law of demeter and hashmap - oop

I have few questions.
First of all does code below violates law of Demeter?
Map map = new HashMap<String, String>();
map.put("foo","bar");
map.put("fooo","baaar");
map.keySet().iterator()
IMO code above violates law of Demeter because map type is Map and keySet() returns Set object. Both are different. I'm thinking about second property to hold only "keys" but is this right solution?

Yes, technically that is a violation of the Law of Demeter when described in terms of methods. However, the way to fix it would be to here would be to add an operation like "keysIterator" to the Map class, and that might be a reasonable action, except that here Map is not your code.
The purpose of the Law of Demeter is to reduce coupling between components of your application. Changing how you use standard library objects does not affect that. Your proposed solution is wasteful of resources and has no particular benefit.
From another perspective, the keySet of a Map is really just a facet of the Map. You should think of it not so much as a third object (where LoD essentially says you shouldn't have more than two objects in any interaction) as a way of categorizing the operations that the Map provides.
Imagine a different scenario: suppose you have an application class like, say, a Category in an online store. It would be a meaningful LoD violation to have
category.itemsSet().iterator()
and this is something that you might want to refactor. Why? Because it constrains the Category class to implement a Set, even if the only operation that is actually needed is iteration (or, generally, fewer operations than the Set interface has), rather than having an implementation which only does the necessary work and can be revised or reimplemented more easily.
On the other hand, if the things you want to do to a Category cover all of the Set operations, then it's silly not to provide a Category.itemsSet() facet.
Note: “Facet” here means an object which is in a 1:1 relationship to another object and is essentially a different view of “the same thing”, especially a narrower view. It is not an entirely standard term.

Related

When is it okay to depend on concrete classes?

Today I was asked a question I could not find an answer for so here I am, asking for your help!
The Dependency Inversion Principle states that both concrete classes and abstractions should depend on abstractions right?
Regardless of that we still depend on framework classes like Integer and String. Is there a good answer as to why that is okay?
I know we should not reinvent the wheel just because it may change ever so slightly, and these particular classes I mentioned will most likely never change in a way their users will notice (their interfaces won't change).
As an additional point, note that the elements you are citing are actually in java.lang, i.e. there is no import statement, and one could say therefore no dependency to anything induced by using these types, besides the fact you use Java.
As soon as you step out of java.lang, I believe you are usually better off applying DIP, i.e. always prefer using a List<T> over using a ArrayList<T>.
The problem is to limit dependencies across borders of "components" (or module/package...) to only functional dependencies (i.e. abstractions, interfaces in Java). At some point you do need concrete implementations, that are necessarily built using at least some data structures, even if it is only arrays of basic int type. This does not violate DIP.
The use of Plain Old Data as suggested in #jaco0646 's answer, that are not violating DIP is kind of borderline ; in most cases you could use a signature that explicitly passes the fields of the struct you are considering instead of packing them into a single object ; this approach is indeed more general, e.g. you can implement it without having that POD class, maybe relying on some relational DBMS, you can interact with code written in any language etc...
However in practice, it can make sense to use POD in signatures, so that if I add a field to a POD, this will automatically propagate to all signatures that use the struct. Some of these functions may not use the new field, so we are now giving them too much information (we are leaking, with respect to strict "need to know"). Still, it can be a pragmatic answer in many cases to opt for this approach.
If we look at e.g. webservices, there is general tendency to consider POD are not a problem in service signatures, and using them helps keep clients compatible even if some new fields appear in the struct.
In OOP, an object is the encapsulated combination of data and behavior. The data is hidden; the behavior is exposed. It is these objects to which the DIP applies. Ideally, these objects should be instantiated in a Composition Root, which is the only component that depends on the objects' concrete classes.
Obviously something has to depend on the concrete classes in order to instantiate them. This is typically your DI container. The idea is that the container's sole concern is instantiating concrete classes, so everything else can obey the DIP.
On the other hand, opposite to objects, we have primitive data structures. These classes are not (necessarily) encapsulated, expose their data, and have little or no behavior. It is fine to depend on the concrete classes of data structures. These are not "objects" in the OOP sense. The DIP does not apply to data structures. Dependencies on concrete data structures should be local; however, and not exposed outside of the object that owns those dependencies.
Note that you will often see "hybrids" in code: classes that behave as both objects and data structures. They expose both their data and behavior. Hybrids are the worst of both worlds, and whether you apply the DIP to them or not, the bigger problem is that they are trying to serve two opposing purposes and violating encapsulation.

A precise explanation of encapsulation, data abstraction and data hiding

The object oriented concepts : encapsulation, data abstraction and data hiding are 3 different concepts, but very much related to each other. So i am having difficulty in understanding the concepts fully by reading the information from internet. The information available at one place contradicts with information at another place in the internet. Could someone guide me to a tutorial which clearly explains the 3 concepts and brings out the difference between the three?
First of all, don't be too ambitious ,as you said these 3 concepts are related (especially the first two) and could be used for one another in many contexts. Using them correctly is much more important than having a complete final definition.
"data hiding" is all about putting a wall between the client and (part of) the implementation. Some objects of a module can be internal to the module and invisible to its users. As such, this is a way, a method to avoid dependency. if I cannot know how one thing is implemented, its implementation can change.
"data abstraction" is regrouping different kind of data under the same abstraction. It is close to the idea of a protocol. You don't know how the object is implemented, but you know it respect a well-known protocol, i.e a set of method that works over different type of data. In python, file-like object are a good example. In Java, one uses interfaces. It is good because you have less to learn, and also because you can check some properties at the abstraction level, i.e for all kind of data regrouped under this abstraction.
"encapsulation" is about putting a shell around objects that simplify their usage. it is linked to the idea that objects in a code base can be regrouped in layers increasingly low-level. One object in a layer calls only those of layers beneath him. For example, if you want to draw a line on the screen, the line obkect may only encapsulate an openGL context, the pixel drawer, and other stuff. These lower-level objects are encapsulated by the line object. Note the encapsulation can be applied to the same object when it is part of different layers at the same time, not good but sometimes unavoidable. For example, the file-like object in python have high-level/encapsulating method (open, close, read) and low-levels ones (seek).
That's it. Obviously, the definition of each could be broader but these make the three concepts a bit more different.
The wrapping up of data and functions into a single unit (called
class) is known as encapsulation. Data encapsulation is the most
striking feature of a class. The data is not accessible to the
outside world, and only those functions, which are wrapped in
the class, can access it. These functions provide the interface
between the object’s data and the program. This insulation of
the data from direct access by the program is called data hiding
or information hiding.
Abstraction refers to the act of representing essential features
without including the background details or explanations.
Classes use the concept of abstraction and are defined as a list
of abstract attributes such as size, weight and cost, and
functions to operate on these attributes. They encapsulate all the
essential properties of the objects that are to be created. The
attributes are sometimes called data members because they hold
information. The functions that operate on these data are
sometimes called methods or member functions.
Since the classes use the concept of data abstraction, they are
known as Abstract Data Types (ADT

OOP - How to choose a possible object candidate?

I 'm concern about what techniques should I use to choose the right object in OOP
Is there any must-read book about OOP in terms of how to choose objects?
Best,
Just write something that gets the job done, even if it's ugly, then refactor continuously:
eliminate duplicate code (don't repeat yourself)
increase cohesion
reduce coupling
But:
don't over-engineer; keep it simple
don't write stuff you ain't gonna need
It's not a precise recipe, just some general guidelines. Keep practicing.
P.S.
Code objects are not related to tangible real-life objects; they are just constructs that hold related information together.
Don't believe what the Java books/schools teach about objects; they're lying.
You probably mean "the right class", rather than "the right object". :-)
There are a few techniques, such as text analysis (a.k.a. underlining the nouns) and Class Responsibility Collaborator (CRC).
With "underlining the nouns", you basically start with a written, natural language (i.e. plain English) description of the problem you want to solve and underline the nouns. That gives you a list of candidate classes. You will need to perform several passes to refine it into a list of classes to implement.
For CRC, check out the Wikipedia.
I suggest The OPEN Toolbox of Techniques for full reference.
Hope it helps.
I am assuming that there is understanding of what is sctruct, type, class, set, state, alphabet, scalar and vector and relationship.
Object is a noun, method is a verb. Object members can represent identity, state or scalar value per field. Relationships between objects usually are represented with references, where references are members of objects. In cases, when relationships are complex, multidirectional, have arity greater than 2, represent some sort of grouping or containment, then relationships can be expressed as objects.
For other, broader technical reasons objects are most likely the only way to represent any form of information in OOP languages.
I am adding a second answer due to demian's comment:
Sometimes the class is so obvious
because it's tangible, but other times
the concept of object it's to abstract
like a db connector.
That is true. My preferred approach is to perform a behavioural analysis of the system (using use cases, for example), and then derive system operations. Once you have a stable list of system operations (such as PrintDocument, SaveDocument, SpellCheck, MergeMail, etc. for a word processor) you need to assign each of them to a class. If you have developed a list of candidate classes with some of the techniques that I mentioned earlier, you will be able to allocate some of the operations. But some will remain unallocated. These will signal the need of more abstract or unintuitive classes, which you will need to make up, using your good judgment.
The whole method is documented in a white paper at www.openmetis.com.
You should check out Domain-Driven Design, by Eric Evans. It provides very useful concepts in thinking about the objects in your model, what their function are in the domain, and how they could be organized to work together. It's not a cookbook, and probably not a beginner book - but then, I read it at different stages of my career, and every time I found something valuable in it...
(source: domaindrivendesign.org)

Should entities have behavior or not?

Should entities have behavior? or not?
Why or why not?
If not, does that violate Encapsulation?
If your entities do not have behavior, then you are not writing object-oriented code. If everything is done with getters and setters and no other behavior, you're writing procedural code.
A lot of shops say they're practicing SOA when they keep their entities dumb. Their justification is that the data structure rarely changes, but the business logic does. This is a fallacy. There are plenty of patterns to deal with this problem, and they don't involve reducing everything to bags of getters and setters.
Entities should not have behavior. They represent data and data itself is passive.
I am currently working on a legacy project that has included behavior in entities and it is a nightmare, code that no one wants to touch.
You can read more on my blog post: Object-Oriented Anti-Pattern - Data Objects with Behavior .
[Preview] Object-Oriented Anti-Pattern - Data Objects with Behavior:
Attributes and Behavior
Objects are made up of attributes and behavior but Data Objects by definition represent only data and hence can have only attributes. Books, Movies, Files, even IO Streams do not have behavior. A book has a title but it does not know how to read. A movie has actors but it does not know how to play. A file has content but it does not know how to delete. A stream has content but it does not know how to open/close or stop. These are all examples of Data Objects that have attributes but do not have behavior. As such, they should be treated as dumb data objects and we as software engineers should not force behavior upon them.
Passing Around Data Instead of Behavior
Data Objects are moved around through different execution environments but behavior should be encapsulated and is usually pertinent only to one environment. In any application data is passed around, parsed, manipulated, persisted, retrieved, serialized, deserialized, and so on. An entity for example usually passes from the hibernate layer, to the service layer, to the frontend layer, and back again. In a distributed system it might pass through several pipes, queues, caches and end up in a new execution context. Attributes can apply to all three layers, but particular behavior such as save, parse, serialize only make sense in individual layers. Therefore, adding behavior to data objects violates encapsulation, modularization and even security principles.
Code written like this:
book.Write();
book.Print();
book.Publish();
book.Buy();
book.Open();
book.Read();
book.Highlight();
book.Bookmark();
book.GetRelatedBooks();
can be refactored like so:
Book book = author.WriteBook();
printer.Print(book);
publisher.Publish(book);
customer.Buy(book);
reader = new BookReader();
reader.Open(Book);
reader.Read();
reader.Highlight();
reader.Bookmark();
librarian.GetRelatedBooks(book);
What a difference natural object-oriented modeling can make! We went from a single monstrous Book class to six separate classes, each of them responsible for their own individual behavior.
This makes the code:
easier to read and understand because it is more natural
easier to update because the functionality is contained in smaller encapsulated classes
more flexible because we can easily substitute one or more of the six individual classes with overridden versions.
easier to test because the functionality is separated, and easier to mock
It depends on what kind of entity they are -- but the term "entity" implies, to me at least, business entities, in which case they should have behavior.
A "Business Entity" is a modeling of a real world object, and it should encapsulate all of the business logic (behavior) and properties/data that the object representation has in the context of your software.
If you're strictly following MVC, your model (entities) won't have any inherent behavior. I do however include whatever helper methods allow the easiest management of the entities persistence, including methods that help with maintaining its relationship to other entities.
If you plan on exposing your entities to the world, you're better off (generally) keeping behavior off of the entity. If you want to centralize your business operations (i.e. ValidateVendorOrder) you wouldn't want the Order to have an IsValid() method that runs some logic to validate itself. You don't want that code running on a client (what if they fudge it. i.e. akin to not providing any client UI to set the price on an item being placed in a shopping cart, but posting a a bogus price on the URL. If you don't have server-side validation, that's not good! And duplicating that validation is...redundant...DRY (Don't Repeat Yourself).
Another example of when having behaviors on an entity just doesn't work is the notion of lazy loading. Alot of ORMs today will allow you to lazy load data when a property is accessed on an entities. If you're building a 3-tier app, this just doesn't work as your client will ultimately inadvertantly try to make database calls when accessing properties.
These are my off-the-top-of-my-head arguments for keeping behavior off of entities.

Is a function an example of encapsulation?

By putting functionality into a function, does that alone constitute an example of encapsulation or do you need to use objects to have encapsulation?
I'm trying to understand the concept of encapsulation. What I thought was if I go from something like this:
n = n + 1
which is executed out in the wild as part of a big body of code and then I take that, and put it in a function such as this one, then I have encapsulated that addition logic in a method:
addOne(n)
n = n + 1
return n
Or is it more the case that it is only encapsulation if I am hiding the details of addOne from the outside world - like if it is an object method and I use an access modifier of private/protected?
I will be the first to disagree with what seems to be the answer trend. Yes, a function encapsulates some amount of implementation. You don't need an object (which I think you use to mean a class).
See Meyers too.
Perhaps you are confusing abstraction with encapsulation, which is understood in the broader context of object orientation.
Encapsulation properly includes all three of the following:
Abstraction
Implementation Hiding
Division of Responsibility
Abstraction is only one component of encapsulation. In your example you have abstracted the adding functionality from the main body of code in which it once resided. You do this by identifying some commonality in the code - recognizing a concept (addition) over a specific case (adding the number one to the variable n). Because of this ability, abstraction makes an encapsulated component - a method or an object - reusable.
Equally important to the notion of encapsulation is the idea of implementation hiding. This is why encapsulation is discussed in the arena of object orientation. Implementation hiding protects an object from its users and vice versa. In OO, you do this by presenting an interface of public methods to the users of your object, while the implementation of the object takes place inside private methods.
This serves two benefits. First, by limiting access to your object, you avoid a situation where users of the object can leave the object in an invalid state. Second, from the user's perspective, when they use your object they are only loosely coupled to it - if you change your implementation later on, they are not impacted.
Finally, division of responsility - in the broader context of an OO design - is something that must be considered to address encapsulation properly. It's no use encapsulating a random collection of functions - responsibility needs to be cleanly and logically defined so that there is as little overlap or ambiguity as possible. For example, if we have a Toilet object we will want to wall off its domain of responsibilities from our Kitchen object.
In a limited sense, though, you are correct that a function, let's say, 'modularizes' some functionality by abstracting it. But, as I've said, 'encapsulation' as a term is understood in the broader context of object orientation to apply to a form of modularization that meets the three criteria listed above.
Sure it is.
For example, a method that operates only on its parameters would be considered "better encapsulated" than a method that operates on global static data.
Encapsulation has been around long before OOP :)
A method is no more an example of encapsulation than a car is an example of good driving. Encapsulation isn't about the synax, it is a logical design issue. Both objects and methods can exhibit good and bad encapsulation.
The simplest way to think about it is whether the code hides/abstracts the details from other parts of the code that don't have a need to know/care about the implementation.
Going back to the car example:
Automatic transmission offers good encapsulation: As a driver you care about forward/back and speed.
Manual Transmission is bad encapsulation: From the driver's perspective the specific gear required for low/high speeds is generally irrelevant to the intent of the driver.
No, objects aren't required for encapsulation. In the very broadest sense, "encapsulation" just means "hiding the details from view" and in that regard a method is encapsulating its implementation details.
That doesn't really mean you can go out and say your code is well-designed just because you divided it up into methods, though. A program consisting of 500 public methods isn't much better than that same program implemented in one 1000-line method.
In building a program, regardless of whether you're using object oriented techniques or not, you need to think about encapsulation at many different places: hiding the implementation details of a method, hiding data from code that doesn't need to know about it, simplifying interfaces to modules, etc.
Update: To answer your updated question, both "putting code in a method" and "using an access modifier" are different ways of encapsulating logic, but each one acts at a different level.
Putting code in a method hides the individual lines of code that make up that method so that callers don't need to care about what those lines are; they only worry about the signature of the method.
Flagging a method on a class as (say) "private" hides that method so that a consumer of the class doesn't need to worry about it; they only worry about the public methods (or properties) of your class.
The abstract concept of encapsulation means that you hide implementation details. Object-orientation is but one example of the use of ecnapsulation. Another example is the language called module-2 that uses (or used) implementation modules and definition modules. The definition modules hid the actual implementation and therefore provided encapsulation.
Encapsulation is used when you can consider something a black box. Objects are a black box. You know the methods they provide, but not how they are implemented.
[EDIT]
As for the example in the updated question: it depends on how narrow or broad you define encapsulation. Your AddOne example does not hide anything I believe. It would be information hiding/encapsulation if your variable would be an array index and you would call your method moveNext and maybe have another function setValue and getValue. This would allow people (together maybe with some other functions) to navigate your structure and setting and getting variables with them being aware of you using an array. If you programming language would support other or richer concepts you could change the implementation of moveNext, setValue and getValue with changing the meaning and the interface. To me that is encapsulation.
It's a component-level thing
Check this out:
In computer science, Encapsulation is the hiding of the internal mechanisms and data structures of a software component behind a defined interface, in such a way that users of the component (other pieces of software) only need to know what the component does, and cannot make themselves dependent on the details of how it does it. The purpose is to achieve potential for change: the internal mechanisms of the component can be improved without impact on other components, or the component can be replaced with a different one that supports the same public interface.
(I don't quite understand your question, let me know if that link doesn't cover your doubts)
Let's simplify this somewhat with an analogy: you turn the key of your car and it starts up. You know that there's more to it than just the key, but you don't have to know what is going on in there. To you, key turn = motor start. The interface of the key (that is, e.g., the function call) hides the implementation of the starter motor spinning the engine, etc... (the implementation). That's encapsulation. You're spared from having to know what's going on under the hood, and you're happy for it.
If you created an artificial hand, say, to turn the key for you, that's not encapsulation. You're turning the key with additional middleman cruft without hiding anything. That's what your example reminds me of - it's not encapsulating implementation details, even though both are accomplished through function calls. In this example, anyone picking up your code will not thank you for it. They will, in fact, be more likely to club you with your artificial hand.
Any method you can think of to hide information (classes, functions, dynamic libraries, macros) can be used for encapsulation.
Encapsulation is a process in which attributes(data member) and behavior(member function) of a objects in combined together as a single entity refer as class.
The Reference Model of Open Distributed Processing - written by the International Organisation for Standardization - defines the following concepts:
Entity: Any concrete or abstract thing of interest.
Object: A model of an entity. An object is characterised by its behaviour and, dually, by its state.
Behaviour (of an object): A collection of actions with a set of constraints on when they may occur.
Interface: An abstraction of the behaviour of an object that consists of a subset of the interactions of that object together with a set of constraints on when they may occur.
Encapsulation: the property that the information contained in an object is accessible only through interactions at the interfaces supported by the object.
These, you will appreciate, are quite broad. Let us see, however, whether putting functionality within a function can logically be considered to constitute towards encapsulation in these terms.
Firstly, a function is clearly a model of a, 'Thing of interest,' in that it represents an algorithm you (presumably) desire executed and that algorithm pertains to some problem you are trying to solve (and thus is a model of it).
Does a function have behaviour? It certainly does: it contains a collection of actions (which could be any number of executable statements) that are executed under the constraint that the function must be called from somewhere before it can execute. A function may not spontaneously be called at any time, without causal factor. Sounds like legalese? You betcha. But let's plough on, nonetheless.
Does a function have an interface? It certainly does: it has a name and a collection of formal parameters, which in turn map to the executable statements contained in the function in that, once a function is called, the name and parameter list are understood to uniquely identify the collection of executable statements to be run without the calling party's specifying those actual statements.
Does a function have the property that the information contained in the function is accessible only through interactions at the interfaces supported by the object? Hmm, well, it can.
As some information is accessible via its interface, some information must be hidden and inaccessible within the function. (The property such information exhibits is called information hiding, which Parnas defined by arguing that modules should be designed to hide both difficult decisions and decisions that are likely to change.) So what information is hidden within a function?
To see this, we should first consider scale. It's easy to claim that, for example, Java classes can be encapsulated within a package: some of the classes will be public (and hence be the package's interface) and some will be package-private (and hence information-hidden within the package). In encapsulation theory, the classes form nodes and the packages form encapsulated regions, with the entirety forming an encapsulated graph; the graph of classes and packages is called the third graph.
It's also easy to claim that functions (or methods) themselves are encapsulated within classes. Again, some functions will be public (and hence be part of the class's interface) and some will be private (and hence information-hidden within the class). The graph of functions and classes is called the second graph.
Now we come to functions. If functions are to be a means of encapsulation themselves they they should contain some information public to other functions and some information that's information-hidden within the function. What could this information be?
One candidate is given to us by McCabe. In his landmark paper on cyclomatic complexity, Thomas McCabe describes source code where, 'Each node in the graph corresponds to a block of code in the program where the flow is sequential and the arcs correspond to branches taken in the program.'
Let us take the McCabian block of sequential execution as the unit of information that may be encapsulated within a function. As the first block within the function is always the first and only guaranteed block to be executed, we can consider the first block to be public, in that it may be called by other functions. All the other blocks within the function, however, cannot be called by other functions (except in languages that allow jumping into functions mid-flow) and so these blocks may be considered information-hidden within the function.
Taking these (perhaps slightly tenuous) definitions, then we may say yes: putting functionality within a function does constitute to encapsulation. The encapsulation of blocks within functions is the first graph.
There is a caveate, however. Would you consider a package whose every class was public to be encapsulated? According to the definitions above, it does pass the test, as you can say that the interface to the package (i.e., all the public classes) do indeed offer a subset of the package's behaviour to other packages. But the subset in this case is the entire package's behaviour, as no classes are information-hidden. So despite regorously satisfying the above definitions, we feel that it does not satisfy the spirit of the definitions, as surely something must be information-hidden for true encapsulation to be claimed.
The same is true for the exampe you give. We can certainly consider n = n + 1 to be a single McCabian block, as it (and the return statement) are a single, sequential flow of executions. But the function into which you put this thus contains only one block, and that block is the only public block of the function, and therefore there are no information-hidden blocks within your proposed function. So it may satisfy the definition of encapsulation, but I would say that it does not satisfy the spirit.
All this, of course, is academic unless you can prove a benefit such encapsulation.
There are two forces that motivate encapsulation: the semantic and the logical.
Semantic encapsulation merely means encapsulation based on the meaning of the nodes (to use the general term) encapsulated. So if I tell you that I have two packages, one called, 'animal,' and one called 'mineral,' and then give you three classes Dog, Cat and Goat and ask into which packages these classes should be encapsulated, then, given no other information, you would be perfectly right to claim that the semantics of the system would suggest that the three classes be encapsulated within the, 'animal,' package, rather than the, 'mineral.'
The other motivation for encapsulation, however, is logic.
The configuration of a system is the precise and exhaustive identification of each node of the system and the encapsulated region in which it resides; a particular configuration of a Java system is - at the third graph - to identify all the classes of the system and specify the package in which each class resides.
To logically encapsulate a system means to identify some mathematical property of the system that depends on its configuration and then to configure that system so that the property is mathematically minimised.
Encapsulation theory proposes that all encapsulated graphs express a maximum potential number of edges (MPE). In a Java system of classes and packages, for example, the MPE is the maximum potential number of source code dependencies that can exist between all the classes of that system. Two classes within the same package cannot be information-hidden from one another and so both may potentially form depdencies on one another. Two package-private classes in separate packages, however, may not form dependencies on one another.
Encapsulation theory tells us how many packages we should have for a given number of classes so that the MPE is minimised. This can be useful because the weak form of the Principle of Burden states that the maximum potential burden of transforming a collection of entities is a function of the maximum potential number of entities transformed - in other words, the more potential source code dependencies you have between your classes, the greater the potential cost of doing any particular update. Minimising the MPE thus minimises the maximum potential cost of updates.
Given n classes and a requirement of p public classes per package, encapsulation theory shows that the number of packages, r, we should have to minimise the MPE is given by the equation: r = sqrt(n/p).
This also applies to the number of functions you should have, given the total number, n, of McCabian blocks in your system. Functions always have just one public block, as we mentioned above, and so the equation for the number of functions, r, to have in your system simplifies to: r = sqrt(n).
Admittedly, few considered the total number of blocks in their system when practicing encapsulation, but it's readily done at the class/package level. And besides, minimising MPE is almost entirely entuitive: it's done by minimising the number of public classes and trying to uniformly distribute classes over packages (or at least avoid have most packages with, say, 30 classes, and one monster pacakge with 500 classes, in which case the internal MPE of the latter can easily overwhelm the MPE of all the others).
Encapsulation thus involves striking a balance between the semantic and the logical.
All great fun.
in strict object-oriented terminology, one might be tempted to say no, a "mere" function is not sufficiently powerful to be called encapsulation...but in the real world the obvious answer is "yes, a function encapsulates some code".
for the OO purists who bristle at this blasphemy, consider a static anonymous class with no state and a single method; if the AddOne() function is not encapsulation, then neither is this class!
and just to be pedantic, encapsulation is a form of abstraction, not vice-versa. ;-)
It's not normally very meaningful to speak of encapsulation without reference to properties rather than solely methods -- you can put access controls on methods, certainly, but it's difficult to see how that's going to be other than nonsensical without any data scoped to the encapsulated method. Probably you could make some argument validating it, but I suspect it would be tortuous.
So no, you're most likely not using encapsulation just because you put a method in a class rather than having it as a global function.