Where are the common typeclasses instances in scalaz? - scalaz

I'm trying to understand how scalaz is organized, and I would like to know where the common monad (or other typeclasses) instances like Monad[Int], Monad[List] ... are defined.
Take for example the Monad[List]. I saw that the scalaz.std module contains the ListInstances trait which contains implicit values for some typeclass instances of lists, like Monoid[List]. This implicit value defines the append function for the list instance of monoid.
Is there a place where to find an implicit value for Monad[List], which defines point and bind for lists?

Here you can find the Monad instance and other instances like Monoid for List: ListInstances. As you can see there's no Monad[List] instance but a MonadPlus[List] instance. A MonadPlus is a Monad plus an ApplicativePlus (no pun intended).
In general there's a trait, AllInstances, that mixes in all instances and you can find it here.

Related

How do I represent the type of an argument in a UML class diagram, when the argument is a function?

For example, a class has a method compute() (using Python syntax and dropping the self argument for clarity):
def compute(computation_fn):
return computation_fn(5)
Let's assume that computation_fn maps int to int. In a UML class diagram, should I write something like this?
+ compute(computation_fn: (num: int): int): int
If this has already been answered somewhere, just drop a link! I've been trying to look for an answer.
UML does only have the basic types Integer, Boolean, String, UnlimitedNatural, and Real.
You can also use any class that you define in your model as type. In this regard, you can very well define a class that corresponds to a kind of functions, for example FunctionOfIntToInt. That's usual business in any design that uses callables.
UML may also be enriched with additional types in a profile. Very often, you'll see types of your favourite language used. This assumes the use of a language specific profile. But usually it's fixed type names (e.g. Date, UInt8, ...). You could imagine a type called as (int):int, but this would be ambiguous in regard of UML's syntax that uses already :.
Unfortunately, there's nothing in UML's typing system that would allow to represent functions with arbitrary number of arguments of flexible type. So it all depends how compliant you need to be with UML:
Python programmers would understand any python type that you'd use in the diagram, including function types, even if it's not "pure" UML. So this would be pragmatic approach. I'll recommend nevertheless to replace the : for the return type with -> to avoid lexical confusion
But if you have to go by the book, profiles don't allow for a syntax extension that would allow to compose types on the top of existing UML mechanisms. There's a workaround. You could use an UML template class to represent functions. The first argument would be the return type, and the remaining template arguments the argument types. You'd then use UML's native template binding syntax to instantiate the template for typing purpose. But I agree, it's more clumsy (even if it'd seem familiar to any user of C++ std::function template.

Practical difference between def f(x: Int) = x+1 and val f = (x: Int) => x+1 in Scala

I'm new to Scala and I'm having a problem understanding this. Why are there two syntaxes for the same concept, and none of them more efficient or shorter at that (merely from a typing standpoint, maybe they differ in behavior - which is what I'm asking).
In Go the analogues have a practical difference - you can't forward-reference the lambda assigned to a variable, but you can reference a named function from anywhere. Scala blends these two if I understand it correctly: you can forward-reference any variable (please correct me if I'm wrong).
Please note that this question is not a duplicate of What is the difference between “def” and “val” to define a function.
I know that def evaluates the expression after = each time it is referenced/called, and val only once. But this is different because the expression in the val definition evaluates to a function.
It is also not a duplicate of Functions vs methods in Scala.
This question concerns the syntax of Scala, and is not asking about the difference between functions and methods directly. Even though the answers may be similar in content, it's still valuable to have this exact point cleared up on this site.
There are three main differences (that I know of):
1. Internal Representation
Function expressions (aka anonymous functions or lambdas) are represented in the generated bytecode as instances of any of the Function traits. This means that function expressions are also objects. Method definitions, on the other hand, are first class citizens on the JVM and have a special bytecode representation. How this impacts performance is hard to tell without profiling.
2. Reference Syntax
References to functions and methods have different syntaxes. You can't just say foo when you want to send the reference of a method as an argument to some other part of your code. You'll have to say foo _. With functions you can just say foo and things will work as intended. The syntax foo _ is effectively wrapping the call to foo inside an anonymous function.
3. Generics Support
Methods support type parametrization, functions do not. For example, there's no way to express the following using a function value:
def identity[A](a: A): A = a
The closest would be this, but it loses the type information:
val identity = (a: Any) => a
As an extension to Ionut's first point, it may be worth taking a quick look at http://www.scala-lang.org/api/current/#scala.Function1.
From my understanding, an instance of a function as you described (ie.
val f = (x: Int) => x + 1) extends the Function1 class. The implications of this are that an instance of a function consumes more memory than defining a method. Methods are innate to the JVM, hence they can be determined at compile time. The obvious cost of a Function is its memory consumption, but with it come added benefits such as composition with other Function objects.
If I understand correctly, the reason defs and lambdas can work together is because the Function class has a self-type (T1) ⇒ R which is implied by its apply() method https://github.com/scala/scala/blob/v2.11.8/src/library/scala/Function1.scala#L36. (At least I THINK that's what going on, please correct me if I'm wrong). This is all just my own speculation, however. There's certain to be some extra compiler magic taking place underneath to allow method and function interoperability.

Why do some languages have metaclasses?

I see Java has only one metaclass (the Class class), but other languages, say Smalltalk, have one metaclass for each Class.
Why is that? What's the need for metaclasses? What difference does it make to have them one way or another?
The fundamental need for at least one metaclass is that if you want objects that represent classes (or want classes to be objects), then those objects must have a type.
Wikipedia says:
In early Smalltalks, there was only one metaclass called Class. This
implied that the methods all classes have were the same, in particular
the method to create new objects, i.e., new. To allow classes to have
their own methods and their own instance variables (called class
instance variables and should not be confused with class variables),
Smalltalk-80 introduced for each class C their own metaclass C class.
So the question is, do you want every class object to have the same type (and hence the same members), or do you want class objects to differ in ways that require them to have different types, so that there are type-checked operations which can be performed on the object that represents class A but not on the object that represents class B? Java and early Smalltalks answered that question differently from later Smalltalks.
So for example java.lang.Class.newInstance() takes no constructor arguments, whereas you can imagine that it might be nice to be able to call clz.newInstance(1) where clz is the class object for a class that has a constructor with takes an int. In Java you can still look through the constructors of the class yourself to find a match for the arguments you want to pass, but the type of the class object doesn't tell you whether you will find one.
Also note that Smalltalk stops at one level. The type of C is C class, but the type of C class is Metaclass. There's no infinite recursion of types C class class etc, because although different class objects in Smalltalk accept different messages, there's no demand for different metaclass objects to accept different messages.

What is the difference between a property and an instance variable?

I think I've been using these terms interchangably / wrongly!
Iain, this is basically a terminology question and is, despite the "language-agnostic" tag associated with this question, very language/environment related.
For design discussions sake, property and instance variable can be used interchangeably, since the idea is that a property is a data item describing an object.
When talking about a specific language these two can be different. For example, in C# a property is actually a function that returns an object, while an instance variable is a non-static member variable of a class.
Hershi is right about this being language specific. But to add to the trail of language specific answers:
In python, an instance variable is an attribute of an instance, (generally) something that is referred to in the instance's dictionary. This is analogous to members or instance variables in Java, except everything is public.
Properties are shortcuts to getter/setter methods that look just like an instance variable. Thus, in the following class definition (modified from Guido's new style object manifesto):
class C(object):
def __init__(self):
self.y = 0
def getx(self):
if self.y < 0: return 0
else: return self.y
def setx(self, x):
self.y = x
x = property(getx, setx)
>>> z = C()
>>> z.x = -3
>>> print z.x
0
>>> print z.y
-3
>>> z.x = 5
>>> print z.x
5
>>> print z.y
5
y is an instance variable of z, x is a property. (In general, where a property is defined, there are some techniques used to obscure the associated instance variable so that other code doesn't directly access it.) The benefit of properties in python is that a designer doesn't have to go around pre-emptively encapsulating all instance variables, since future encapsulation by converting an instance variable to a property should not break any existing code (unless the code is taking advantage of loopholes your encapsulation is trying to fix, or relying on class inspection or some other meta-programming technique).
All this is a very long answer to say that at the design level, it's good to talk about properties. It is agnostic as to what type of encapsulation you may need to perform. I guess this principle isn't language agnostic, but does apply to languages beside python.
In objective c, a property is an instance variable which can take advantage of an overloaded dot operator to call its setter and getter. So my.food = "cheeseburger" is actually interpreted as [my setFood:"cheeseburger"]. This is another case where the definition is definitely not language agnostic because objective-c defines the #property keyword.
code example done in C#
public class ClassName
{
private string variable;
public string property
{
get{ return variable; }
set { variable = value; }
}
}
Maybe thats because you first came from C++ right?!
In my school days I had professors that said class properties or class atributes all the time. Since I moved to the Java C# world, I started hearing about members. Class members, instance members...
And then Properties apear! in Java and .NET. So I think its better for you to call it members. Wheather they are instance members (or as you called it instance variable) or class Members....
Cheers!
A property can, and I suppose mostly does, return an instance variable but it can do more. You could put logic in a property, aggregate values or update other instance variables etc. I think it is best to avoid doing so however. Logic should go into methods.
In Java we have something called JavaBeans Properties, but that is basically a instance variable that follows a certain naming pattern for its getter and setter.
At add to what has been said, in a langauge like C#, a property is essentially a get and set function. As a result, it can have custom logic that runs in addition to the getting/setting. An instance variable cannot do this.
A property is some sort of data associated with an object. For instance, a property of a circle is its diameter, and another is its area.
An instance variable is a piece of data that is stored within an object. It doesn't necessarily need to correspond directly with a property. For instance (heh), a circle may store its radius in an instance variable, and calculate its diameter and area based on that radius. All three are still properties, but only the radius is stored in an instance variable.
Some languages have the concept of "first class" properties. This means that to a client application, the property looks and is used like an instance variable. That is, instead of writing something like circle.getDiameter(), you would write circle.diameter, and instead of circle.setRadius(5), you would write circle.radius = 5.
In contrast to the other answers given, I do think that there is a useful distinction between member variables and properties that is language-agnostic.
The distinction is most apparent in component-oriented programming, which is useful anywhere, but easiest to understand in a graphical UI. In that context, I tend to think of the design-time configuration of a component as manipulating the "properties" of an object. For example, I choose the foreground and background colors, the border style, and font of a text input field by setting its properties. While these properties could be changed at runtime, they typically aren't. At runtime, a different set of variables, representing the content of the field, are much more likely to be read and written. I think of this information as the "state" of the component.
Why is this distinction useful? When creating an abstraction for wiring components together, usually only the "state" variables need to be exposed. Going back to the text field example, you might declare an interface that provides access to the current content. But the "properties" that control the look and feel of the component are only defined on a concrete implementation class.

What is the difference between Type and Class?

What makes a type different from class and vice versa?
(In the general language-agnostic sense)
The following answer is from Gof book (Design Patterns)
An object's class defines how the
object is implemented. The class
defines object's internal state and
the implementation of its
operations.
In contrast, an object's
type only refers to its interface - a
set of requests to which it can
respond.
An object can have many types,
and objects of different classes can
have the same type.
//example in c++
template<typename T>
const T & max(T const &a,T const &b)
{
return a>b?a:b; //> operator of the type is used for comparison
}
max function requires a type with operation > with its own type as one of it interface any class that satisfies the above requirement can be used to generate specific max<particular class/primitive type> function for that class.
Inspired by Wikipedia...
In type theory terms;
A type is an abstract interface.
Types generally represent nouns, such as a person, place or thing, or something nominalized,
A class represents an implementation of the type.
It is a concrete data structure and collection of subroutines
Different concrete classes can produce objects of the same abstract type (depending on type system).
*For example, one might implement the type Stack with two classes: SmallStack (fast for small stacks, but scales poorly) and ScalableStack (scales well but high overhead for small stacks).*
Similarly, a given class may have several different constructors.
The banana example.
A Banana type would represent the properties and functionality of bananas in general.
The ABCBanana and XYZBanana classes would represent ways of producing bananas.
(Different banana suppliers in real life, or different data structures and functions to represent and draw bananas in a video game).
The ABCBanana class could then produce particular bananas which are
instances of the ABCBanana class, they would be objects of type Banana.
It is not rare the programmer provide a single and only implementation for a type. In this case the class name is often identical with the type name. But there is still a type (which could be extracted in an interface if required), and an implementation (which would implement the separate interface) which builds instances (objects) of the class.
I always think of a 'type' as an umbrella term for 'classes' and 'primitives'.
int foo; // Type is int, class is nonexistent.
MyClass foo; // Type is MyClass, class is MyClass
Type is the umbrella term for all the available object templates or concepts. A class is one such object template. So is the structure type, the Integer type, the Interface type etc. These are all types
If you want, you can look at it this way: A type is the parent concept. All the other concepts: Class, Interface, Structure, Integer etc inherit from this concept.i.e They are types
Taken from the GoF citation from below:
An objects's class defines how the
object is implemented .The class
defines the object's internal state and
the implementation of its
operations.
In contrast, an objects's
type only refers to its interface - the
set of requests to which it can
respond.
I want to provide an example using Java:
public interface IType {
}
public class A implements IType {
public A{};
}
public class B implements IType {
public B{};
}
Both classes A and B implement the interface and thus are of the type IType. Additionally in Java, both classes produce their own type (respectively to their class name). Thus the class A is of type A and IType and the class B is of type B and IType satisfying:
An object can have many types,
and objects of different classes can
have the same type.
The difference between subtypes and subclass probably helps to understand that issue as well:
https://www.cs.princeton.edu/courses/archive/fall98/cs441/mainus/node12.html
In general language-agnostic sense - Class is an realization of the Type.
Often when this is the only realization of that type, you can use both terms to reference it in some context.
On the contrary, for example, in C# context - Class is just one of the many more implementations of a Type concept like primitives, structs, pointers etc.
Type contains description of the data (i.e. properties, operations, etc),
Class is a specific type - it is a template to create instances of objects.
Strictly speaking class is a special concept, it can be seen as a package containing subset of metadata describing some aspects of an object.
For example in C# you can find interfaces and classes. Both of them are types, but interface can only define some contract and can not be instantiated unlike classes.
Simply speaking class is a specialized type used to encapsulate properties and behavior of an object.
Wikipedia can give you a more complete answer:
Definition of class
Definition of data type
Type is conceptually a superset of class. In the broader sense, a class is one form of type.
Closely related to classes are interfaces, which can bee seen as a very special kind of class - a purely abstract one. These too are types.
So "type" encompasses classes, interfaces and in most languages primitives too. Also platforms like the dot-net CLR have structure types too.
To illustrate it the fastest way:
A Struct is a Type, but a Struct is not a Class.
As you can see, a Type is an "abstract" term for not only definitions of classes, but also structs and primitive data types like float, int, bool.
I think of a type as being the set of things you can do with a particular value. For instance, if you have an integer value, you can add it to other integers (or perform other arithmetic operations), or pass it to functions which accept an integer argument. If you have an object value, you can call methods on it that are defined by its class.
Because a class defines what you can do with objects of that class, a class defines a type. A class is more than that though, since it also provides a description of how the methods are implemented (something not implied by the type) and how the fields of the object are laid out.
Note also that an object value can only have one class, but it may have multiple types, since every superclass provides a subset of the functionality available in the object's class.
So although objects and types are closely related, they are really not the same thing.
To add another example of distinction: in C++ you have pointer and reference types which can refer to classes, but are not classes in and of themselves.
Bar b; // b is of type "class Bar"
Bar *b2 = &b; // b2 is of type "pointer to Class Bar"
Bar &b3 = b; // b3 is of type "reference to Class Bar"
Bar *b4[7]; // b4 is of type "7-element array of pointers to Class Bar"
Bar ***b5; //b5 is of type "pointer to a pointer to a pointer to Class Bar"
Note that only one class is involved, but a near infinite number of types can be used. In some languages, function are considered "first-class-objects" in which case, the type of a function is a class. In others, the type of a function is merely a pointer. Classes generally have the concepts of being able to hold data, as well as operations on that data.
My thoughts are pretty much in line with aku's answer.
I see classes as a template for building objects, while types are a way to classify those objects, and provide us with an interface to them.
Python also adds metaclasses, that are just a mechanism to build classes, in the same way as classes build objects (and well, classes and metaclasses are both objects).
This response to the same question in lamba the ultimate seems to me like a perfect explanation.
Types in C, like Int Float, char etc define data that can be acted on with specific methods that can operate on them. It's no more complicated than that. Like for int I can add, subtract multiply and maybe divide. Those are my methods (or operations) for int. A Class is simply a definition of a new type. I first define what the data looks like. Maybe its a single bit. Maybe it's two words like a complex with a real and imaginary part. Or maybe its this complex thingy with 309734325 bytes representing the atomic makeup of a weird particle on Jupiter. I don't care. Just like an integer, I get to make up the operations I can do with this new data type. In the case of the integer I had add, subtract, etc. With this new data type I can define whatever operations I think make sense. They might be add subtract etc. but they may add other things. These are whatever methods I decide to add to my class.
The bottom line is that with a type in C, you have a definition of what the data is, ie; a byte, word, float, char etc. But any of these also implies what operations are legal and will produce reliable results.
A class is no different except it is up to you to define the interface and acceptable operations. The class defines these things and when you instantiate it in an Object it defines the behavior of the object just like a type definition defines the behavior of an integer when you operate on it.
Classes just give you the flexibility to define new types and everything about how they operate.
Once this is defined, every time I instantiate an object of class "thingy", it has the data structure I defined and the operations (methods) that I said you can do with it. The class "thingy" is clearly nothing more or less than a new type that C++ lets me define.
Type generally refers to the classification of primitive values - integers, strings, arrays, booleans, null, etc. Usually, you can't create any new types.
Class refers to the named set of properties and methods which an object is associated with when it is created. You can usually define as many new classes as you want, although some languages you have to create a new object and then attach methods to it.
This definition is mostly true, but some languages have attempted to combine types and classes in various ways, with various beneficial results.
Types and classes are related but not identical. My take is that classes are used for implementation inheritance, whereas types are used for runtime substitution.
Here is a link explaining the substitution principle and why subclasses and subtypes are not always the same thing (in Java for example). The wikipedia page on covariance and contravariance has more information on this distinction.
In langugages like Haskell, the concept of Class doesn't exist. It only has Types. (And Type Class. Not to be confused with Class, Type Class is more of an abstracted version of Type).
Monad is a Type Class.
class Monad m where
(>>=) :: m a -> ( a -> m b) -> m b
(>>) :: m a -> m b -> m b
return :: a -> m a
fail :: String -> m a
From a (pure) functional programming perspective, Type is more fundemental than Class as one can trace its root to Type Theory (e.g. from a PTL perspective, lambda calculus with types and without types behave quite differently), while Class is really just a construct to enable OO.
In languages that only support Type and don't support Class, functions are often treated as first-class citizen.
Meanwhile, when a language makes a distinction between Type and Class, functions are more of a second-class citizens that can be attached to Objects, etc. And yup, often you can attach a function onto a Class itself (aka a static function).
Interesting question. I think aku's answer is spot on. Take the java ArrayList class as an example
public class ArrayList<E> extends AbstractList<E>
implements List<E>, RandomAccess, Cloneable, java.io.Serializable
An instance of the ArrayList class is said to be of type of every superclass it extends and every interface it implements. Therefore, an instance of the ArrayList class has a type ArrayList, RandomAccess, Cloneable, and so forth. In other words, values (or instances) belong to one or more types, classes define what these types are.
Different classes may describe the same type.
Type consists of these parts:
Operations = syntax
Description of operations = semantics
Class consists of these parts:
Operations = syntax
Implementation (= various implementations describe same semantics)
Some notes:
Interface (as in Java) is not type, because it does not describe semantics (describes only syntax)
Subclass is not subtype, because subclass may change semantics defined in superclass, subtype cannot change supertype semantics (see Liskov Substitution Principle, e.g. this LSP example).
Obviously, as there are languages with type system that are not OO programming languages, type must be a broader concept than class
Even in languages like Java, int is a (primitive) type, but not a class.
Hence: every class is a type, but not every type is a class.
If we think to this question in C# context, we reach bellow answer.
C# type system is divided into following categories:
Value types:
Simple types: like int, long, float, etc.
Enum types
Struct types
Nullable types
Reference types:
Class types
Interface types
Array types
Delegate types
As you can see there are many types in C# which Class is only one of them.
There is just one important note:
C#’s type system is unified such that a value of any type can be treated as an object. Every type in C# directly or indirectly derives from the object class type, and object is the ultimate base class of all types. Values of reference types are treated as objects simply by viewing the values as type object. Values of value types are treated as objects by performing boxing and unboxing operations.
so as I see, type is an umbrella over many items which class is one of them.
Referece: CSahrp Language Specification doc, page 4
This was a good question for me, which made me think hard. I would dare to say that Class is a compiletime thingy and Type is a runtime thingy. I say this because you write classes not types. The compiler then creates types from classes, and the runtime use types to create instances of objects.
types are programming constructs that helps the compiler to perform type checking and ensure that the variables have the right properties for an operation.
classes are user defined types that an objects or variables referencing them could have. These are also subjected to type checking.