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I've read the Wikipedia articles for both procedural programming and functional programming, but I'm still slightly confused. Could someone boil it down to the core?
A functional language (ideally) allows you to write a mathematical function, i.e. a function that takes n arguments and returns a value. If the program is executed, this function is logically evaluated as needed.1
A procedural language, on the other hand, performs a series of sequential steps. (There's a way of transforming sequential logic into functional logic called continuation passing style.)
As a consequence, a purely functional program always yields the same value for an input, and the order of evaluation is not well-defined; which means that uncertain values like user input or random values are hard to model in purely functional languages.
1 As everything else in this answer, that’s a generalisation. This property, evaluating a computation when its result is needed rather than sequentially where it’s called, is known as “laziness”. Not all functional languages are actually universally lazy, nor is laziness restricted to functional programming. Rather, the description given here provides a “mental framework” to think about different programming styles that are not distinct and opposite categories but rather fluid ideas.
Basically the two styles, are like Yin and Yang. One is organized, while the other chaotic. There are situations when Functional programming is the obvious choice, and other situations were Procedural programming is the better choice. This is why there are at least two languages that have recently come out with a new version, that embraces both programming styles. ( Perl 6 and D 2 )
#Procedural:#
The output of a routine does not always have a direct correlation with the input.
Everything is done in a specific order.
Execution of a routine may have side effects.
Tends to emphasize implementing solutions in a linear fashion.
##Perl 6 ##
sub factorial ( UInt:D $n is copy ) returns UInt {
# modify "outside" state
state $call-count++;
# in this case it is rather pointless as
# it can't even be accessed from outside
my $result = 1;
loop ( ; $n > 0 ; $n-- ){
$result *= $n;
}
return $result;
}
##D 2##
int factorial( int n ){
int result = 1;
for( ; n > 0 ; n-- ){
result *= n;
}
return result;
}
#Functional:#
Often recursive.
Always returns the same output for a given input.
Order of evaluation is usually undefined.
Must be stateless. i.e. No operation can have side effects.
Good fit for parallel execution
Tends to emphasize a divide and conquer approach.
May have the feature of Lazy Evaluation.
##Haskell##
( copied from Wikipedia );
fac :: Integer -> Integer
fac 0 = 1
fac n | n > 0 = n * fac (n-1)
or in one line:
fac n = if n > 0 then n * fac (n-1) else 1
##Perl 6 ##
proto sub factorial ( UInt:D $n ) returns UInt {*}
multi sub factorial ( 0 ) { 1 }
multi sub factorial ( $n ) { $n * samewith $n-1 } # { $n * factorial $n-1 }
##D 2##
pure int factorial( invariant int n ){
if( n <= 1 ){
return 1;
}else{
return n * factorial( n-1 );
}
}
#Side note:#
Factorial is actually a common example to show how easy it is to create new operators in Perl 6 the same way you would create a subroutine. This feature is so ingrained into Perl 6 that most operators in the Rakudo implementation are defined this way. It also allows you to add your own multi candidates to existing operators.
sub postfix:< ! > ( UInt:D $n --> UInt )
is tighter(&infix:<*>)
{ [*] 2 .. $n }
say 5!; # 120
This example also shows range creation (2..$n) and the list reduction meta-operator ([ OPERATOR ] LIST) combined with the numeric infix multiplication operator. (*)
It also shows that you can put --> UInt in the signature instead of returns UInt after it.
( You can get away with starting the range with 2 as the multiply "operator" will return 1 when called without any arguments )
I've never seen this definition given elsewhere, but I think this sums up the differences given here fairly well:
Functional programming focuses on expressions
Procedural programming focuses on statements
Expressions have values. A functional program is an expression who's value is a sequence of instructions for the computer to carry out.
Statements don't have values and instead modify the state of some conceptual machine.
In a purely functional language there would be no statements, in the sense that there's no way to manipulate state (they might still have a syntactic construct named "statement", but unless it manipulates state I wouldn't call it a statement in this sense). In a purely procedural language there would be no expressions, everything would be an instruction which manipulates the state of the machine.
Haskell would be an example of a purely functional language because there is no way to manipulate state. Machine code would be an example of a purely procedural language because everything in a program is a statement which manipulates the state of the registers and memory of the machine.
The confusing part is that the vast majority of programming languages contain both expressions and statements, allowing you to mix paradigms. Languages can be classified as more functional or more procedural based on how much they encourage the use of statements vs expressions.
For example, C would be more functional than COBOL because a function call is an expression, whereas calling a sub program in COBOL is a statement (that manipulates the state of shared variables and doesn't return a value). Python would be more functional than C because it allows you to express conditional logic as an expression using short circuit evaluation (test && path1 || path2 as opposed to if statements). Scheme would be more functional than Python because everything in scheme is an expression.
You can still write in a functional style in a language which encourages the procedural paradigm and vice versa. It's just harder and/or more awkward to write in a paradigm which isn't encouraged by the language.
Funtional Programming
num = 1
def function_to_add_one(num):
num += 1
return num
function_to_add_one(num)
function_to_add_one(num)
function_to_add_one(num)
function_to_add_one(num)
function_to_add_one(num)
#Final Output: 2
Procedural Programming
num = 1
def procedure_to_add_one():
global num
num += 1
return num
procedure_to_add_one()
procedure_to_add_one()
procedure_to_add_one()
procedure_to_add_one()
procedure_to_add_one()
#Final Output: 6
function_to_add_one is a function
procedure_to_add_one is a procedure
Even if you run the function five times, every time it will return 2
If you run the procedure five times, at the end of fifth run it will give you 6.
DISCLAIMER: Obviously this is a hyper-simplified view of reality. This answer just gives a taste of "functions" as opposed to "procedures". Nothing more. Once you have tasted this superficial yet deeply penetrative intuition, start exploring the two paradigms, and you will start to see the difference quite clearly.
Helps my students, hope it helps you too.
In computer science, functional programming is a programming paradigm that treats computation as the evaluation of mathematical functions and avoids state and mutable data. It emphasizes the application of functions, in contrast with the procedural programming style that emphasizes changes in state.
I believe that procedural/functional/objective programming are about how to approach a problem.
The first style would plan everything in to steps, and solves the problem by implementing one step (a procedure) at a time. On the other hand, functional programming would emphasize the divide-and-conquer approach, where the problem is divided into sub-problem, then each sub-problem is solved (creating a function to solve that sub problem) and the results are combined to create the answer for the whole problem. Lastly, Objective programming would mimic the real world by create a mini-world inside the computer with many objects, each of which has a (somewhat) unique characteristics, and interacts with others. From those interactions the result would emerge.
Each style of programming has its own advantages and weaknesses. Hence, doing something such as "pure programming" (i.e. purely procedural - no one does this, by the way, which is kind of weird - or purely functional or purely objective) is very difficult, if not impossible, except some elementary problems specially designed to demonstrate the advantage of a programming style (hence, we call those who like pureness "weenie" :D).
Then, from those styles, we have programming languages that is designed to optimized for some each style. For example, Assembly is all about procedural. Okay, most early languages are procedural, not only Asm, like C, Pascal, (and Fortran, I heard). Then, we have all famous Java in objective school (Actually, Java and C# is also in a class called "money-oriented," but that is subject for another discussion). Also objective is Smalltalk. In functional school, we would have "nearly functional" (some considered them to be impure) Lisp family and ML family and many "purely functional" Haskell, Erlang, etc. By the way, there are many general languages such as Perl, Python, Ruby.
To expand on Konrad's comment:
As a consequence, a purely functional program always yields the same value for an input, and the order of evaluation is not well-defined;
Because of this, functional code is generally easier to parallelize. Since there are (generally) no side effects of the functions, and they (generally) just act on their arguments, a lot of concurrency issues go away.
Functional programming is also used when you need to be capable of proving your code is correct. This is much harder to do with procedural programming (not easy with functional, but still easier).
Disclaimer: I haven't used functional programming in years, and only recently started looking at it again, so I might not be completely correct here. :)
One thing I hadn't seen really emphasized here is that modern functional languages such as Haskell really more on first class functions for flow control than explicit recursion. You don't need to define factorial recursively in Haskell, as was done above. I think something like
fac n = foldr (*) 1 [1..n]
is a perfectly idiomatic construction, and much closer in spirit to using a loop than to using explicit recursion.
A functional programming is identical to procedural programming in which global variables are not being used.
Procedural languages tend to keep track of state (using variables) and tend to execute as a sequence of steps. Purely functional languages don't keep track of state, use immutable values, and tend to execute as a series of dependencies. In many cases the status of the call stack will hold the information that would be equivalent to that which would be stored in state variables in procedural code.
Recursion is a classic example of functional style programming.
Konrad said:
As a consequence, a purely functional program always yields the same value for an input,
and the order of evaluation is not well-defined; which means that uncertain values like
user input or random values are hard to model in purely functional languages.
The order of evaluation in a purely functional program may be hard(er) to reason about (especially with laziness) or even unimportant but I think that saying it is not well defined makes it sound like you can't tell if your program is going to work at all!
Perhaps a better explanation would be that control flow in functional programs is based on when the value of a function's arguments are needed. The Good Thing about this that in well written programs, state becomes explicit: each function lists its inputs as parameters instead of arbitrarily munging global state. So on some level, it is easier to reason about order of evaluation with respect to one function at a time. Each function can ignore the rest of the universe and focus on what it needs to do. When combined, functions are guaranteed to work the same[1] as they would in isolation.
... uncertain values like user input or random values are hard to model in purely
functional languages.
The solution to the input problem in purely functional programs is to embed an imperative language as a DSL using a sufficiently powerful abstraction. In imperative (or non-pure functional) languages this is not needed because you can "cheat" and pass state implicitly and order of evaluation is explicit (whether you like it or not). Because of this "cheating" and forced evaluation of all parameters to every function, in imperative languages 1) you lose the ability to create your own control flow mechanisms (without macros), 2) code isn't inherently thread safe and/or parallelizable by default, 3) and implementing something like undo (time travel) takes careful work (imperative programmer must store a recipe for getting the old value(s) back!), whereas pure functional programming buys you all these things—and a few more I may have forgotten—"for free".
I hope this doesn't sound like zealotry, I just wanted to add some perspective. Imperative programming and especially mixed paradigm programming in powerful languages like C# 3.0 are still totally effective ways to get things done and there is no silver bullet.
[1] ... except possibly with respect memory usage (cf. foldl and foldl' in Haskell).
To expand on Konrad's comment:
and the order of evaluation is not
well-defined
Some functional languages have what is called Lazy Evaluation. Which means a function is not executed until the value is needed. Until that time the function itself is what is passed around.
Procedural languages are step 1 step 2 step 3... if in step 2 you say add 2 + 2, it does it right then. In lazy evaluation you would say add 2 + 2, but if the result is never used, it never does the addition.
If you have a chance, I would recommand getting a copy of Lisp/Scheme, and doing some projects in it. Most of the ideas that have lately become bandwagons were expressed in Lisp decades ago: functional programming, continuations (as closures), garbage collection, even XML.
So that would be a good way to get a head start on all these current ideas, and a few more besides, like symbolic computation.
You should know what functional programming is good for, and what it isn't good for. It isn't good for everything. Some problems are best expressed in terms of side-effects, where the same question gives differet answers depending on when it is asked.
#Creighton:
In Haskell there is a library function called product:
prouduct list = foldr 1 (*) list
or simply:
product = foldr 1 (*)
so the "idiomatic" factorial
fac n = foldr 1 (*) [1..n]
would simply be
fac n = product [1..n]
Procedural programming divides sequences of statements and conditional constructs into separate blocks called procedures that are parameterized over arguments that are (non-functional) values.
Functional programming is the same except that functions are first-class values, so they can be passed as arguments to other functions and returned as results from function calls.
Note that functional programming is a generalization of procedural programming in this interpretation. However, a minority interpret "functional programming" to mean side-effect-free which is quite different but irrelevant for all major functional languages except Haskell.
None of the answers here show idiomatic functional programming. The recursive factorial answer is great for representing recursion in FP, but the majority of code is not recursive so I don't think that answer is fully representative.
Say you have an arrays of strings, and each string represents an integer like "5" or "-200". You want to check this input array of strings against your internal test case (Using integer comparison). Both solutions are shown below
Procedural
arr_equal(a : [Int], b : [Str]) -> Bool {
if(a.len != b.len) {
return false;
}
bool ret = true;
for( int i = 0; i < a.len /* Optimized with && ret*/; i++ ) {
int a_int = a[i];
int b_int = parseInt(b[i]);
ret &= a_int == b_int;
}
return ret;
}
Functional
eq = i, j => i == j # This is usually a built-in
toInt = i => parseInt(i) # Of course, parseInt === toInt here, but this is for visualization
arr_equal(a : [Int], b : [Str]) -> Bool =
zip(a, b.map(toInt)) # Combines into [Int, Int]
.map(eq)
.reduce(true, (i, j) => i && j) # Start with true, and continuously && it with each value
While pure functional languages are generally research languages (As the real-world likes free side-effects), real-world procedural languages will use the much simpler functional syntax when appropriate.
This is usually implemented with an external library like Lodash, or available built-in with newer languages like Rust. The heavy lifting of functional programming is done with functions/concepts like map, filter, reduce, currying, partial, the last three of which you can look up for further understanding.
Addendum
In order to be used in the wild, the compiler will normally have to work out how to convert the functional version into the procedural version internally, as function call overhead is too high. Recursive cases such as the factorial shown will use tricks such as tail call to remove O(n) memory usage. The fact that there are no side effects allows functional compilers to implement the && ret optimization even when the .reduce is done last. Using Lodash in JS, obviously does not allow for any optimization, so it is a hit to performance (Which isn't usually a concern with web development). Languages like Rust will optimize internally (And have functions such as try_fold to assist && ret optimization).
To Understand the difference, one needs to to understand that "the godfather" paradigm of both procedural and functional programming is the imperative programming.
Basically procedural programming is merely a way of structuring imperative programs in which the primary method of abstraction is the "procedure." (or "function" in some programming languages). Even Object Oriented Programming is just another way of structuring an imperative program, where the state is encapsulated in objects, becoming an object with a "current state," plus this object has a set of functions, methods, and other stuff that let you the programmer manipulate or update the state.
Now, in regards to functional programming, the gist in its approach is that it identifies what values to take and how these values should be transferred. (so there is no state, and no mutable data as it takes functions as first class values and pass them as parameters to other functions).
PS: understanding every programming paradigm is used for should clarify the differences between all of them.
PSS: In the end of the day, programming paradigms are just different approaches to solving problems.
PSS: this quora answer has a great explanation.
I've been recently learning about functional languages and how many don't include for loops. While I don't personally view recursion as more difficult than a for loop (and often easier to reason out) I realized that many examples of recursion aren't tail recursive and therefor cannot use simple tail recursion optimization in order to avoid stack overflows. According to this question, all iterative loops can be translated into recursion, and those iterative loops can be transformed into tail recursion, so it confuses me when the answers on a question like this suggest that you have to explicitly manage the translation of your recursion into tail recursion yourself if you want to avoid stack overflows. It seems like it should be possible for a compiler to do all the translation from either recursion to tail recursion, or from recursion straight to an iterative loop with out stack overflows.
Are functional compilers able to avoid stack overflows in more general recursive cases? Are you really forced to transform your recursive code in order to avoid stack overflows yourself? If they aren't able to perform general recursive stack-safe compilation, why aren't they?
Any recursive function can be converted into a tail recursive one.
For instance, consider the transition function of a Turing machine, that
is the mapping from a configuration to the next one. To simulate the
turing machine you just need to iterate the transition function until
you reach a final state, that is easily expressed in tail recursive
form. Similarly, a compiler typically translates a recursive program into
an iterative one simply adding a stack of activation records.
You can also give a translation into tail recursive form using continuation
passing style (CPS). To make a classical example, consider the fibonacci
function.
This can be expressed in CPS style in the following way, where the second
parameter is the continuation (essentially, a callback function):
def fibc(n, cont):
if n <= 1:
return cont(n)
return fibc(n - 1, lambda a: fibc(n - 2, lambda b: cont(a + b)))
Again, you are simulating the recursion stack using a dynamic data structure:
in this case, lambda abstractions.
The use of dynamic structures (lists, stacks, functions, etc.) in all previous
examples is essential. That is to say, that in order to simulate a generic
recursive function iteratively, you cannot avoid dynamic memory allocation,
and hence you cannot avoid stack overflow, in general.
So, memory consumption is not only related to the iterative/recursive
nature of the program. On the other side, if you prevent dynamic memory
allocation, your
programs are essentially finite state machines, with limited computational
capabilities (more interesting would be to parametrise memory according to
the dimension of inputs).
In general, in the same way as you cannot predict termination, you cannot
predict an unbound memory consumption of your program: working with
a Turing complete language, at compile time
you cannot avoid divergence, and you cannot avoid stack overflow.
Tail Call Optimization:
The natural way to do arguments and calls is to sort out the cleaning up when exiting or when returning.
For tail calls to work you need to alter it so that the tail call inherits the current frame. Thus instead of making a new frame it massages the frame so that the next call returns to the current functions caller instead of this function, which really only cleans up and returns if it's a tail call.
Thus TCO is all about cleaning up before the last call.
Continuation Passing Style - make tail calls out of everything
A compiler can change the code such that it only does primitive operations and pass it to continuations. Thus the stack usage gets moved onto the heap since the computation to be continued is made a function.
An example is:
function hypotenuse(k1, k2) {
return sqrt(add(square(k1), square(k2)))
}
becomes
function hypotenuse(k, k1, k2) {
(function (sk1) {
(function (sk2) {
(function (ar) {
k(sqrt(ar));
}(add(sk1,sk2));
}(square(k2));
}(square(k1));
}
Notice every function has exactly one call now and the order of evaluation is set.
According to this question, all iterative loops can be translated into recursion
"Translated" might be a bit of a stretch. The proof that for every iterative loop there is an equivalent recursive program is trivial if you understand Turing completeness: since a Turing machine can be implemented using strictly iterative structures and strictly recursive structures, every program that can be expressed in an iterative language can be expressed in a recursive language, and vice-versa. This means that for every iterative loop there is an equivalent recursive construct (and the other way around). However, that doesn't mean we have some automated way of transforming one into the other.
and those iterative loops can be transformed into tail recursion
Tail recursion can perhaps be easily transformed into an iterative loop, and the other way around. But not all recursion is tail recursion. Here's an example. Suppose we have some binary tree. It consists of nodes. Each node can have a left and a right child and a value. If a node has no children, then isLeaf returns true for it. We'll assume there's some function max that returns the maximum of two values, and if one of the values is null it returns the other one. Now we want to define a function that finds the maximum value among all the leaf nodes. Here it is in some pseudo-code I cooked up.
findmax(node) {
if (node == null) {
return null
}
if (node.isLeaf) {
return node.value
} else {
return max(findmax(node.left), findmax(node.right))
}
}
There's two recursive calls in the max function, so we can't optimize for tail recursion. We need the results of both before we can supply them to the max function and determine the result of the call for the current node.
Now, there may be a way of getting the same result, using recursion and only a single tail-recursive call. It is functionally equivalent, but it is a different algorithm. Compilers can do a lot of transformations to create a functionally equivalent program with lots of optimizations, but they're not quite clever enough to create functionally equivalent algorithms.
Even the transformation of a function that only calls itself recursively once into a tail-recursive version would be far from trivial. Such an adaptation usually employs some argument passed into the recursive invocation that is used as an "accumulator" for the current results.
Look at the next naive implementation for calculating a factorial of a number (e.g. fact(5) = 5*4*3*2*1):
fact(number) {
if (number == 1) {
return 1
} else {
return number * fact(number - 1)
}
}
It's not tail-recursive. But it can be made so in this way:
fact(number, acc) {
if (number == 1) {
return acc
} else {
return fact(number - 1, number * acc)
}
}
// Helper function
fact(number) {
return fact(number, 1)
}
This requires an interpretation of what is being done. Recognizing the case for stuff like this is easy enough, but what if you call a function instead of a multiplication? How will the compiler know that for the initial call the accumulator must be 1 and not, say, 0? How do you translate this program?
recsub(number) {
if (number == 1) {
return 1
} else {
return number - recsub(number - 1)
}
}
This is as of yet outside the scope of the sort of compiler we have now, and may in fact always be.
Maybe it would be interesting to ask this on the computer science Stack Exchange to see if they know of some papers or proofs that investigate this more in-depth.
I've been writing (unsophisticated) code for a decent while, and I feel like I have a somewhat firm grasp on while and for loops and if/else statements. I should also say that I feel like I understand (at my level, at least) the concept of recursion. That is, I understand how a method keeps calling itself until the parameters of an iteration match a base case in the method, at which point the methods begin to terminate and pass control (along with values) to previous instances and eventually an overall value of the first call is determined. I may not have explained it very well, but I think I understand it, and I can follow/make traces of the structured examples I've seen. But my question is on creating recursive methods in the wild, ie, in unstructured circumstances.
Our professor wants us to write recursively at every opportunity, and has made the (technically inaccurate?) statement that all loops can be replaced with recursion. But, since many times recursive operations are contained within while or for loops, this means, to state the obvious, not every loop can be replaced with recursion. So...
For unstructured/non-classroom situations,
1) how can I recognize that a loop situation can/cannot be turned into a recursion, and
2) what is the overall idea/strategy to use when applying recursion to a situation? I mean, how should I approach the problem? What aspects of the problem will be used as recursive criteria, etc?
Thanks!
Edit 6/29:
While I appreciate the 2 answers, I think maybe the preamble to my question was too long because it seems to be getting all of the attention. What I'm really asking is for someone to share with me, a person who "thinks" in loops, an approach for implementing recursive solutions. (For purposes of the question, please assume I have a sufficient understanding of the solution, but just need to create recursive code.) In other words, to apply a recursive solution, what am I looking for in the problem/solution that I will then use for the recursion? Maybe some very general statements about applying recursion would be helpful too. (note: please, not definitions of recursion, since I think I pretty much understand the definition. It's just the process of applying them I am asking about.) Thanks!
Every loop CAN be turned into recursion fairly easily. (It's also true that every recursion can be turned into loops, but not always easily.)
But, I realize that saying "fairly easily" isn't actually very helpful if you don't see how, so here's the idea:
For this explanation, I'm going to assume a plain vanilla while loop--no nested loops or for loops, no breaking out of the middle of the loop, no returning from the middle of the loop, etc. Those other things can also be handled but would muddy up the explanation.
The plain vanilla while loop might look like this:
1. x = initial value;
2. while (some condition on x) {
3. do something with x;
4. x = next value;
5. }
6. final action;
Then the recursive version would be
A. def Recursive(x) {
B. if (some condition on x) {
C. do something with x;
D. Recursive(next value);
E. }
F. else { # base case = where the recursion stops
G. final action;
H. }
I.
J. Recursive(initial value);
So,
the initial value of x in line 1 became the orginial argument to Recursive on line J
the condition of the loop on line 2 became the condition of the if on line B
the first action inside the loop on line 3 became the first action inside the if on line C
the next value of x on line 4 became the next argument to Recursive on line D
the final action on line 6 became the action in the base case on line G
If more than one variable was being updated in the loop, then you would often have a corresponding number of arguments in the recursive function.
Again, this basic recipe can be modified to handle fancier situations than plain vanilla while loops.
Minor comment: In the recursive function, it would be more common to put the base case on the "then" side of the if instead of the "else" side. In that case, you would flip the condition of the if to its opposite. That is, the condition in the while loop tests when to keep going, whereas the condition in the recursive function tests when to stop.
I may not have explained it very well, but I think I understand it, and I can follow/make traces of the structured examples I've seen
That's cool, if I understood your explanation well, then how you think recursion works is correct at first glance.
Our professor wants us to write recursively at every opportunity, and has made the (technically inaccurate?) statement that all loops can be replaced with recursion
That's not inaccurate. That's the truth. And the inverse is also possible: every time a recursive function is used, that can be rewritten using iteration. It may be hard and unintuitive (like traversing a tree), but it's possible.
how can I recognize that a loop can/cannot be turned into a recursion
Simple:
what is the overall idea/strategy to use when doing the conversion?
There's no such thing, unfortunately. And by that I mean that there's no universal or general "work-it-all-out" method, you have to think specifically for considering each case when solving a particular problem. One thing may be helpful, however. When converting from an iterative algorithm to a recursive one, think about patterns. How long and where exactly is the part that keeps repeating itself with a small difference only?
Also, if you ever want to convert a recursive algorithm to an iterative one, think about that the overwhelmingly popular approach for implementing recursion at hardware level is by using a (call) stack. Except when solving trivially convertible algorithms, such as the beloved factorial or Fibonacci functions, you can always think about how it might look in assembler, and create an explicit stack. Dirty, but works.
for(int i = 0; i < 50; i++)
{
for(int j = 0; j < 60; j++)
{
}
}
Is equal to:
rec1(int i)
{
if(i < 50)
return;
rec2(0);
rec1(i+1);
}
rec2(int j)
{
if(j < 60)
return;
rec2(j + 1);
}
Every loop can be recursive. Trust your professor, he is right!
This question already has answers here:
Can every recursion be converted into iteration?
(18 answers)
Closed 2 years ago.
As far as I know, most recursive functions can be rewritten using loops. Some may be harder than others, but most of them can be rewritten.
Under which conditions does it become impossible to rewrite a recursive function using a loop (if such conditions exist)?
When you use a function recursively, the compiler takes care of stack management for you, which is what makes recursion possible. Anything you can do recursively, you can do by managing a stack yourself (for indirect recursion, you just have to make sure your different functions share that stack).
So, no, there is nothing that can be done with recursion and that cannot be done with a loop and a stack.
Any recursive function can be made to iterate (into a loop) but you need to use a stack yourself to keep the state.
Normally, tail recursion is easy to convert into a loop:
A(x) {
if x<0 return 0;
return something(x) + A(x-1)
}
Can be translated into:
A(x) {
temp = 0;
for i in 0..x {
temp = temp + something(i);
}
return temp;
}
Other kinds of recursion that can be translated into tail recursion are also easy to change. The other require more work.
The following:
treeSum(tree) {
if tree=nil then 0
else tree.value + treeSum(tree.left) + treeSum(tree.right);
}
Is not that easy to translate. You can remove one piece of the recursion, but the other one is not possible without a structure to hold the state.
treeSum(tree) {
walk = tree;
temp = 0;
while walk != nil {
temp = temp + walk.value + treeSum(walk.right);
walk = walk.left;
}
}
Every recursive function can be implemented with a single loop.
Just think what a processor does, it executes instructions in a single loop.
I don't know about examples where recursive functions cannot be converted to an iterative version, but impractical or extremely inefficient examples are:
tree traversal
fast Fourier
quicksorts (and some others iirc)
Basically, anything where you have to start keeping track of boundless potential states.
It's not so much a matter of that they can't be implemented using loops, it's the fact that the way the recursive algorithm works, it's much clearer and more concise (and in many cases mathematically provable) that a function is correct.
Many recursive functions can be written to be tail loop recursive, which can be optimised to a loop, but this is dependent on both the algorithm and the language used.
They all can be written as an iterative loop (but some might still need a stack to keep previous state for later iterations).
One example which would be extremely difficult to convert from recursive to iterative would be the Ackermann function.
Indirect recursion is still possible to convert to a non-recursive loop; just start with one of the functions, and inline the calls to the others until you have a directly recursive function, which can then be translated to a loop that uses a stack structure.
In SICP, the authors challenge the reader to come up with a purely iterative method of implementing the 'counting change' problem (here's an example one from Project Euler).
But the strict answer to your question was already given - loops and stacks can implement any recursion.
You can always use a loop, but you may have to create more data structure (e.g. simulate a stack).
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I've read the Wikipedia articles for both procedural programming and functional programming, but I'm still slightly confused. Could someone boil it down to the core?
A functional language (ideally) allows you to write a mathematical function, i.e. a function that takes n arguments and returns a value. If the program is executed, this function is logically evaluated as needed.1
A procedural language, on the other hand, performs a series of sequential steps. (There's a way of transforming sequential logic into functional logic called continuation passing style.)
As a consequence, a purely functional program always yields the same value for an input, and the order of evaluation is not well-defined; which means that uncertain values like user input or random values are hard to model in purely functional languages.
1 As everything else in this answer, that’s a generalisation. This property, evaluating a computation when its result is needed rather than sequentially where it’s called, is known as “laziness”. Not all functional languages are actually universally lazy, nor is laziness restricted to functional programming. Rather, the description given here provides a “mental framework” to think about different programming styles that are not distinct and opposite categories but rather fluid ideas.
Basically the two styles, are like Yin and Yang. One is organized, while the other chaotic. There are situations when Functional programming is the obvious choice, and other situations were Procedural programming is the better choice. This is why there are at least two languages that have recently come out with a new version, that embraces both programming styles. ( Perl 6 and D 2 )
#Procedural:#
The output of a routine does not always have a direct correlation with the input.
Everything is done in a specific order.
Execution of a routine may have side effects.
Tends to emphasize implementing solutions in a linear fashion.
##Perl 6 ##
sub factorial ( UInt:D $n is copy ) returns UInt {
# modify "outside" state
state $call-count++;
# in this case it is rather pointless as
# it can't even be accessed from outside
my $result = 1;
loop ( ; $n > 0 ; $n-- ){
$result *= $n;
}
return $result;
}
##D 2##
int factorial( int n ){
int result = 1;
for( ; n > 0 ; n-- ){
result *= n;
}
return result;
}
#Functional:#
Often recursive.
Always returns the same output for a given input.
Order of evaluation is usually undefined.
Must be stateless. i.e. No operation can have side effects.
Good fit for parallel execution
Tends to emphasize a divide and conquer approach.
May have the feature of Lazy Evaluation.
##Haskell##
( copied from Wikipedia );
fac :: Integer -> Integer
fac 0 = 1
fac n | n > 0 = n * fac (n-1)
or in one line:
fac n = if n > 0 then n * fac (n-1) else 1
##Perl 6 ##
proto sub factorial ( UInt:D $n ) returns UInt {*}
multi sub factorial ( 0 ) { 1 }
multi sub factorial ( $n ) { $n * samewith $n-1 } # { $n * factorial $n-1 }
##D 2##
pure int factorial( invariant int n ){
if( n <= 1 ){
return 1;
}else{
return n * factorial( n-1 );
}
}
#Side note:#
Factorial is actually a common example to show how easy it is to create new operators in Perl 6 the same way you would create a subroutine. This feature is so ingrained into Perl 6 that most operators in the Rakudo implementation are defined this way. It also allows you to add your own multi candidates to existing operators.
sub postfix:< ! > ( UInt:D $n --> UInt )
is tighter(&infix:<*>)
{ [*] 2 .. $n }
say 5!; # 120
This example also shows range creation (2..$n) and the list reduction meta-operator ([ OPERATOR ] LIST) combined with the numeric infix multiplication operator. (*)
It also shows that you can put --> UInt in the signature instead of returns UInt after it.
( You can get away with starting the range with 2 as the multiply "operator" will return 1 when called without any arguments )
I've never seen this definition given elsewhere, but I think this sums up the differences given here fairly well:
Functional programming focuses on expressions
Procedural programming focuses on statements
Expressions have values. A functional program is an expression who's value is a sequence of instructions for the computer to carry out.
Statements don't have values and instead modify the state of some conceptual machine.
In a purely functional language there would be no statements, in the sense that there's no way to manipulate state (they might still have a syntactic construct named "statement", but unless it manipulates state I wouldn't call it a statement in this sense). In a purely procedural language there would be no expressions, everything would be an instruction which manipulates the state of the machine.
Haskell would be an example of a purely functional language because there is no way to manipulate state. Machine code would be an example of a purely procedural language because everything in a program is a statement which manipulates the state of the registers and memory of the machine.
The confusing part is that the vast majority of programming languages contain both expressions and statements, allowing you to mix paradigms. Languages can be classified as more functional or more procedural based on how much they encourage the use of statements vs expressions.
For example, C would be more functional than COBOL because a function call is an expression, whereas calling a sub program in COBOL is a statement (that manipulates the state of shared variables and doesn't return a value). Python would be more functional than C because it allows you to express conditional logic as an expression using short circuit evaluation (test && path1 || path2 as opposed to if statements). Scheme would be more functional than Python because everything in scheme is an expression.
You can still write in a functional style in a language which encourages the procedural paradigm and vice versa. It's just harder and/or more awkward to write in a paradigm which isn't encouraged by the language.
Funtional Programming
num = 1
def function_to_add_one(num):
num += 1
return num
function_to_add_one(num)
function_to_add_one(num)
function_to_add_one(num)
function_to_add_one(num)
function_to_add_one(num)
#Final Output: 2
Procedural Programming
num = 1
def procedure_to_add_one():
global num
num += 1
return num
procedure_to_add_one()
procedure_to_add_one()
procedure_to_add_one()
procedure_to_add_one()
procedure_to_add_one()
#Final Output: 6
function_to_add_one is a function
procedure_to_add_one is a procedure
Even if you run the function five times, every time it will return 2
If you run the procedure five times, at the end of fifth run it will give you 6.
DISCLAIMER: Obviously this is a hyper-simplified view of reality. This answer just gives a taste of "functions" as opposed to "procedures". Nothing more. Once you have tasted this superficial yet deeply penetrative intuition, start exploring the two paradigms, and you will start to see the difference quite clearly.
Helps my students, hope it helps you too.
In computer science, functional programming is a programming paradigm that treats computation as the evaluation of mathematical functions and avoids state and mutable data. It emphasizes the application of functions, in contrast with the procedural programming style that emphasizes changes in state.
I believe that procedural/functional/objective programming are about how to approach a problem.
The first style would plan everything in to steps, and solves the problem by implementing one step (a procedure) at a time. On the other hand, functional programming would emphasize the divide-and-conquer approach, where the problem is divided into sub-problem, then each sub-problem is solved (creating a function to solve that sub problem) and the results are combined to create the answer for the whole problem. Lastly, Objective programming would mimic the real world by create a mini-world inside the computer with many objects, each of which has a (somewhat) unique characteristics, and interacts with others. From those interactions the result would emerge.
Each style of programming has its own advantages and weaknesses. Hence, doing something such as "pure programming" (i.e. purely procedural - no one does this, by the way, which is kind of weird - or purely functional or purely objective) is very difficult, if not impossible, except some elementary problems specially designed to demonstrate the advantage of a programming style (hence, we call those who like pureness "weenie" :D).
Then, from those styles, we have programming languages that is designed to optimized for some each style. For example, Assembly is all about procedural. Okay, most early languages are procedural, not only Asm, like C, Pascal, (and Fortran, I heard). Then, we have all famous Java in objective school (Actually, Java and C# is also in a class called "money-oriented," but that is subject for another discussion). Also objective is Smalltalk. In functional school, we would have "nearly functional" (some considered them to be impure) Lisp family and ML family and many "purely functional" Haskell, Erlang, etc. By the way, there are many general languages such as Perl, Python, Ruby.
To expand on Konrad's comment:
As a consequence, a purely functional program always yields the same value for an input, and the order of evaluation is not well-defined;
Because of this, functional code is generally easier to parallelize. Since there are (generally) no side effects of the functions, and they (generally) just act on their arguments, a lot of concurrency issues go away.
Functional programming is also used when you need to be capable of proving your code is correct. This is much harder to do with procedural programming (not easy with functional, but still easier).
Disclaimer: I haven't used functional programming in years, and only recently started looking at it again, so I might not be completely correct here. :)
One thing I hadn't seen really emphasized here is that modern functional languages such as Haskell really more on first class functions for flow control than explicit recursion. You don't need to define factorial recursively in Haskell, as was done above. I think something like
fac n = foldr (*) 1 [1..n]
is a perfectly idiomatic construction, and much closer in spirit to using a loop than to using explicit recursion.
A functional programming is identical to procedural programming in which global variables are not being used.
Procedural languages tend to keep track of state (using variables) and tend to execute as a sequence of steps. Purely functional languages don't keep track of state, use immutable values, and tend to execute as a series of dependencies. In many cases the status of the call stack will hold the information that would be equivalent to that which would be stored in state variables in procedural code.
Recursion is a classic example of functional style programming.
Konrad said:
As a consequence, a purely functional program always yields the same value for an input,
and the order of evaluation is not well-defined; which means that uncertain values like
user input or random values are hard to model in purely functional languages.
The order of evaluation in a purely functional program may be hard(er) to reason about (especially with laziness) or even unimportant but I think that saying it is not well defined makes it sound like you can't tell if your program is going to work at all!
Perhaps a better explanation would be that control flow in functional programs is based on when the value of a function's arguments are needed. The Good Thing about this that in well written programs, state becomes explicit: each function lists its inputs as parameters instead of arbitrarily munging global state. So on some level, it is easier to reason about order of evaluation with respect to one function at a time. Each function can ignore the rest of the universe and focus on what it needs to do. When combined, functions are guaranteed to work the same[1] as they would in isolation.
... uncertain values like user input or random values are hard to model in purely
functional languages.
The solution to the input problem in purely functional programs is to embed an imperative language as a DSL using a sufficiently powerful abstraction. In imperative (or non-pure functional) languages this is not needed because you can "cheat" and pass state implicitly and order of evaluation is explicit (whether you like it or not). Because of this "cheating" and forced evaluation of all parameters to every function, in imperative languages 1) you lose the ability to create your own control flow mechanisms (without macros), 2) code isn't inherently thread safe and/or parallelizable by default, 3) and implementing something like undo (time travel) takes careful work (imperative programmer must store a recipe for getting the old value(s) back!), whereas pure functional programming buys you all these things—and a few more I may have forgotten—"for free".
I hope this doesn't sound like zealotry, I just wanted to add some perspective. Imperative programming and especially mixed paradigm programming in powerful languages like C# 3.0 are still totally effective ways to get things done and there is no silver bullet.
[1] ... except possibly with respect memory usage (cf. foldl and foldl' in Haskell).
To expand on Konrad's comment:
and the order of evaluation is not
well-defined
Some functional languages have what is called Lazy Evaluation. Which means a function is not executed until the value is needed. Until that time the function itself is what is passed around.
Procedural languages are step 1 step 2 step 3... if in step 2 you say add 2 + 2, it does it right then. In lazy evaluation you would say add 2 + 2, but if the result is never used, it never does the addition.
If you have a chance, I would recommand getting a copy of Lisp/Scheme, and doing some projects in it. Most of the ideas that have lately become bandwagons were expressed in Lisp decades ago: functional programming, continuations (as closures), garbage collection, even XML.
So that would be a good way to get a head start on all these current ideas, and a few more besides, like symbolic computation.
You should know what functional programming is good for, and what it isn't good for. It isn't good for everything. Some problems are best expressed in terms of side-effects, where the same question gives differet answers depending on when it is asked.
#Creighton:
In Haskell there is a library function called product:
prouduct list = foldr 1 (*) list
or simply:
product = foldr 1 (*)
so the "idiomatic" factorial
fac n = foldr 1 (*) [1..n]
would simply be
fac n = product [1..n]
Procedural programming divides sequences of statements and conditional constructs into separate blocks called procedures that are parameterized over arguments that are (non-functional) values.
Functional programming is the same except that functions are first-class values, so they can be passed as arguments to other functions and returned as results from function calls.
Note that functional programming is a generalization of procedural programming in this interpretation. However, a minority interpret "functional programming" to mean side-effect-free which is quite different but irrelevant for all major functional languages except Haskell.
None of the answers here show idiomatic functional programming. The recursive factorial answer is great for representing recursion in FP, but the majority of code is not recursive so I don't think that answer is fully representative.
Say you have an arrays of strings, and each string represents an integer like "5" or "-200". You want to check this input array of strings against your internal test case (Using integer comparison). Both solutions are shown below
Procedural
arr_equal(a : [Int], b : [Str]) -> Bool {
if(a.len != b.len) {
return false;
}
bool ret = true;
for( int i = 0; i < a.len /* Optimized with && ret*/; i++ ) {
int a_int = a[i];
int b_int = parseInt(b[i]);
ret &= a_int == b_int;
}
return ret;
}
Functional
eq = i, j => i == j # This is usually a built-in
toInt = i => parseInt(i) # Of course, parseInt === toInt here, but this is for visualization
arr_equal(a : [Int], b : [Str]) -> Bool =
zip(a, b.map(toInt)) # Combines into [Int, Int]
.map(eq)
.reduce(true, (i, j) => i && j) # Start with true, and continuously && it with each value
While pure functional languages are generally research languages (As the real-world likes free side-effects), real-world procedural languages will use the much simpler functional syntax when appropriate.
This is usually implemented with an external library like Lodash, or available built-in with newer languages like Rust. The heavy lifting of functional programming is done with functions/concepts like map, filter, reduce, currying, partial, the last three of which you can look up for further understanding.
Addendum
In order to be used in the wild, the compiler will normally have to work out how to convert the functional version into the procedural version internally, as function call overhead is too high. Recursive cases such as the factorial shown will use tricks such as tail call to remove O(n) memory usage. The fact that there are no side effects allows functional compilers to implement the && ret optimization even when the .reduce is done last. Using Lodash in JS, obviously does not allow for any optimization, so it is a hit to performance (Which isn't usually a concern with web development). Languages like Rust will optimize internally (And have functions such as try_fold to assist && ret optimization).
To Understand the difference, one needs to to understand that "the godfather" paradigm of both procedural and functional programming is the imperative programming.
Basically procedural programming is merely a way of structuring imperative programs in which the primary method of abstraction is the "procedure." (or "function" in some programming languages). Even Object Oriented Programming is just another way of structuring an imperative program, where the state is encapsulated in objects, becoming an object with a "current state," plus this object has a set of functions, methods, and other stuff that let you the programmer manipulate or update the state.
Now, in regards to functional programming, the gist in its approach is that it identifies what values to take and how these values should be transferred. (so there is no state, and no mutable data as it takes functions as first class values and pass them as parameters to other functions).
PS: understanding every programming paradigm is used for should clarify the differences between all of them.
PSS: In the end of the day, programming paradigms are just different approaches to solving problems.
PSS: this quora answer has a great explanation.