview with Tony Hoare. The tools Jorg's referring to, I think, are PREfast and PREfix. See here for more information.
Besides of other more procedural approaches, Hoare logic was in the basis of Design by Contract, introduced as an object oriented technique by Bertrand Meyer in Eiffel (see Meyer's article of 1992, page 4). While Design by Contract is not the same as formal verification methods (for one thing, DbC doesn't prove anything until the software is executed), in my opinion it provides a more practical use.