Difference between OOP and Functional Programming (scheme) [closed] - oop

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.
Closed 11 years ago.
I'm watching a video course/lectures from Stanford. The course is "The Structure and Interpretation of Computer Programs"
In the first OOP lecture, the instructor (Brian Harvey) describes an OOP method as one that gives different answers for the same question, while a function in functional programming gives a certain output for a certain input.
The following code is an example of a method in OOP that gives a different answer each time it's called:-
(define-class (counter)
instance-vars (count 0))
(method (next)
(set! count (+ count 1))
count) )
Now although the course is illustrated by scheme, I didn't pay much attention to the language itself, and so I can't explain the code; but can't a similar function "next" do the same thing as this "next" function?
In C, I would declare a global variable, and each time increase it by one when calling next. I know C is procedural, but I'm guessing a similar thing can be done in Scheme.

Well. With all due respect to the lecturer, these are slightly fishy definitions of both "OOP" and "functional programming". Both terms are consistently used, well, inconsistently, both in industry and academic contexts, not to mention informal use. If you dig a bit deeper, what's really going on is that there are several orthogonal concepts--different axes along which a choice is made in how to approach a program--that are being conflated, with one set of choices being arbitrarily called "OOP" despite not having anything else tying them together.
Probably the two biggest distinctions involved here are:
Identity vs. value: Do you model things by implicit identity (based on memory location or whatnot) and allow them to change arbitrarily? Or do you model things by their value, with no inherent notion of identity? If you say x = 4 does that mean that x is an alias to the timeless Platonic ideal of the number 4, or is x the name of a thing that's currently a four, but could be something else later (while still being x)?
Data vs. behavior: Do you work with simple data structures whose representation can be inspected, manipulated, and transformed? Or do you work with abstracted behaviors that do things, representing data only in terms of the things you can do with it, and let these behavioral abstractions operate on each other?
Most standard imperative languages lean toward using identity and data--pointers to C structs are about as purely this approach as possible. OOP languages tend to be defined largely by opting for behavior over data, often leaning toward identity as well but not consistently (cf. the popularity of "immutable" objects).
Functional programming usually leans more toward values rather than identity, while mixing data and behavior to various degrees.
There's a lot more going on here as well but I think that's the key part of what you're wondering here.
If anyone's curious I've elaborated a bit on some of this before: Analyzing some essential concepts of many OOP languages, more on the identity/value issue and also formal vs. informal approaches, a look at the data/behavior distinction in functional programming, probably others I can't think of. Warning, I'm kind of long-winded, these are not for the faint of heart. :P

There is a page on the excellent Haskell wiki, where differences in Functional Programming and OOP are contrasted. The Haskell wiki is a wonderful resource for everything about functional programming in general in addition to helping with the Haskell language.
Functional programming and OOP Differences
The important difference between pure functional programming and object-oriented programming is:
Object-oriented:
Data:
OOP asks What can I do with the data?
Producer: Class
Consumer: Class method
State:
The methods and objects in OOP have some internal state (method variables and object attributes) and they possibly have side effects affecting the state of computer’s peripherals, the global scope, or the state of an object or method. Variable assignment is one good sign of something having a state.
Functional:
Data:
Functional programming asks How the data is constructed?
Producer: Type Constructor
Consumer: Function
State:
If a pure functional programming ever assigns to a variable, the variable must be considered and handled as immutable. There must not be a state in pure functional programming.
Code with side effects is often separated from the main purely functional body of code
State can be passed around as an argument to a function, this is called a continuation.
Functional substitutes for OOP generators
The way to do something similar to OOP style generators (which have an internal state) with pure functional programming is to approach the problem from a different point of view, by using one of these solutions depending on the use case:
1. Process some or all values in a sequence:
Type of sequence can be list, array, sequence or vector.
Lisp has car and Haskell has first, which take first item from a list.
Haskell also has take, which takes the first n items, and which supports lazy evaluation and thus infinite or cyclic sequences – like OOP generators do.
Both have first, and different map, reduce or fold functions for processing sequences with a function.
Matrices usually also have some ways to map or apply a function to each item.
2. Some values from a function are needed:
The indices might be from a discrete or continuous scale (integers or floats).
Make one pure function to generate the indices (events) and feed those to another pure function (behaviour). This is called Functional reactive programming. This is a form of Dataflow programming along with cell-oriented programming. The Actor model is also somewhat similar in operation, and a very interesting alternative to threads with handling concurrency!
3. Use a closure to confine and encapsulate the state from the outside
This is the closest subsitute to OOP way with generators (which I think actually originated to imitate closures), and also farthest from pure functional programming, because a closure has a state.

"Functional" in functional programming has traditionally referred to the meaning of mathematical functions. That is, the output of a mathematical function is based solely on the inputs passed to it. Nowadays such programming is more often called pure functional programming.
In pure functional programming reassigning state is not allowed, thus writing a function such as your C example would not be possible. You are only allowed to bind a value to a variable once. An example of a language where this would not be possible is Haskell.
Most functional programming languages (Scheme included) are unpure and would allow you to do so. Said that, what the lecturer is telling is that writing such a function is not possible in the traditional sense of functional programming.

Well, yeah, you could do that in C.
But its not the same - in C++ you can make each object have its own count.

Related

Should I use OOP when encapsulation is essentially ignored?

I am making a Mathematics web program which allows the user to compute and prove various quantities or statements, e.g. determinant of a matrix, intersection of sets, determine whether a given map is a homomorphism. I decided to write the code using the OOP paradigm (in PHP, to handle some of the super heavy computations that a user's browser might not appreciate), since I could easily declare sets as Set objects, matrices as Matrix objects, etc. and keep some of the messy details of determining things such as cardinality, determinants, etc. in the background. However, after getting knee-deep in code, I'm wondering if deciding on OOP was a mistake. Here's why.
I'll use my Matrix class as a simple example. Matrix has the following attributes:
name (type String) (stores name of this matrix)
size (type array) (stores # rows and # columns of this matrix)
entries (type array) (stores this matrix's entries)
is_invertible (type Boolean) (stores whether this matrix can be inverted)
determinant (type Int) (stores the determinant of this matrix)
transpose (type array) (stores the transpose of this matrix)
Creating a new matrix called A would be done like so:
$A = new Matrix("A");
Now, in a general math problem concerning matrices, it could be that we know the matrix's name, size, entries, whether it's invertible, its determinant, or its transpose, or any combination of the above. This means that all of these properties need to be accessible, and certainly any of these properties can be changed by the user, depending on what's given in the problem. (I can give examples of problems for any of these cases, if needed.)
The issue I'm having, then, is that this would break the encapsulation "rule" of OOP ("rule" in quotes since, from what I understand, it's not a hard-and-fast rule, just one that should be upheld to the greatest extent possible). I did some searching on when getters and setters should be used, or even IF they should be used (seems odd to me that they wouldn't, in an OOP setting...), but this did not seem to help me much, as I found many contradictory answers and case-specific opinions.
So, my overall questions are: when the user needs access to modify many (if not all) of an object's attributes, but a class-oriented design seems to be ideal for addressing the programming problem,
Is OOP the best way to structure the code, despite essentially ignoring encapsulation altogether?
Is there an alternative to OOP which allows high user access while maintaining the OO "flavor" (i.e. keeping sets, matrices, etc. as objects)
Is it ok to break the encapsulation rule altogether once in a while, if the problem calls for it? Or is that not in the spirit of OOP?
What you are trying to do is not necessarily outside the scope of OOP. The thing is that you have a different model than what would usually be described in programming textbooks (where, for example, the values of the matrix would be always present and all of the functions could be simple methods). (Perhaps this is why the question was unfairly downvoted.) Nothing prevents you from storing values like "is_invertible" internally and implementing setter and getter methods. Doing this might make sense if you are trying to learn OOP. But I think other problems (see coding textbooks) might be easier for learning purposes. I see that a remote goal would be to capture some of mathematics as an OOP framework. But the whole mathematical universe is immensely richer than any fixed architecture (results like Gödel's theorem put a theoretical limit). You can only succeed in developing a framework for a very narrow application, for example solving certain equations. That's what symbolic algebra programs do: you can look at how, for example, SymPy or perhaps parts of Maple and Mathematica are implemented. In my view, the OOP paradigm can be both very useful and too restrictive / unnecessary depending on the task (you can certainly find more about shorcomings of OOP in Wikipedia or elsewhere). Also, your problem can be seen as writing a small programming language - in many of them you have sets, numbers, etc as objects.
You can use only rudimentary OOP or no OOP at all. You can use functional programming.
You should Google/read more about this on this or other sites. Is it OK to sometimes walk across the road when the red traffic light is on?

Achieving polymorphism in functional programming

I'm currently enjoying the transition from an object oriented language to a functional language. It's a breath of fresh air, and I'm finding myself much more productive than before.
However - there is one aspect of OOP that I've not yet seen a satisfactory answer for on the FP side, and that is polymorphism. i.e. I have a large collection of data items, which need to be processed in quite different ways when they are passed into certain functions. For the sake of argument, let's say that there are multiple factors driving polymorphic behaviour so potentially exponentially many different behaviour combinations.
In OOP that can be handled relatively well using polymorphism: either through composition+inheritance or a prototype-based approach.
In FP I'm a bit stuck between:
Writing or composing pure functions that effectively implement polymorphic behaviours by branching on the value of each data item - feels rather like assembling a huge conditional or even simulating a virtual method table!
Putting functions inside pure data structures in a prototype-like fashion - this seems like it works but doesn't it also violate the idea of defining pure functions separately from data?
What are the recommended functional approaches for this kind of situation? Are there other good alternatives?
Putting functions inside pure data structures in a prototype-like fashion - this seems like it works but doesn't it also violate the idea of defining pure functions separately from data?
If virtual method dispatch is the way you want to approach the problem, this is a perfectly reasonable approach. As for separating functions from data, that is a distinctly non-functional notion to begin with. I consider the fundamental principle of functional programming to be that functions ARE data. And as for your feeling that you're simulating a virtual function, I would argue that it's not a simulation at all. It IS a virtual function table, and that's perfectly OK.
Just because the language doesn't have OOP support built in doesn't mean it's not reasonable to apply the same design principles - it just means you'll have to write more of the machinery that other languages provide built-in, because you're fighting against the natural spirit of the language you're using. Modern typed functional languages do have very deep support for polymorphism, but it's a very different approach to polymorphism.
Polymorphism in OOP is a lot like "existential quantification" in logic - a polymorphic value has SOME run-time type but you don't know what it is. In many functional programming languages, polymorphism is more like "universal quantification" - a polymorphic value can be instantiated to ANY compatible type its user wants. They're two sides of the exact same coin (in particular, they swap places depending on whether you're looking at a function from the "inside" or the "outside"), but it turns out to be extremely hard when designing a language to "make the coin fair", especially in the presence of other language features such as subtyping or higher-kinded polymorphism (polymorphism over polymorphic types).
If it helps, you may want to think of polymorphism in functional languages as something very much like "generics" in C# or Java, because that's exactly the type of polymorphism that, e.g., ML and Haskell, favor.
Well, in Haskell you can always make a type-class to achieve a kind of polymorphism. Basically, it is defining functions that are processed for different types. Examples are the classes Eq and Show:
data Foo = Bar | Baz
instance Show Foo where
show Bar = 'bar'
show Baz = 'baz'
main = putStrLn $ show Bar
The function show :: (Show a) => a -> String is defined for every data type that instances the typeclass Show. The compiler finds the correct function for you, depending on the type.
This allows to define functions more generally, for example:
compare a b = a < b
will work with any type of the typeclass Ord. This is not exactly like OOP, but you even may inherit typeclasses like so:
class (Show a) => Combinator a where
combine :: a -> a -> String
It is up to the instance to define the actual function, you only define the type - similar to virtual functions.
This is not complete, and as far as I know, many FP languages do not feature type classes. OCaml does not, it pushes that over to its OOP part. And Scheme does not have any types. But in Haskell it is a powerful way to achieve a kind of polymorphism, within limits.
To go even further, newer extensions of the 2010 standard allow type families and suchlike.
Hope this helped you a bit.
Who said
defining pure functions separately from data
is best practice?
If you want polymorphic objects, you need objects. In a functional language, objects can be constructed by glueing together a set of "pure data" with a set of "pure functions" operating on that data. This works even without the concept of a class. In this sense, a class is nothing but a piece of code that constructs objects with the same set of associated "pure functions".
And polymorphic objects are constructed by replacing some of those functions of an object by different functions with the same signature.
If you want to learn more about how to implement objects in a functional language (like Scheme), have a look into this book:
Abelson / Sussman: "Structure and Interpration of Computer programs"
Mike, both your approaches are perfectly acceptable, and the pros and cons of each are discussed, as Doc Brown says, in Chapter 2 of SICP. The first suffers from having a big type table somewhere, which needs to be maintained. The second is just traditional single-dispatch polymorphism/virtual function tables.
The reason that scheme doesn't have a built-in system is that using the wrong object system for the problem leads to all sorts of trouble, so if you're the language designer, which to choose? Single despatch single inheritance won't deal well with 'multiple factors driving polymorphic behaviour so potentially exponentially many different behaviour combinations.'
To synopsize, there are many ways of constructing objects, and scheme, the language discussed in SICP, just gives you a basic toolkit from which you can construct the one you need.
In a real scheme program, you'd build your object system by hand and then hide the associated boilerplate with macros.
In clojure you actually have a prebuilt object/dispatch system built in with multimethods, and one of its advantages over the traditional approach is that it can dispatch on the types of all arguments. You can (apparently) also use the heirarchy system to give you inheritance-like features, although I've never used it, so you should take that cum grano salis.
But if you need something different from the object scheme chosen by the language designer, you can just make one (or several) that suits.
That's effectively what you're proposing above.
Build what you need, get it all working, hide the details with macros.
The argument between FP and OO is not about whether data abstraction is bad, it's about whether the data abstraction system is the place to stuff all the separate concerns of the program.
"I believe that a programming language should allow one to define new data types. I do not believe that a program should consist solely of definitions of new data types."
http://www.haskell.org/haskellwiki/OOP_vs_type_classes#Everything_is_an_object.3F nicely discusses some solutions.

Object-oriented programming in a purely functional programming context?

Are there any advantages to using object-oriented programming (OOP) in a functional programming (FP) context?
I have been using F# for some time now, and I noticed that the more my functions are stateless, the less I need to have them as methods of objects. In particular, there are advantages to relying on type inference to have them usable in as wide a number of situations as possible.
This does not preclude the need for namespaces of some form, which is orthogonal to being OOP. Nor is the use of data structures discouraged. In fact, real use of FP languages depend heavily on data structures. If you look at the F# stack implemented in F Sharp Programming/Advanced Data Structures, you will find that it is not object-oriented.
In my mind, OOP is heavily associated with having methods that act on the state of the object mostly to mutate the object. In a pure FP context that is not needed nor desired.
A practical reason may be to be able to interact with OOP code, in much the same way F# works with .NET. Other than that however, are there any reasons? And what is the experience in the Haskell world, where programming is more pure FP?
I will appreciate any references to papers or counterfactual real world examples on the issue.
The disconnect you see is not of FP vs. OOP. It's mostly about immutability and mathematical formalisms vs. mutability and informal approaches.
First, let's dispense with the mutability issue: you can have FP with mutability and OOP with immutability just fine. Even more-functional-than-thou Haskell lets you play with mutable data all you want, you just have to be explicit about what is mutable and the order in which things happen; and efficiency concerns aside, almost any mutable object could construct and return a new, "updated" instance instead of changing its own internal state.
The bigger issue here is mathematical formalisms, in particular heavy use of algebraic data types in a language little removed from lambda calculus. You've tagged this with Haskell and F#, but realize that's only half of the functional programming universe; the Lisp family has a very different, much more freewheeling character compared to ML-style languages. Most OO systems in wide use today are very informal in nature--formalisms do exist for OO but they're not called out explicitly the way FP formalisms are in ML-style languages.
Many of the apparent conflicts simply disappear if you remove the formalism mismatch. Want to build a flexible, dynamic, ad-hoc OO system on top of a Lisp? Go ahead, it'll work just fine. Want to add a formalized, immutable OO system to an ML-style language? No problem, just don't expect it to play nicely with .NET or Java.
Now, you may be wondering, what is an appropriate formalism for OOP? Well, here's the punch line: In many ways, it's more function-centric than ML-style FP! I'll refer back to one of my favorite papers for what seems to be the key distinction: structured data like algebraic data types in ML-style languages provide a concrete representation of the data and the ability to define operations on it; objects provide a black-box abstraction over behavior and the ability to easily replace components.
There's a duality here that goes deeper than just FP vs. OOP: It's closely related to what some programming language theorists call the Expression Problem: With concrete data, you can easily add new operations that work with it, but changing the data's structure is more difficult. With objects you can easily add new data (e.g., new subclasses) but adding new operations is difficult (think adding a new abstract method to a base class with many descendants).
The reason why I say that OOP is more function-centric is that functions themselves represent a form of behavioral abstraction. In fact, you can simulate OO-style structure in something like Haskell by using records holding a bunch of functions as objects, letting the record type be an "interface" or "abstract base class" of sorts, and having functions that create records replace class constructors. So in that sense, OO languages use higher-order functions far, far more often than, say, Haskell would.
For an example of something like this type of design actually put to very nice use in Haskell, read the source for the graphics-drawingcombinators package, in particular the way that it uses an opaque record type containing functions and combines things only in terms of their behavior.
EDIT: A few final things I forgot to mention above.
If OO indeed makes extensive use of higher-order functions, it might at first seem that it should fit very naturally into a functional language such as Haskell. Unfortunately this isn't quite the case. It is true that objects as I described them (cf. the paper mentioned in the LtU link) fit just fine. in fact, the result is a more pure OO style than most OO languages, because "private members" are represented by values hidden by the closure used to construct the "object" and are inaccessible to anything other than the one specific instance itself. You don't get much more private than that!
What doesn't work very well in Haskell is subtyping. And, although I think inheritance and subtyping are all too often misused in OO languages, some form of subtyping is quite useful for being able to combine objects in flexible ways. Haskell lacks an inherent notion of subtyping, and hand-rolled replacements tend to be exceedingly clumsy to work with.
As an aside, most OO languages with static type systems make a complete hash of subtyping as well by being too lax with substitutability and not providing proper support for variance in method signatures. In fact, I think the only full-blown OO language that hasn't screwed it up completely, at least that I know of, is Scala (F# seemed to make too many concessions to .NET, though at least I don't think it makes any new mistakes). I have limited experience with many such languages, though, so I could definitely be wrong here.
On a Haskell-specific note, its "type classes" often look tempting to OO programmers, to which I say: Don't go there. Trying to implement OOP that way will only end in tears. Think of type classes as a replacement for overloaded functions/operators, not OOP.
As for Haskell, classes are less useful there because some OO features are more easily achieved in other ways.
Encapsulation or "data hiding" is frequently done through function closures or existential types, rather than private members. For example, here is a data type of random number generator with encapsulated state. The RNG contains a method to generate values and a seed value. Because the type 'seed' is encapsulated, the only thing you can do with it is pass it to the method.
data RNG a where RNG :: (seed -> (a, seed)) -> seed -> RNG a
Dynamic method dispatch in the context of parametric polymorphism or "generic programming" is provided by type classes (which are not OO classes). A type class is like an OO class's virtual method table. However, there's no data hiding. Type classes do not "belong" to a data type the way that class methods do.
data Coordinate = C Int Int
instance Eq Coordinate where C a b == C d e = a == b && d == e
Dynamic method dispatch in the context of subtyping polymorphism or "subclassing" is almost a translation of the class pattern in Haskell using records and functions.
-- An "abstract base class" with two "virtual methods"
data Object =
Object
{ draw :: Image -> IO ()
, translate :: Coord -> Object
}
-- A "subclass constructor"
circle center radius = Object draw_circle translate_circle
where
-- the "subclass methods"
translate_circle center radius offset = circle (center + offset) radius
draw_circle center radius image = ...
I think that there are several ways of understanding what OOP means. For me, it is not about encapsulating mutable state, but more about organizing and structuring programs. This aspect of OOP can be used perfectly fine in conjunction with FP concepts.
I believe that mixing the two concepts in F# is a very useful approach - you can associate immutable state with operations working on that state. You'll get the nice features of 'dot' completion for identifiers, the ability to easy use F# code from C#, etc., but you can still make your code perfectly functional. For example, you can write something like:
type GameWorld(characters) =
let calculateSomething character =
// ...
member x.Tick() =
let newCharacters = characters |> Seq.map calculateSomething
GameWorld(newCharacters)
In the beginning, people don't usually declare types in F# - you can start just by writing functions and later evolve your code to use them (when you better understand the domain and know what is the best way to structure code). The above example:
Is still purely functional (the state is a list of characters and it is not mutated)
It is object-oriented - the only unusual thing is that all methods return a new instance of "the world"

Theory behind object oriented programming

Alonzo Church's lambda calculus is the mathematical theory behind functional languages. Has object oriented programming some formal theory ?
Object Orientation comes from psychology not math.
If you think about it, it resembles more how humans work than how computers work.
We think in objects that we class-ify. For instance this table is a seating furniture.
Take Jean Piaget (1896-1980), who worked on a theory of children's cognitive development.
Wikipedia says:
Piaget also had a considerable effect in the field of computer science and artificial intelligence.
Some cognitive concepts he discovered (that imply to the Object Orientation concept):
Classification The ability to group objects together on the basis of common features.
Class Inclusion The understanding, more advanced than simple classification, that some classes or sets of objects are also sub-sets of a larger class. (E.g. there is a class of objects called dogs. There is also a class called animals. But all dogs are also animals, so the class of animals includes that of dogs)
Read more: Piaget's developmental theory http://www.learningandteaching.info/learning/piaget.htm#ixzz1CipJeXyZ
OOP is a bit of a mixed bag of features that various languages implement in slightly different ways. There is no single formal definition of OOP but a number of people have tried to describe OOP based on the common features of languages that claim to be object oriented. From Wikipedia:
Benjamin Cuire Pierce and some other researchers view as futile any attempt to distill OOP to a minimal set of features. He nonetheless identifies fundamental features that support the OOP programming style in most object-oriented languages:
Dynamic dispatch – when a method is invoked on an object, the object itself determines what code gets executed by looking up the method at run time in a table associated with the object. This feature distinguishes an object from an abstract data type (or module), which has a fixed (static) implementation of the operations for all instances. It is a programming methodology that gives modular component development while at the same time being very efficient.
Encapsulation (or multi-methods, in which case the state is kept separate)
Subtype polymorphism
object inheritance (or delegation)
Open recursion – a special variable (syntactically it may be a keyword), usually called this or self, that allows a method body to invoke another method body of the same object. This variable is late-bound; it allows a method defined in one class to invoke another method that is defined later, in some subclass thereof.
Abadi and Cardelli have written A Theory Of Objects, you might want to look into that. Another exposition is given the venerable TAPL (IIRC, they approach objects as recursive records in a typed lambda calculus). I don't really know much about this stuff.
One formal definition I've run into for strongly defining and constraining subtyping is the Liskov Substitution Principle. It is certainly not all of object-oriented programming, but yet it might serve as a link into the formal foundations in development.
I'd check out wikipedia's page on OO http://en.wikipedia.org/wiki/Object-oriented_programming It's got the principles and fundamentals and history.
My understanding is that it was an evolutionary progression of features and ideas in a variety of languages that finally came together with the push in the 90's for GUI's going mainstream. But i could be horribly wrong :-D
Edit: What's even more interesting is that people still argue about "what makes an OO language OO"..i'm not sure the feature set is even generally agreed upon that defines an OO language.
The history (simplified) goes that way :
First came the spagetti code.
Then came the procedural code (Like C and Pascal).
Then came modular code (Like in modula).
Then came the object oriented code (Like in smalltalk).
Whats the porpuse of object oriented programming ?
You can only understand if you recall history.
At first code was simply a sequence of instructions given to the computer (Literally in binary representation)
Then came the macro assemblers. With mneomonics for instructions.
Then people detected that sometimes you have code that is repeated around.
So they created GOTO. But GOTO (Or branch or jump etc) cannot return back to where it was called, and cannot give direct return values, nor can accept formal parameters (You had to use global variables).
Against the first problem, people created subroutines (GOSUB-like). Groups of instructions that could be called repeatedly and return to where it was called.
Then people detected that routines would be more usefull if they had parameters and could return values.
For this they created functions, procedures and calling conventions. Those abstractions where called on top of an abstraction called the stack.
The stack allows formal parameters, return values and something called recursion (direct or indirect).
With the stack and the ability for a function to be called arbitrarely (even indirectly), came the procedural programming, solving the GOTO problem.
But then came the large projects, and the necessity to group procedures into logical entities (modules).
Thats where you will understand why object oriented programming evolved.
When you have a module, you have module local variables.
Think about this :
Module MyScreenModule;
Var X, Y : Integer;
Procedure SetX(value : Integer);
Procedure SetY(value : Integer);
End Module.
There are X and Y variables that are local to that module. In that example, X and Y holds the position of the cursor. But lets suppose your computer has more than one screen. So what can we do now ? X and Y alone arent able to hold the X and Y values of all screens you have. You need a way to INSTANTIATE that information. Thats where the jump from modular programming goes to object oriented programming.
In a non object oriented language you would usually do :
Var Screens : Array of Record X, Y : Integer End;
And then pass a index value to each module call :
Procedure SetX(ScreenID : Integer; X : Integer);
Procedure SetY(ScreenID : Integer; Y : Integer);
Here screenid refers to wich of the multiple screens that you are talking about.
Object oriented inverts the relationship. Instead of a module with multiple data instances (Effectively what screenid does here), you make the data the first class citizen and attach code to it, like this :
Class MyScreenModule;
Field X, Y : Integer;
Procedure SetX(value : Integer);
Procedure SetY(value : Integer);
End Class.
Its almost same thing as a module !
Now you instantiate it by providing a implicit pointer to a instance, like :
ScreenNumber1 := New MyScreenModule;
And then proceed to use it :
ScreenNumber1::SetX(100);
You effectively turned your modular programming into a multi-instance programming where the variable holding the module pointer itself differentiates each instance. Gotcha ?
Its an evolution of the abstraction.
So now you have multiple-instances, whats the next level ?
Polymorphism. Etc. The rest is pretty standard object oriented lessons.
Whats the point ? The point is that object oriented (like procedures, like subroutines etc) did not evolve from a theoretical standpoint but from the praxys of many coders working around decades. Its a evolution of computer programming, a continual evolution.
IMO a good example of what makes a successful OO language could be found by comparing the similarities between JAVA and C#. Both are extremely popular and very similar. Though I think the general idea of a minimum OO language can be found by looking at Simula67. I believe the general idea behind Object Oriented programming to be that it makes it seem like the computer thinks more like a human, this is supported by things like inheritance (both class "mountain bike" and "road bike" belong to parent class "bicycle", and have the same basic features). Another important idea is that objects (which can be executable lines of code) can be passed around like variables, effectively allowing the program to edit itself based on certain criteria (although this point is highly arguable, I cite the ability to change every instance of an object based on one comparison). Another point to make is modularity. As entire programs could effectively be passed around like a variable (because everything is treated as an object), it becomes easier to modify large programs, by simply modifying the class or method being called, and never having to modify the main method. Because of this, expanding the functionality of a program can become much simpler. This is why web businesses love languages like C# and JAVA (which are full fledged OO). Gaming companies like C++ because it gives them some of the control of an imperative language (like C) and some of the features of object orientation (like C# or JAVA).
Object-oriented is a bit of a misnomer and I don't really think classes or type systems have much to do with OO programming. Alan Kay's inspiration was biological and what's really going on that matters is communication. A better name would be message-oriented programming. There is plenty of theory about messaging, for example Pi calculus and the actor model both have rigorous mathematical descriptions. And that is really just the tip of the iceberg.
What about Petri nets? Object might be a place, a composition an arc, messages tokens. I have not though about it very thoroughly, so there might be some flaws I am not aware of, but you can investigate - there is a lot of theoretical works related to Petri nets.
I found this, for example:
http://link.springer.com/book/10.1007%2F3-540-45397-0
Readable PDF: http://www.informatik.uni-hamburg.de/bib/medoc/M-329.pdf
In 2000 in my degree thesys I proposed this model; very shortly:
y + 1 = f(u, x)
x + 1 = g(u, x)
where:
u: input
y: output
x: state
f: output function
g: state function
Formally it's very similar to finite state machine, but the difference is that U, Y, S are set not finite, but infinite (numerable) and f and g are Touring Machine (TM).
f and g togheter form a class; if we add an initial state x0 we have an object. So OOP in something more than a TM a TM is a specific case of OOP. Note that the state x is of a different level than the state "inside" the TM. Inside the TM there are not side effect, the x state count for side effect.

Can Procedural Programming use Objects?

I have seen a number of different topics on StackOverFlow discussing the differences between Procedural and Object-Oriented Programming. The question is: If the program uses an object can it still be considered procedural?
Yes, and a lot of early Java was exactly that; you had a bunch of C programmers get into Java because it was "hot", people who didn't think in OOP. Lots of big classes with lots of static methods, lots of RTTI in case statements, lots of use of instanceof.
GLib has GObject which is object oriented programming implemented in pure C. While you can build up an API which begins to "feel" like OOP, it's still just plain "C" code with no actual classes (from the compiler's point of view). If you get far enough so you're starting to implement Object Oriented design patterns then I would call that OOP no matter what language it's written in. It's all about the feel of the code and how you have to think to write against it.
Procedural programming has to do with how you structure your program and model your domain. Just because at some point you instantiate an object, doesn't alone make your program oriented towards objects (i.e., object-oriented).
The distinction is entirely subjective. For example, if you code a C library using state passing, you are implementing something of a "tell" pattern, with the state as the object.
Classes can be considered as super types. When we converted from VB3 to VB6 our first pass was finding all the types we used, then finding all the subroutines and functions that took that type as a parameter. We moved those into the class definition, removed the parameter and then tested leaving the original flow of control intact
Then we refactored our flow of control to use various patterns and object oriented techniques.
The heart of object orientation is about how you decompose the problem into smaller parts, and how these parts work together. It's about the philosophy. Using OO language does not necessarily mean a program written in it is OO; it's just easier to do OO with a language that supports common OO concepts out of the box.
To answer the question: "If the program uses an object can it still be considered procedural?" - That depends on what your definitions of object and procedural programming are. But in my opinion, the answer is resounding "Yes". "Objects" are only a part of the philosophy that is OO and using them "somewhere in your application" does not mean you're doing OO.
The answer to your question is, yes. For example. I've got an old php legacy page to maintain. Most of the code is procedural but I decided that some things can be maintained much easier if I plug Zend Framework into the existing stuff and write some of my own classes to replace some of the old code. In general this application is still written and functioning in a mainly procedural way but here and then a class or another are instantiated and used. I guess there is no clear border between procedural and OO. You can do it cleaner or less clean. If you don't have enough layers for the size and complexity of your app you'll end up with more procedural code automatically too...