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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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.
Has anybody seen a GP implemented with online learning rather than the standard offline learning? I've done some stuff with genetic programs and I simply can't figure out what would be a good way to make the learning process online.
Please let me know if you have any ideas, seen any implementations, or have any references that I can look at.
Per the Wikipedia link, online learning "learns one instance at a time." The online/offline labels usually refer to how training data is feed to a supervised regression or classification algorithm. Since genetic programming is a heuristic search that uses an evaluation function to evaluate the fitness of its solutions, and not a training set with labels, those terms don't really apply.
If what you're asking is if the output of the GP algorithm (i.e. the best phenotype), can be used while it's still "searching" for better solutions, I see no reason why not, assuming it makes sense for your domain/application. Once the fitness of your GA/GP's population reaches a certain threshold, you can apply that solution to your application, and continue to run the GP, switching to a new solution when a better one becomes available.
One approach along this line is an algorithm called rtNEAT, which attempts to use a genetic algorithm to generate and update a neural network in real time.
I found a few examples by doing a Google scholar search for online Genetic Programming.
An On-Line Method to Evolve Behavior and to Control a Miniature Robot in Real Time with Genetic Programming
It actually looks like they found a way to make GP modify the machine code of the robot's control system during actual activities - pretty cool!
Those same authors went on to produce more related work, such as this improvement:
Evolution of a world model for a miniature robot using genetic programming
Hopefully their work will be enough to get you started - I don't have enough experience with genetic programming to be able to give you any specific advice.
It actually looks like they found a way to make GP modify the machine code of the robot's control system during actual activities - pretty cool!
Yes, the department at Uni Dortmund was heavily into linear GP :-)
Direct execution of GP programs vs. interpreted code has some advantages, though in these days you'd probably rather want to go with dynamic languages such as Java, C# or Obj-C that allow you to write classes/methods at runtime while still you can still benefit from some runtime rather than run on the raw CPU.
The online-learning approach doesn't seem like anything absolutely novel or different from 'classic GP' to me.
From my understanding it's just a case of extending the set of training/fitness/test cases during runtime?
Cheers,
Jay
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.
Is there a trivial, or at least moderately straight-forward way to generate territory maps (e.g. Risk)?
I have looked in the past and the best I could find were vague references to Voronoi diagrams. An example of a Voronoi diagram is this:
.
These hold promise, but I guess i haven't seen any straight-forward ways of rendering these, let alone holding them in some form of data structure to treat each territory as an object.
Another approach that holds promise is flood fill, but again I'm unsure on the best way to start with this approach.
Any advice would be much appreciated.
The best reference I've seen on them is Computational Geometry: Algorithms and Applications, which covers Voronoi diagrams, Delaunay triangulations (similar to Voronoi diagrams and each can be converted into the other), and other similar data structures.
They talk about all the data structures you need but they don't give you the code necessary to implement it (which may be a good exercise). In terms of code, an Amazon search shows the book Computational Geometry in C, which presumably comes with the code (although since you're stuck in C, you'd mind as well get the other one and implement it in whatever language you want). I also don't have any experience with this book, only the first.
Sorry to have only books to recommend! The only decent online resource I've seen on them are the two Wikipedia articles, which doesn't really tell you implementation details. This link may be helpful though.
Why not use a map of primitives (triangles, squares), distribute the starting points for the countries (the "capitals"), and then randomly expanding the countries by adding a random adjacent primitive to the country.
CGAL is a C++ library that has data structures and algorithms used in Computational Geometry.
I'm actually dealing with exactly this kind of stuff for my company's video game. The most useful info I've found are at these two links:
Paul Bourke's page at UWA, with his 1989 paper on Delaunay and a series of implementation links.
A great explanation of the psudocode and a visual of doing Delaunay at codeGuru.com.
In terms of rendering these - most of the implementations I've found will need massaging to get what you'd want, but since using this for a game map would lead to a number of points plus lines between them, it could be a very simple matter to do draw this out to screen.