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I'm writing a small tool for generating php checks from javascript code, and I would like to know if anyone knows of a standard way of transforming functional code into imperative code?
I found this paper: Defunctionalization at Work it explains defunctionalization pretty well.
Lambdalifting and defunctionalization somewhat answered the question, but what about datastructures, we are still parsing lists as if they are all linkedlists. Would there be a way of transforming the linkedlists of functional languages into other high-level datastructures like c++ vectors or java arraylists?
Here are a few additions to the list of #Artyom:
you can convert tail recursion into loops and assignments
linear types can be used to introduce assignments, e.g. y = f x can be replaced with x := f x if x is linear and has the same type as y
at least two kinds of defunctionalization are possible: Reynolds-type defunctionalization when you replace a high-order application with a switch full of first-order applications, and inlining (however, recursive functions is not always possible to inline)
Perhaps you are interested in removing some language elements (such as higher-order functions), right?
For eliminating HOFs from a program, there are techniques such as defunctionalization. For removing closures, you can use lambda-lifting (aka closure conversion). Is this something you are interested in?
I think you need to provide a concrete example of code you have, and the target code you intend to produce, so that others may propose solutions.
Added:
Would there be a way of transforming the linkedlists of functional languages into other high-level datastructures like c++ vectors or java arraylists?
Yes. Linked lists are represented with pointers in C++ (a structure "node" with two fields: one for the "payload", another for the "next" pointer; empty list is then represented as a NULL pointer, but sometimes people prefer to use special "sentinel values"). Note that, if the code in the source language does not rely on the representation of singly linked lists (in the source language implementation), you can also implement the "cons"/"nil" operations using a vector in the target language (not sure if this suits your needs, though). The idea here is to give an alternative implementations for the familiar operations.
No, there is not.
The reason is that there is no such concrete and well defined thing like functional code or imperative code.
Such transformations exist only for concrete instances of your abstraction: for example, there are transformations from Haskell code to LLVM bytecode, F# code to CLI bytecode or Frege code to Java code.
(I doubt if there is one from Javascript to PHP.)
Depends on what you need. The usual answer is "there is no such tool", because the result will not be usable. However look at this from this standpoint:
The set of Assembler instructions in a computer defines an imperative machine. Hence the compiler needs to do such a translation. However I assume you do not want to have assembler code but something more readable.
Usually these kinds of heavy program transformations are done manually, if one is interested in the result, or automatically if the result will never be looked at by a human.
I know that memoization seems to be a perennial topic here on the haskell tag on stack overflow, but I think this question has not been asked before.
I'm aware of several different 'off the shelf' memoization libraries for Haskell:
The memo-combinators and memotrie packages, which make use of a beautiful trick involving lazy infinite data structures to achieve memoization in a purely functional way. (As I understand it, the former is slightly more flexible, while the latter is easier to use in simple cases: see this SO answer for discussion.)
The uglymemo package, which uses unsafePerformIO internally but still presents a referentially transparent interface. The use of unsafePerformIO internally results in better performance than the previous two packages. (Off the shelf, its implementation uses comparison-based search data structures, rather than perhaps-slightly-more-efficient hash functions; but I think that if you find and replace Cmp for Hashable and Data.Map for Data.HashMap and add the appropraite imports, you get a hash based version.)
However, I'm not aware of any library that looks answers up based on object identity rather than object value. This can be important, because sometimes the kinds of object which are being used as keys to your memo table (that is, as input to the function being memoized) can be large---so large that fully examining the object to determine whether you've seen it before is itself a slow operation. Slow, and also unnecessary, if you will be applying the memoized function again and again to an object which is stored at a given 'location in memory' 1. (This might happen, for example, if we're memoizing a function which is being called recursively over some large data structure with a lot of structural sharing.) If we've already computed our memoized function on that exact object before, we can already know the answer, even without looking at the object itself!
Implementing such a memoization library involves several subtle issues and doing it properly requires several special pieces of support from the language. Luckily, GHC provides all the special features that we need, and there is a paper by Peyton-Jones, Marlow and Elliott which basically worries about most of these issues for you, explaining how to build a solid implementation. They don't provide all details, but they get close.
The one detail which I can see which one probably ought to worry about, but which they don't worry about, is thread safety---their code is apparently not threadsafe at all.
My question is: does anyone know of a packaged library which does the kind of memoization discussed in the Peyton-Jones, Marlow and Elliott paper, filling in all the details (and preferably filling in proper thread-safety as well)?
Failing that, I guess I will have to code it up myself: does anyone have any ideas of other subtleties (beyond thread safety and the ones discussed in the paper) which the implementer of such a library would do well to bear in mind?
UPDATE
Following #luqui's suggestion below, here's a little more data on the exact problem I face. Let's suppose there's a type:
data Node = Node [Node] [Annotation]
This type can be used to represent a simple kind of rooted DAG in memory, where Nodes are DAG Nodes, the root is just a distinguished Node, and each node is annotated with some Annotations whose internal structure, I think, need not concern us (but if it matters, just ask and I'll be more specific.) If used in this way, note that there may well be significant structural sharing between Nodes in memory---there may be exponentially more paths which lead from the root to a node than there are nodes themselves. I am given a data structure of this form, from an external library with which I must interface; I cannot change the data type.
I have a function
myTransform : Node -> Node
the details of which need not concern us (or at least I think so; but again I can be more specific if needed). It maps nodes to nodes, examining the annotations of the node it is given, and the annotations its immediate children, to come up with a new Node with the same children but possibly different annotations. I wish to write a function
recursiveTransform : Node -> Node
whose output 'looks the same' as the data structure as you would get by doing:
recursiveTransform Node originalChildren annotations =
myTransform Node recursivelyTransformedChildren annotations
where
recursivelyTransformedChildren = map recursiveTransform originalChildren
except that it uses structural sharing in the obvious way so that it doesn't return an exponential data structure, but rather one on the order of the same size as its input.
I appreciate that this would all be easier if say, the Nodes were numbered before I got them, or I could otherwise change the definition of a Node. I can't (easily) do either of these things.
I am also interested in the general question of the existence of a library implementing the functionality I mention quite independently of the particular concrete problem I face right now: I feel like I've had to work around this kind of issue on a few occasions, and it would be nice to slay the dragon once and for all. The fact that SPJ et al felt that it was worth adding not one but three features to GHC to support the existence of libraries of this form suggests that the feature is genuinely useful and can't be worked around in all cases. (BUT I'd still also be very interested in hearing about workarounds which will help in this particular case too: the long term problem is not as urgent as the problem I face right now :-) )
1 Technically, I don't quite mean location in memory, since the garbage collector sometimes moves objects around a bit---what I really mean is 'object identity'. But we can think of this as being roughly the same as our intuitive idea of location in memory.
If you only want to memoize based on object identity, and not equality, you can just use the existing laziness mechanisms built into the language.
For example, if you have a data structure like this
data Foo = Foo { ... }
expensive :: Foo -> Bar
then you can just add the value to be memoized as an extra field and let the laziness take care of the rest for you.
data Foo = Foo { ..., memo :: Bar }
To make it easier to use, add a smart constructor to tie the knot.
makeFoo ... = let foo = Foo { ..., memo = expensive foo } in foo
Though this is somewhat less elegant than using a library, and requires modification of the data type to really be useful, it's a very simple technique and all thread-safety issues are already taken care of for you.
It seems that stable-memo would be just what you needed (although I'm not sure if it can handle multiple threads):
Whereas most memo combinators memoize based on equality, stable-memo does it based on whether the exact same argument has been passed to the function before (that is, is the same argument in memory).
stable-memo only evaluates keys to WHNF.
This can be more suitable for recursive functions over graphs with cycles.
stable-memo doesn't retain the keys it has seen so far, which allows them to be garbage collected if they will no longer be used. Finalizers are put in place to remove the corresponding entries from the memo table if this happens.
Data.StableMemo.Weak provides an alternative set of combinators that also avoid retaining the results of the function, only reusing results if they have not yet been garbage collected.
There is no type class constraint on the function's argument.
stable-memo will not work for arguments which happen to have the same value but are not the same heap object. This rules out many candidates for memoization, such as the most common example, the naive Fibonacci implementation whose domain is machine Ints; it can still be made to work for some domains, though, such as the lazy naturals.
Ekmett just uploaded a library that handles this and more (produced at HacPhi): http://hackage.haskell.org/package/intern. He assures me that it is thread safe.
Edit: Actually, strictly speaking I realize this does something rather different. But I think you can use it for your purposes. It's really more of a stringtable-atom type interning library that works over arbitrary data structures (including recursive ones). It uses WeakPtrs internally to maintain the table. However, it uses Ints to index the values to avoid structural equality checks, which means packing them into the data type, when what you want are apparently actually StableNames. So I realize this answers a related question, but requires modifying your data type, which you want to avoid...
Many a times, I've come across statements of the form
X does/doesn't compose well.
I can remember few instances that I've read recently :
Macros don't compose well (context: clojure)
Locks don't compose well (context: clojure)
Imperative programming doesn't compose well... etc.
I want to understand the implications of composability in terms of designing/reading/writing code ? Examples would be nice.
"Composing" functions basically just means sticking two or more functions together to make a big function that combines their functionality in a useful way. Essentially, you define a sequence of functions and pipe the results of each one into the next, finally giving the result of the whole process. Clojure provides the comp function to do this for you, you could do it by hand too.
Functions that you can chain with other functions in creative ways are more useful in general than functions that you can only call in certain conditions. For example, if we didn't have the last function and only had the traditional Lisp list functions, we could easily define last as (def last (comp first reverse)). Look at that — we didn't even need to defn or mention any arguments, because we're just piping the result of one function into another. This would not work if, for example, reverse took the imperative route of modifying the sequence in-place. Macros are problematic as well because you can't pass them to functions like comp or apply.
Composition in programming means assembling bigger pieces out of smaller ones.
Composition of unary functions creates a more complicated unary function by chaining simpler ones.
Composition of control flow constructs places control flow constructs inside other control flow constructs.
Composition of data structures combines multiple simpler data structures into a more complicated one.
Ideally, a composed unit works like a basic unit and you as a programmer do not need to be aware of the difference. If things fall short of the ideal, if something doesn't compose well, your composed program may not have the (intended) combined behavior of its individual pieces.
Suppose I have some simple C code.
void run_with_resource(void) {
Resource *r = create_resource();
do_some_work(r);
destroy_resource(r);
}
C facilitates compositional reasoning about control flow at the level of functions. I don't have to care about what actually happens inside do_some_work(); I know just by looking at this small function that every time a resource is created on line 2 with create_resource(), it will eventually be destroyed on line 4 by destroy_resource().
Well, not quite. What if create_resource() acquires a lock and destroy_resource() frees it? Then I have to worry about whether do_some_work acquires the same lock, which would prevent the function from finishing. What if do_some_work() calls longjmp(), and skips the end of my function entirely? Until I know what goes on in do_some_work(), I won't be able to predict the control flow of my function. We no longer have compositionality: we can no longer decompose the program into parts, reason about the parts independently, and carry our conclusions back to the whole program. This makes designing and debugging much harder and it's why people care whether something composes well.
"Bang for the Buck" - composing well implies a high ratio of expressiveness per rule-of-composition. Each macro introduces its own rules of composition. Each custom data structure does the same. Functions, especially those using general data structures have far fewer rules.
Assignment and other side effects, especially wrt concurrency have even more rules.
Think about when you write functions or methods. You create a group of functionality to do a specific task. When working in an Object Oriented language you cluster your behavior around the actions you think a distinct entity in the system will perform. Functional programs break away from this by encouraging authors to group functionality according to an abstraction. For example, the Clojure Ring library comprises a group of abstractions that cover routing in web applications.
Ring is composable where functions that describe paths in the system (routes) can be grouped into higher order functions (middlewhere). In fact, Clojure is so dynamic that it is possible (and you are encouraged) to come up with patterns of routes that can be dynamically created at runtime. This is the essence of composablilty, instead of coming up with patterns that solve a certain problem you focus on patterns that generate solutions to a certain class of problem. Builders and code generators are just two of the common patterns used in functional programming. Function programming is the art of patterns that generate other patterns (and so on and so on).
The idea is to solve a problem at its most basic level then come up with patterns or groups of the lowest level functions that solve the problem. Once you start to see patterns in the lowest level you've discovered composition. As folks discover second order patterns in groups of functions they may start to see a third level. And so on...
Composition (in the context you describe at a functional level) is typically the ability to feed one function into another cleanly and without intermediate processing. Such an example of composition is in std::cout in C++:
cout << each << item << links << on;
That is a simple example of composition which doesn't really "look" like composition.
Another example with a form more visibly compositional:
foo(bar(baz()));
Wikipedia Link
Composition is useful for readability and compactness, however chaining large collections of interlocking functions which can potentially return error codes or junk data can be hazardous (this is why it is best to minimize error code or null return values.)
Provided your functions use exceptions, or alternatively return null objects you can minimize the requirement for branching (if) on errors and maximize the compositional potential of your code at no extra risk.
Object composition (vs inheritance) is a separate issue (and not what you are asking, but it shares the name). It is one of containment to derive object hierarchy as opposed to direct inheritance.
Within the context of clojure, this comment addresses certain aspects of composability. In general, it seems to emerge when units of the system do one thing well, do not require other units to understand its internals, eschew side-effects, and accept and return the system's pervasive data structures. All of the above can be seen in M2tM's C++ example.
composability, applied to functions, means that the functions are smaller and well-defined, thus easy to integrate into other functions (i have seen this idea in the book "the joy of clojure")
the concept can apply to other things that are supposed be composed into something else.
the purpose of composability is reuse. for example, a function well-build (composable) is easier to reuse
macros aren't that well-composable because you can't pass them as parameters
lock are crap because you can't really give them names (define them well) or reuse them. you just do them inplace
imperative languages aren't that composable because (some of them, at least) don't have closures. if you want functionality passed as parameter, you're screwed. you have to build an object and pass that; disclaimer here: this last idea i'm not entirely convinced is true, therefore research more before taking it for granted
another idea on imperative languages is that they don't compose well because they imply state (from wikipedia knowledgebase :) "Imperative programming - describes computation in terms of statements that change a program state").
state does not compose well because although you have given a specific "something" in input, that "something" generates an output according to it's state. different internal state, different behaviour. and thus you can say good-bye to what you where expecting to happen.
with state, you depend to much on knowing what the current state of an object is... if you want to predict it's behavior. more stuff to keep in the back of your mind, less composable (remember well-defined ? or "small and simple", as in "easy to use" ?)
ps: thinking of learning clojure, huh ? investigating... ? good for you ! :P
I am a big fan of Stephen Wolfram, but he is definitely one not shy of tooting his own horn. In many references, he extols Mathematica as a different symbolic programming paradigm. I am not a Mathematica user.
My questions are: what is this symbolic programming? And how does it compare to functional languages (such as Haskell)?
When I hear the phrase "symbolic programming", LISP, Prolog and (yes) Mathematica immediately leap to mind. I would characterize a symbolic programming environment as one in which the expressions used to represent program text also happen to be the primary data structure. As a result, it becomes very easy to build abstractions upon abstractions since data can easily be transformed into code and vice versa.
Mathematica exploits this capability heavily. Even more heavily than LISP and Prolog (IMHO).
As an example of symbolic programming, consider the following sequence of events. I have a CSV file that looks like this:
r,1,2
g,3,4
I read that file in:
Import["somefile.csv"]
--> {{r,1,2},{g,3,4}}
Is the result data or code? It is both. It is the data that results from reading the file, but it also happens to be the expression that will construct that data. As code goes, however, this expression is inert since the result of evaluating it is simply itself.
So now I apply a transformation to the result:
% /. {c_, x_, y_} :> {c, Disk[{x, y}]}
--> {{r,Disk[{1,2}]},{g,Disk[{3,4}]}}
Without dwelling on the details, all that has happened is that Disk[{...}] has been wrapped around the last two numbers from each input line. The result is still data/code, but still inert. Another transformation:
% /. {"r" -> Red, "g" -> Green}
--> {{Red,Disk[{1,2}]},{Green,Disk[{3,4}]}}
Yes, still inert. However, by a remarkable coincidence this last result just happens to be a list of valid directives in Mathematica's built-in domain-specific language for graphics. One last transformation, and things start to happen:
% /. x_ :> Graphics[x]
--> Graphics[{{Red,Disk[{1,2}]},{Green,Disk[{3,4}]}}]
Actually, you would not see that last result. In an epic display of syntactic sugar, Mathematica would show this picture of red and green circles:
But the fun doesn't stop there. Underneath all that syntactic sugar we still have a symbolic expression. I can apply another transformation rule:
% /. Red -> Black
Presto! The red circle became black.
It is this kind of "symbol pushing" that characterizes symbolic programming. A great majority of Mathematica programming is of this nature.
Functional vs. Symbolic
I won't address the differences between symbolic and functional programming in detail, but I will contribute a few remarks.
One could view symbolic programming as an answer to the question: "What would happen if I tried to model everything using only expression transformations?" Functional programming, by contrast, can been seen as an answer to: "What would happen if I tried to model everything using only functions?" Just like symbolic programming, functional programming makes it easy to quickly build up layers of abstractions. The example I gave here could be easily be reproduced in, say, Haskell using a functional reactive animation approach. Functional programming is all about function composition, higher level functions, combinators -- all the nifty things that you can do with functions.
Mathematica is clearly optimized for symbolic programming. It is possible to write code in functional style, but the functional features in Mathematica are really just a thin veneer over transformations (and a leaky abstraction at that, see the footnote below).
Haskell is clearly optimized for functional programming. It is possible to write code in symbolic style, but I would quibble that the syntactic representation of programs and data are quite distinct, making the experience suboptimal.
Concluding Remarks
In conclusion, I advocate that there is a distinction between functional programming (as epitomized by Haskell) and symbolic programming (as epitomized by Mathematica). I think that if one studies both, then one will learn substantially more than studying just one -- the ultimate test of distinctness.
Leaky Functional Abstraction in Mathematica?
Yup, leaky. Try this, for example:
f[x_] := g[Function[a, x]];
g[fn_] := Module[{h}, h[a_] := fn[a]; h[0]];
f[999]
Duly reported to, and acknowledged by, WRI. The response: avoid the use of Function[var, body] (Function[body] is okay).
You can think of Mathematica's symbolic programming as a search-and-replace system where you program by specifying search-and-replace rules.
For instance you could specify the following rule
area := Pi*radius^2;
Next time you use area, it'll be replaced with Pi*radius^2. Now, suppose you define new rule
radius:=5
Now, whenever you use radius, it'll get rewritten into 5. If you evaluate area it'll get rewritten into Pi*radius^2 which triggers rewriting rule for radius and you'll get Pi*5^2 as an intermediate result. This new form will trigger a built-in rewriting rule for ^ operation so the expression will get further rewritten into Pi*25. At this point rewriting stops because there are no applicable rules.
You can emulate functional programming by using your replacement rules as function. For instance, if you want to define a function that adds, you could do
add[a_,b_]:=a+b
Now add[x,y] gets rewritten into x+y. If you want add to only apply for numeric a,b, you could instead do
add[a_?NumericQ, b_?NumericQ] := a + b
Now, add[2,3] gets rewritten into 2+3 using your rule and then into 5 using built-in rule for +, whereas add[test1,test2] remains unchanged.
Here's an example of an interactive replacement rule
a := ChoiceDialog["Pick one", {1, 2, 3, 4}]
a+1
Here, a gets replaced with ChoiceDialog, which then gets replaced with the number the user chose on the dialog that popped up, which makes both quantities numeric and triggers replacement rule for +. Here, ChoiceDialog as a built-in replacement rule along the lines of "replace ChoiceDialog[some stuff] with the value of button the user clicked".
Rules can be defined using conditions which themselves need to go through rule-rewriting in order to produce True or False. For instance suppose you invented a new equation solving method, but you think it only works when the final result of your method is positive. You could do the following rule
solve[x + 5 == b_] := (result = b - 5; result /; result > 0)
Here, solve[x+5==20] gets replaced with 15, but solve[x + 5 == -20] is unchanged because there's no rule that applies. The condition that prevents this rule from applying is /;result>0. Evaluator essentially looks the potential output of rule application to decide whether to go ahead with it.
Mathematica's evaluator greedily rewrites every pattern with one of the rules that apply for that symbol. Sometimes you want to have finer control, and in such case you could define your own rules and apply them manually like this
myrules={area->Pi radius^2,radius->5}
area//.myrules
This will apply rules defined in myrules until result stops changing. This is pretty similar to the default evaluator, but now you could have several sets of rules and apply them selectively. A more advanced example shows how to make a Prolog-like evaluator that searches over sequences of rule applications.
One drawback of current Mathematica version comes up when you need to use Mathematica's default evaluator (to make use of Integrate, Solve, etc) and want to change default sequence of evaluation. That is possible but complicated, and I like to think that some future implementation of symbolic programming will have a more elegant way of controlling evaluation sequence
As others here already mentioned, Mathematica does a lot of term rewriting. Maybe Haskell isn't the best comparison though, but Pure is a nice functional term-rewriting language (that should feel familiar to people with a Haskell background). Maybe reading their Wiki page on term rewriting will clear up a few things for you:
http://code.google.com/p/pure-lang/wiki/Rewriting
Mathematica is using term rewriting heavily. The language provides special syntax for various forms of rewriting, special support for rules and strategies. The paradigm is not that "new" and of course it's not unique, but they're definitely on a bleeding edge of this "symbolic programming" thing, alongside with the other strong players such as Axiom.
As for comparison to Haskell, well, you could do rewriting there, with a bit of help from scrap your boilerplate library, but it's not nearly as easy as in a dynamically typed Mathematica.
Symbolic shouldn't be contrasted with functional, it should be contrasted with numerical programming. Consider as an example MatLab vs Mathematica. Suppose I want the characteristic polynomial of a matrix. If I wanted to do that in Mathematica, I could do get an identity matrix (I) and the matrix (A) itself into Mathematica, then do this:
Det[A-lambda*I]
And I would get the characteristic polynomial (never mind that there's probably a characteristic polynomial function), on the other hand, if I was in MatLab I couldn't do it with base MatLab because base MatLab (never mind that there's probably a characteristic polynomial function) is only good at calculating finite-precision numbers, not things where there are random lambdas (our symbol) in there. What you'd have to do is buy the add-on Symbolab, and then define lambda as its own line of code and then write this out (wherein it would convert your A matrix to a matrix of rational numbers rather than finite precision decimals), and while the performance difference would probably be unnoticeable for a small case like this, it would probably do it much slower than Mathematica in terms of relative speed.
So that's the difference, symbolic languages are interested in doing calculations with perfect accuracy (often using rational numbers as opposed to numerical) and numerical programming languages on the other hand are very good at the vast majority of calculations you would need to do and they tend to be faster at the numerical operations they're meant for (MatLab is nearly unmatched in this regard for higher level languages - excluding C++, etc) and a piss poor at symbolic operations.
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I keep hearing this term tossed around in several different contexts. What is it?
Declarative programming is when you write your code in such a way that it describes what you want to do, and not how you want to do it. It is left up to the compiler to figure out the how.
Examples of declarative programming languages are SQL and Prolog.
The other answers already do a fantastic job explaining what declarative programming is, so I'm just going to provide some examples of why that might be useful.
Context Independence
Declarative Programs are context-independent. Because they only declare what the ultimate goal is, but not the intermediary steps to reach that goal, the same program can be used in different contexts. This is hard to do with imperative programs, because they often depend on the context (e.g. hidden state).
Take yacc as an example. It's a parser generator aka. compiler compiler, an external declarative DSL for describing the grammar of a language, so that a parser for that language can automatically be generated from the description. Because of its context independence, you can do many different things with such a grammar:
Generate a C parser for that grammar (the original use case for yacc)
Generate a C++ parser for that grammar
Generate a Java parser for that grammar (using Jay)
Generate a C# parser for that grammar (using GPPG)
Generate a Ruby parser for that grammar (using Racc)
Generate a tree visualization for that grammar (using GraphViz)
simply do some pretty-printing, fancy-formatting and syntax highlighting of the yacc source file itself and include it in your Reference Manual as a syntactic specification of your language
And many more …
Optimization
Because you don't prescribe the computer which steps to take and in what order, it can rearrange your program much more freely, maybe even execute some tasks in parallel. A good example is a query planner and query optimizer for a SQL database. Most SQL databases allow you to display the query that they are actually executing vs. the query that you asked them to execute. Often, those queries look nothing like each other. The query planner takes things into account that you wouldn't even have dreamed of: rotational latency of the disk platter, for example or the fact that some completely different application for a completely different user just executed a similar query and the table that you are joining with and that you worked so hard to avoid loading is already in memory anyway.
There is an interesting trade-off here: the machine has to work harder to figure out how to do something than it would in an imperative language, but when it does figure it out, it has much more freedom and much more information for the optimization stage.
Loosely:
Declarative programming tends towards:-
Sets of declarations, or declarative statements, each of which has meaning (often in the problem domain) and may be understood independently and in isolation.
Imperative programming tends towards:-
Sequences of commands, each of which perform some action; but which may or may not have meaning in the problem domain.
As a result, an imperative style helps the reader to understand the mechanics of what the system is actually doing, but may give little insight into the problem that it is intended to solve. On the other hand, a declarative style helps the reader to understand the problem domain and the approach that the system takes towards the solution of the problem, but is less informative on the matter of mechanics.
Real programs (even ones written in languages that favor the ends of the spectrum, such as ProLog or C) tend to have both styles present to various degrees at various points, to satisfy the varying complexities and communication needs of the piece. One style is not superior to the other; they just serve different purposes, and, as with many things in life, moderation is key.
Here's an example.
In CSS (used to style HTML pages), if you want an image element to be 100 pixels high and 100 pixels wide, you simply "declare" that that's what you want as follows:
#myImageId {
height: 100px;
width: 100px;
}
You can consider CSS a declarative "style sheet" language.
The browser engine that reads and interprets this CSS is free to make the image appear this tall and this wide however it wants. Different browser engines (e.g., the engine for IE, the engine for Chrome) will implement this task differently.
Their unique implementations are, of course, NOT written in a declarative language but in a procedural one like Assembly, C, C++, Java, JavaScript, or Python. That code is a bunch of steps to be carried out step by step (and might include function calls). It might do things like interpolate pixel values, and render on the screen.
I am sorry, but I must disagree with many of the other answers. I would like to stop this muddled misunderstanding of the definition of declarative programming.
Definition
Referential transparency (RT) of the sub-expressions is the only required attribute of a declarative programming expression, because it is the only attribute which is not shared with imperative programming.
Other cited attributes of declarative programming, derive from this RT. Please click the hyperlink above for the detailed explanation.
Spreadsheet example
Two answers mentioned spreadsheet programming. In the cases where the spreadsheet programming (a.k.a. formulas) does not access mutable global state, then it is declarative programming. This is because the mutable cell values are the monolithic input and output of the main() (the entire program). The new values are not written to the cells after each formula is executed, thus they are not mutable for the life of the declarative program (execution of all the formulas in the spreadsheet). Thus relative to each other, the formulas view these mutable cells as immutable. An RT function is allowed to access immutable global state (and also mutable local state).
Thus the ability to mutate the values in the cells when the program terminates (as an output from main()), does not make them mutable stored values in the context of the rules. The key distinction is the cell values are not updated after each spreadsheet formula is performed, thus the order of performing the formulas does not matter. The cell values are updated after all the declarative formulas have been performed.
Declarative programming is the picture, where imperative programming is instructions for painting that picture.
You're writing in a declarative style if you're "Telling it what it is", rather than describing the steps the computer should take to get to where you want it.
When you use XML to mark-up data, you're using declarative programming because you're saying "This is a person, that is a birthday, and over there is a street address".
Some examples of where declarative and imperative programming get combined for greater effect:
Windows Presentation Foundation uses declarative XML syntax to describe what a user interface looks like, and what the relationships (bindings) are between controls and underlying data structures.
Structured configuration files use declarative syntax (as simple as "key=value" pairs) to identify what a string or value of data means.
HTML marks up text with tags that describe what role each piece of text has in relation to the whole document.
Declarative Programming is programming with declarations, i.e. declarative sentences. Declarative sentences have a number of properties that distinguish them from imperative sentences. In particular, declarations are:
commutative (can be reordered)
associative (can be regrouped)
idempotent (can repeat without change in meaning)
monotonic (declarations don't subtract information)
A relevant point is that these are all structural properties and are orthogonal to subject matter. Declarative is not about "What vs. How". We can declare (represent and constrain) a "how" just as easily as we declare a "what". Declarative is about structure, not content. Declarative programming has a significant impact on how we abstract and refactor our code, and how we modularize it into subprograms, but not so much on the domain model.
Often, we can convert from imperative to declarative by adding context. E.g. from "Turn left. (... wait for it ...) Turn Right." to "Bob will turn left at intersection of Foo and Bar at 11:01. Bob will turn right at the intersection of Bar and Baz at 11:06." Note that in the latter case the sentences are idempotent and commutative, whereas in the former case rearranging or repeating the sentences would severely change the meaning of the program.
Regarding monotonic, declarations can add constraints which subtract possibilities. But constraints still add information (more precisely, constraints are information). If we need time-varying declarations, it is typical to model this with explicit temporal semantics - e.g. from "the ball is flat" to "the ball is flat at time T". If we have two contradictory declarations, we have an inconsistent declarative system, though this might be resolved by introducing soft constraints (priorities, probabilities, etc.) or leveraging a paraconsistent logic.
Describing to a computer what you want, not how to do something.
imagine an excel page. With columns populated with formulas to calculate you tax return.
All the logic is done declared in the cells, the order of the calculation is by determine by formula itself rather than procedurally.
That is sort of what declarative programming is all about. You declare the problem space and the solution rather than the flow of the program.
Prolog is the only declarative language I've use. It requires a different kind of thinking but it's good to learn if just to expose you to something other than the typical procedural programming language.
I have refined my understanding of declarative programming, since Dec 2011 when I provided an answer to this question. Here follows my current understanding.
The long version of my understanding (research) is detailed at this link, which you should read to gain a deep understanding of the summary I will provide below.
Imperative programming is where mutable state is stored and read, thus the ordering and/or duplication of program instructions can alter the behavior (semantics) of the program (and even cause a bug, i.e. unintended behavior).
In the most naive and extreme sense (which I asserted in my prior answer), declarative programming (DP) is avoiding all stored mutable state, thus the ordering and/or duplication of program instructions can NOT alter the behavior (semantics) of the program.
However, such an extreme definition would not be very useful in the real world, since nearly every program involves stored mutable state. The spreadsheet example conforms to this extreme definition of DP, because the entire program code is run to completion with one static copy of the input state, before the new states are stored. Then if any state is changed, this is repeated. But most real world programs can't be limited to such a monolithic model of state changes.
A more useful definition of DP is that the ordering and/or duplication of programming instructions do not alter any opaque semantics. In other words, there are not hidden random changes in semantics occurring-- any changes in program instruction order and/or duplication cause only intended and transparent changes to the program's behavior.
The next step would be to talk about which programming models or paradigms aid in DP, but that is not the question here.
It's a method of programming based around describing what something should do or be instead of describing how it should work.
In other words, you don't write algorithms made of expressions, you just layout how you want things to be. Two good examples are HTML and WPF.
This Wikipedia article is a good overview: http://en.wikipedia.org/wiki/Declarative_programming
Since I wrote my prior answer, I have formulated a new definition of the declarative property which is quoted below. I have also defined imperative programming as the dual property.
This definition is superior to the one I provided in my prior answer, because it is succinct and it is more general. But it may be more difficult to grok, because the implication of the incompleteness theorems applicable to programming and life in general are difficult for humans to wrap their mind around.
The quoted explanation of the definition discusses the role pure functional programming plays in declarative programming.
Declarative vs. Imperative
The declarative property is weird, obtuse, and difficult to capture in a technically precise definition that remains general and not ambiguous, because it is a naive notion that we can declare the meaning (a.k.a semantics) of the program without incurring unintended side effects. There is an inherent tension between expression of meaning and avoidance of unintended effects, and this tension actually derives from the incompleteness theorems of programming and our universe.
It is oversimplification, technically imprecise, and often ambiguous to define declarative as “what to do” and imperative as “how to do”. An ambiguous case is the “what” is the “how” in a program that outputs a program— a compiler.
Evidently the unbounded recursion that makes a language Turing complete, is also analogously in the semantics— not only in the syntactical structure of evaluation (a.k.a. operational semantics). This is logically an example analogous to Gödel's theorem— “any complete system of axioms is also inconsistent”. Ponder the contradictory weirdness of that quote! It is also an example that demonstrates how the expression of semantics does not have a provable bound, thus we can't prove2 that a program (and analogously its semantics) halt a.k.a. the Halting theorem.
The incompleteness theorems derive from the fundamental nature of our universe, which as stated in the Second Law of Thermodynamics is “the entropy (a.k.a. the # of independent possibilities) is trending to maximum forever”. The coding and design of a program is never finished— it's alive!— because it attempts to address a real world need, and the semantics of the real world are always changing and trending to more possibilities. Humans never stop discovering new things (including errors in programs ;-).
To precisely and technically capture this aforementioned desired notion within this weird universe that has no edge (ponder that! there is no “outside” of our universe), requires a terse but deceptively-not-simple definition which will sound incorrect until it is explained deeply.
Definition:
The declarative property is where there can exist only one possible set of statements that can express each specific modular semantic.
The imperative property3 is the dual, where semantics are inconsistent under composition and/or can be expressed with variations of sets of statements.
This definition of declarative is distinctively local in semantic scope, meaning that it requires that a modular semantic maintain its consistent meaning regardless where and how it's instantiated and employed in global scope. Thus each declarative modular semantic should be intrinsically orthogonal to all possible others— and not an impossible (due to incompleteness theorems) global algorithm or model for witnessing consistency, which is also the point of “More Is Not Always Better” by Robert Harper, Professor of Computer Science at Carnegie Mellon University, one of the designers of Standard ML.
Examples of these modular declarative semantics include category theory functors e.g. the Applicative, nominal typing, namespaces, named fields, and w.r.t. to operational level of semantics then pure functional programming.
Thus well designed declarative languages can more clearly express meaning, albeit with some loss of generality in what can be expressed, yet a gain in what can be expressed with intrinsic consistency.
An example of the aforementioned definition is the set of formulas in the cells of a spreadsheet program— which are not expected to give the same meaning when moved to different column and row cells, i.e. cell identifiers changed. The cell identifiers are part of and not superfluous to the intended meaning. So each spreadsheet result is unique w.r.t. to the cell identifiers in a set of formulas. The consistent modular semantic in this case is use of cell identifiers as the input and output of pure functions for cells formulas (see below).
Hyper Text Markup Language a.k.a. HTML— the language for static web pages— is an example of a highly (but not perfectly3) declarative language that (at least before HTML 5) had no capability to express dynamic behavior. HTML is perhaps the easiest language to learn. For dynamic behavior, an imperative scripting language such as JavaScript was usually combined with HTML. HTML without JavaScript fits the declarative definition because each nominal type (i.e. the tags) maintains its consistent meaning under composition within the rules of the syntax.
A competing definition for declarative is the commutative and idempotent properties of the semantic statements, i.e. that statements can be reordered and duplicated without changing the meaning. For example, statements assigning values to named fields can be reordered and duplicated without changed the meaning of the program, if those names are modular w.r.t. to any implied order. Names sometimes imply an order, e.g. cell identifiers include their column and row position— moving a total on spreadsheet changes its meaning. Otherwise, these properties implicitly require global consistency of semantics. It is generally impossible to design the semantics of statements so they remain consistent if randomly ordered or duplicated, because order and duplication are intrinsic to semantics. For example, the statements “Foo exists” (or construction) and “Foo does not exist” (and destruction). If one considers random inconsistency endemical of the intended semantics, then one accepts this definition as general enough for the declarative property. In essence this definition is vacuous as a generalized definition because it attempts to make consistency orthogonal to semantics, i.e. to defy the fact that the universe of semantics is dynamically unbounded and can't be captured in a global coherence paradigm.
Requiring the commutative and idempotent properties for the (structural evaluation order of the) lower-level operational semantics converts operational semantics to a declarative localized modular semantic, e.g. pure functional programming (including recursion instead of imperative loops). Then the operational order of the implementation details do not impact (i.e. spread globally into) the consistency of the higher-level semantics. For example, the order of evaluation of (and theoretically also the duplication of) the spreadsheet formulas doesn't matter because the outputs are not copied to the inputs until after all outputs have been computed, i.e. analogous to pure functions.
C, Java, C++, C#, PHP, and JavaScript aren't particularly declarative.
Copute's syntax and Python's syntax are more declaratively coupled to
intended results, i.e. consistent syntactical semantics that eliminate the extraneous so one can readily
comprehend code after they've forgotten it. Copute and Haskell enforce
determinism of the operational semantics and encourage “don't repeat
yourself” (DRY), because they only allow the pure functional paradigm.
2 Even where we can prove the semantics of a program, e.g. with the language Coq, this is limited to the semantics that are expressed in the typing, and typing can never capture all of the semantics of a program— not even for languages that are not Turing complete, e.g. with HTML+CSS it is possible to express inconsistent combinations which thus have undefined semantics.
3 Many explanations incorrectly claim that only imperative programming has syntactically ordered statements. I clarified this confusion between imperative and functional programming. For example, the order of HTML statements does not reduce the consistency of their meaning.
Edit: I posted the following comment to Robert Harper's blog:
in functional programming ... the range of variation of a variable is a type
Depending on how one distinguishes functional from imperative
programming, your ‘assignable’ in an imperative program also may have
a type placing a bound on its variability.
The only non-muddled definition I currently appreciate for functional
programming is a) functions as first-class objects and types, b)
preference for recursion over loops, and/or c) pure functions— i.e.
those functions which do not impact the desired semantics of the
program when memoized (thus perfectly pure functional
programming doesn't exist in a general purpose denotational semantics
due to impacts of operational semantics, e.g. memory
allocation).
The idempotent property of a pure function means the function call on
its variables can be substituted by its value, which is not generally
the case for the arguments of an imperative procedure. Pure functions
seem to be declarative w.r.t. to the uncomposed state transitions
between the input and result types.
But the composition of pure functions does not maintain any such
consistency, because it is possible to model a side-effect (global
state) imperative process in a pure functional programming language,
e.g. Haskell's IOMonad and moreover it is entirely impossible to
prevent doing such in any Turing complete pure functional programming
language.
As I wrote in 2012 which seems to the similar consensus of
comments in your recent blog, that declarative programming is an
attempt to capture the notion that the intended semantics are never
opaque. Examples of opaque semantics are dependence on order,
dependence on erasure of higher-level semantics at the operational
semantics layer (e.g. casts are not conversions and reified generics
limit higher-level semantics), and dependence on variable values
which can not be checked (proved correct) by the programming language.
Thus I have concluded that only non-Turing complete languages can be
declarative.
Thus one unambiguous and distinct attribute of a declarative language
could be that its output can be proven to obey some enumerable set of
generative rules. For example, for any specific HTML program (ignoring
differences in the ways interpreters diverge) that is not scripted
(i.e. is not Turing complete) then its output variability can be
enumerable. Or more succinctly an HTML program is a pure function of
its variability. Ditto a spreadsheet program is a pure function of its
input variables.
So it seems to me that declarative languages are the antithesis of
unbounded recursion, i.e. per Gödel's second incompleteness
theorem self-referential theorems can't be proven.
Lesie Lamport wrote a fairytale about how Euclid might have
worked around Gödel's incompleteness theorems applied to math proofs
in the programming language context by to congruence between types and
logic (Curry-Howard correspondence, etc).
Declarative programming is "the act of programming in languages that conform to the mental model of the developer rather than the operational model of the machine".
The difference between declarative and imperative programming is well
illustrated by the problem of parsing structured data.
An imperative program would use mutually recursive functions to consume input
and generate data. A declarative program would express a grammar that defines
the structure of the data so that it can then be parsed.
The difference between these two approaches is that the declarative program
creates a new language that is more closely mapped to the mental model of the
problem than is its host language.
It may sound odd, but I'd add Excel (or any spreadsheet really) to the list of declarative systems. A good example of this is given here.
I'd explain it as DP is a way to express
A goal expression, the conditions for - what we are searching for. Is there one, maybe or many?
Some known facts
Rules that extend the know facts
...and where there is a deduct engine usually working with a unification algorithm to find the goals.
As far as I can tell, it started being used to describe programming systems like Prolog, because prolog is (supposedly) about declaring things in an abstract way.
It increasingly means very little, as it has the definition given by the users above. It should be clear that there is a gulf between the declarative programming of Haskell, as against the declarative programming of HTML.
A couple other examples of declarative programming:
ASP.Net markup for databinding. It just says "fill this grid with this source", for example, and leaves it to the system for how that happens.
Linq expressions
Declarative programming is nice because it can help simplify your mental model* of code, and because it might eventually be more scalable.
For example, let's say you have a function that does something to each element in an array or list. Traditional code would look like this:
foreach (object item in MyList)
{
DoSomething(item);
}
No big deal there. But what if you use the more-declarative syntax and instead define DoSomething() as an Action? Then you can say it this way:
MyList.ForEach(DoSometing);
This is, of course, more concise. But I'm sure you have more concerns than just saving two lines of code here and there. Performance, for example. The old way, processing had to be done in sequence. What if the .ForEach() method had a way for you to signal that it could handle the processing in parallel, automatically? Now all of a sudden you've made your code multi-threaded in a very safe way and only changed one line of code. And, in fact, there's a an extension for .Net that lets you do just that.
If you follow that link, it takes you to a blog post by a friend of mine. The whole post is a little long, but you can scroll down to the heading titled "The Problem" _and pick it up there no problem.*
It depends on how you submit the answer to the text. Overall you can look at the programme at a certain view but it depends what angle you look at the problem. I will get you started with the programme:
Dim Bus, Car, Time, Height As Integr
Again it depends on what the problem is an overall. You might have to shorten it due to the programme. Hope this helps and need the feedback if it does not.
Thank You.