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I have seen many places the mention that Julia is "Composable". I know that the word itself means:
Composability is a system design principle that deals with the inter-relationships of components. A highly composable system provides components that can be selected and assembled in various combinations to satisfy specific user requirements.
But I am curious what the specific components of Julia are that make it composable. Is it the ability to override base functions with my own implementation?
I guess I'll hazard an answer, though my understanding may be no more complete than yours!
As far as I understand it (in no small part from Stefan's "Unreasonable Effectiveness of Multiple Dispatch" JuliaCon talk as linked by Oscar in the comments), I would say that it is in part:
As you say, the ability override base functions with your own implementation [and, critically, then have it "just work" (be dispatched to) whenever appropriate thanks to multiple dispatch] ...since this means if you make a custom type and define all the fundamental / primitive operations on that type (as in https://docs.julialang.org/en/v1/manual/interfaces/ -- say +-*/ et al. for numeric types, or getindex, setindex! et al. for an array-like type, etc.), then any more complex program built on those fundamentals will also "just work" with your new custom type. And that in turn means your custom type will also work (AKA compose) with other people's packages without any need for (e.g.) explicit compatibility shims as long as people haven't over-constrained their function argument types (which is, incidentally, why over-constraining function argument types is a Julia antipattern )
Following on 1), the fact that so many Base methods are also just plain Julia, so will also work with your new custom type as long as the proper fundamental operations are defined
The fact that Julia's base types and methods are generally performant and convenient enough that in many cases there's no need to do anything custom, so you can just put together blocks that all operate on, e.g., plain Julia arrays or tuples or etc.This last point is perhaps most notable in contrast to a language like Python where, for example, every sufficiently large subset of the ecosystem (numpy, tensorflow, etc.) has their own reimplementation of (e.g.) arrays, which for better performance are all ultimately implemented in some other language entirely (C++, for numpy and TF) and thus probably do not compose with each other.
Over at http://diditwith.net, I see that, in F#, it isn't strictly necessary to pass out parameters to a function that otherwise requires them. The language will auto-magically stuff the result and the output parameter into a tuple. (!)
Is this some kind of side effect (pardon the pun) of the general mechanics of the language, or a feature that was specifically articulated in the F# specification and deliberately programmed into the language?
It's an awesome feature, and if it was expressly put into F#, then I'm wondering what other nuggets of gold like this are lurking within the language, because I've pored over dozens of web pages and read through three books (by D. Syme, T. Petricek, and C. Smith) and I hadn't seen this particular trick mentioned at all.
EDIT: As Mr. Petricek has responded, below, he does mention the feature in at least two places in his book, Real-World Functional Programming. My bad.
This is not a side-effect of some other, more general, mechanism in the F# language.
It has been added specifically for this purpose. .NET libraries often return multiple values by adding out (or ref) parameters at the end of the method signature. In F#, returning multiple values is done by returning tuple, so it makes sense to turn the .NET style into the typical F# pattern.
I don't think F# does many similar tricks, especially when it comes to interoperability, but you can browse through some of the handy snippets here and here.
(I quickly checked and Real-World Functional Programming mentions the trick briefly on pages 88 and 111.)
This is a specific feature to make interop with .NET methods more pleasant - all trailing out parameters can instead be treated as part of the return value (but note that this only affects trailing out parameters, so a method with the C# signature like void f(out int i, int j) can't be called this way).
Arguably, out parameters are just a way to work around the lack of tuples in .NET 1.0, anyway. It seems likely that many methods that use them would be written differently if they targeted later versions of the framework (by using Nullable<_> types or tuples as return types).
I often find developers use the terms functional language and dynamic language together, and wonder why are they always being put together.
What are the differences between them? Can a language be both dynamic and functional? Do they complement each other? Why do we need them anyway?
I'm a C# programmer and don't yet understand this whole dynamic/functional thing (C# is going to have some dynamic features in ver 4. Will it also be functional? what's going on here?).
Thanks,
Abraham
To put it in a simple (but not accurate) answer
Dynamic languages are ones in which the Type (Name of the Class) is not as important as compared to its nemesis statically typed languages. A variable may have objects of different types assigned to it at any given point of time. Method invocations are resolved at run-time. This means you lose the benefits of static typing (compiler warnings) but simple methods turn generic - sort(list) works for a list of strings as well as list of ints. e.g. Ruby et. all
Functional languages value immutability. The programs are written in terms of bigger and bigger functions (usually bottom up). The concept of object state and mutability is frowned upon. A function in this context is self-sufficient (The term is Pure as per Wikipedia): everything it needs to produce output, lies in the input that it receives. It also produces no side-effects (unless it explicitly mentions it) and returns consistent output for a given input. This can lead to elegant code (see: fluent interfaces), where input data is pipelined through diff functions to produce the eventual output e.g. LISP et.all
However the boundaries are being muddied with languages picking up the best of all worlds... You could have a language which is both, one or neither.
e.g. predominantly static C# picking up lambda expressions in 3.0 and bringing in dynamic capabilities with 4.0
Dynamic typing, a type system, is orthogonal to 'functional', a programming paradigm.
Dynamic 'languages' are actually dynamically typed. This means that you don't have compile-time checking of your variable types.
Functional languages offer loads of support for e.g. lambda calculus - anonymous functions.
An example of a language that does dynamic typing, and supports anonymous functions: javascript. Ruby has some functional style support, too. And there are others.
Dynamic typing and functional programming are independent concepts. You can have either, neither or both in a language.
Static typing means that types of objects are known at compilation time. In dynamic typing they are known at runtime.
Functional programming means programming style where computation is done by evaluating functions while avoiding state changes. (example: you use recursion instead of for-loops, because a loop would need changing of a counter variable, etc.) This helps to avoid bugs and makes concurrent programming easier. Pure languages require you to program in functional style, others just enable it.
Example languages:
|----------------+---------+---------|
| | Dynamic | Static |
|----------------+---------+---------|
| Functional | LISP | Haskell |
| Not functional | PHP | Java |
|----------------+---------+---------|
Dynamic languages on the other hand are a broader concept. There is no exact definition, but usually the more features of the compiler are moved to the runtime, more dynamic the language is. This means that in dynamic languages you can usually evaluate expressions, change object structure etc. at runtime.
If you're interested in paradigms, the paper Programming Paradigms for Dummies: What Every Programmer Should Know covers them.
In functional programming, state is implicit - the program executes by calling functions which call other functions. In imperative programming and object oriented programming, state is explicit - you change the value of a variable or object's field.
In a way, functional and imperative systems can be seen as duals - what's fixed in one is a dynamic value in the other.
Closures - which trap some explicit, mutable state in an object which can be called as a function - sit somewhere between, being neither pure functional programming but not quite fully fledged objects; they are more like anonymous objects than functions.
'Dynamic languages' is vague term, usually meaning one of the following:
Dynamically Typed Languages - languages which delay determination of type to runtime, but the set of types is fixed. Examples are Smalltalk, Lisps, current Fortress implementations. Some otherwise statically typed languages also allow some dynamic type checks - Java, C#, C++ and Ada. ( it was a failed dynamic type cast from float to int in Ada that crashed Ariane 5 )
Languages with dynamic types - languages where new types can be created at runtime. The most popular is JavaScript. Because you have to run the program to determine the types, it's harder to make IDEs for these with type aware autocompletion.
Languages which are dynamically compiled - languages where new scripts can be compiled at runtime. This is true of bash, JSP, PHP and ASP at the page scale, and true for at a finer scale for lisps and JavaScript which support an 'eval' function which compiles and runs an expression.
Functional languages which are strongly typed often perform a large amount of type inference, so it's common for their programs to have less explicit typing than poorly implemented static typed languages. This can confuse people who have only seen the lack of explicit typing in dynamic typed languages into believing that type inference is the same as dynamic typing.
xtofl has already offered a good overall picture. I can speak to the C# point.
C# has been becoming easier to work with in a functional way for a while now:
C# 2 introduced anonymous methods, which made it easier to create delegates which used state which was otherwise local to a method
C# 3 introduced lambda expressions which are mostly like anonymous methods but even more compact
LINQ support in both C# 3 and .NET 3.5 made it easier to query data in a functional way, chaining together predicates, projections etc
None of the C# 4 features directly contributes to functional programming IMO, although named arguments and optional parameters may make it easier to create/use immutable types, which is one of the biggest features missing from the functional picture IMO.
(There are other things functional languages often have, such as pattern matching and more impressive type inference, but you can write a lot of functional-style code reasonably easily in C#.)
C# 4 will gain some dynamic abilities through the dynamic type (which itself is effectively a static type you can do anything with). This will be somewhat "opt in" - if you never use the dynamic type, C# will still be fully static language. There's no language support for responding dynamically, but the DLR has support for this - if you implement IDynamicMetaObjectProvider or derive from DynamicObject, for example, you can add dynamic behaviour.
I would say that C# isn't becoming a functional language or a dynamic language, but one in which you can code in a functional style and interoperate with dynamic platforms.
There are many methods for representing structure of a program (like UML class diagrams etc.). I am interested if there is a convention which describes programs in a strict, mathematical way. I am especially interested in the use of mathematical notation for this purpose.
An example: Classes are represented as sets (fields, properties) and functions (operating on the elements of sets). A parent class' fields are a subset of child class'. Functions are described in pseudocode which has to look like this and that...
I know that Z Notation has been used to some extent in the formal verification of software, such as the Tokeneer project.
Z Notation
Z Reference Manual
http://www.amazon.com/Concrete-Mathematics-Foundation-Computer-Science/dp/0201558025
Yes, there is, Floyd-Hoare Logic.
There are a lot of way, but i think most of them are inconvenient for expressing the structure since the structure is often not expressable in default mathematical concepts. The main exception is of course functional programing languages. Think about folds (catamorphisme), groups, algebra's etc.
For imperative programming I know of the existence of Z, which uses (pure and extended) lambda calculus set theory and (first order) predicate logic. However, i dont think it's very convenient. The only upside of using mathematics to express structure is the fact that you can prove stuff about it. But if you want to do that, take a look at JML, Spec# or Eiffel.
Depends on what you're trying to accomplish, but going down this road with specific languages can get you into trouble.
For example, see the circle-ellipse discussion on C++ FAQ Lite.
This book applies the deductive method
to programming by affiliating programs
with the abstract mathematical
theories that enable them work. [...]
I believe that Elements of Programming by Alexander Stepanov and Paul McJones, is pretty close to what you are looking for.
Concepts
A concept is a description of
requirements on one or more types
stated in terms of the existence and
properties of procedures, type
attributes, and type functions defined
on the types.
Z, which has already been mentioned, is pretty much what you describe. There are some variants of it for object-oriented modelling, but I think you can get quite far with "standard Z's" schemas if you wish to model classes.
There's also Alloy, which is newer and inspired by Z. Its notation is perhaps a bit closer to object-orientation. It is also analysable, i.e. you can check the models you create whether they fulfill certain conditions, but it cannot prove that properties hold, just attempt to refute within a finite scope.
The article Dependable Software by Design is a nice introduction to Alloy and its ilk, along with a table of available similar tools.
You are looking for functional programming. There are several functional programming languages, and they are all based on a fundamental mathematical theory called the Lambda calculus. Programs written in a functional programming language such as LISP are a mathematical representation of themselves. ;-)
There is a mathematical language which actually describes a program or rather it's operations. You take the initial state and then transform this state until you reach the desired target state. The transformations yield the program code which must be executed.
See the Wikipedia article about Hoare logic.
The basic idea is that for every function (no matter if you put that into a class or into an old style function), you have a pre- and a post-condition. For example, the precondition can be that you have an array which has >= 0 elements. the post-condition is that every element[i] must by <= element[j] for every i <= j.
The usual description would be "the function sorts the array". But the mathematical terms allow you to transform the input (which must match the precondition) into the output (which must match the postcondition).
It's a bit unwieldy to use, especially for more complex programs but some of the examples are pretty impressive. Often, you get really compact code as the result which looks quite complex but works at first try.
I'd like to suggest Algebra of Programming. It's a calculational approach to programs, using Relational Algebra, and Galois Connections.
If you have further interest on this topic, you can find an amazing paper, here, by Shin-Cheng Mu, and José Nuno Oliveira (slides).
Using Relational Algebra and First-Order Logic, also has a nice synergy with Alloy, Functional Programming, and Design by Contract (easily applied to Object-Oriented Programming).
Can someone tell me what Strong typing and weak typing means and which one is better?
That'll be the theory answers taken care of, but the practice side seems to have been neglected...
Strong-typing means that you can't use one type of variable where another is expected (or have restrictions to doing so). Weak-typing means you can mix different types. In PHP for example, you can mix numbers and strings and PHP won't complain because it is a weakly-typed language.
$message = "You are visitor number ".$count;
If it was strongly typed, you'd have to convert $count from an integer to a string, usually with either with casting:
$message = "you are visitor number ".(string)$count;
...or a function:
$message = "you are visitor number ".strval($count);
As for which is better, that's subjective. Advocates of strong-typing will tell you that it will help you to avoid some bugs and/or errors and help communicate the purpose of a variable etc. They'll also tell you that advocates of weak-typing will call strong-typing "unnecessary language fluff that is rendered pointless by common sense", or something similar. As a card-carrying member of the weak-typing group, I'd have to say that they've got my number... but I have theirs too, and I can put it in a string :)
"Strong typing" and its opposite "weak typing" are rather weak in meaning, partly since the notion of what is considered to be "strong" can vary depending on whom you ask. E.g. C has been been called both "strongly typed" and "weakly typed" by different authors, it really depends on what you compare it to.
Generally a type system should be considered stronger if it can express the same constraints as another and more. Quite often two type systems are not be comparable, though -- one might have features the other lacks and vice versa. Any discussion of relative strengths is then up to personal taste.
Having a stronger type system means that either the compiler or the runtime will report more errors, which is usually a good thing, although it might come at the cost of having to provide more type information manually, which might be considered effort not worthwhile. I would claim "strong typing" is generally better, but you have to look at the cost.
It's also important to realize that "strongly typed" is often incorrectly used instead of "statically typed" or even "manifest typed". "Statically typed" means that there are type checks at compile-time, "manifest typed" means that the types are declared explicitly. Manifest-typing is probably the best known way of making a type system stronger (think Java), but you can add strength by other means such as type-inference.
I would like to reiterate that weak typing is not the same as dynamic typing.
This is a rather well written article on the subject and I would definitely recommend giving it a read if you are unsure about the differences between strong, weak, static and dynamic type systems. It details the differences much better than can be expected in a short answer, and has some very enlightening examples.
http://en.wikipedia.org/wiki/Type_system
Strong typing is the most common type model in modern programming languages. Those languages have one simple feature - knowing about type values in run time. We can say that strong typed languages prevent mixing operations between two or more different kind of types. Here is an example in Java:
String foo = "Hello, world!";
Object obj = foo;
String bar = (String) obj;
Date baz = (Date) obj; // This line will throw an error
The previous example will work perfectly well until program hit the last line of code where the ClassCastException is going to be thrown because Java is strong typed programming language.
When we talk about weak typed languages, Perl is one of them. The following example shows how Perl doesn't have any problems with mixing two different types.
$a = 10;
$b = "a";
$c = $a . $b;
print $c; # returns 10a
I hope you find this useful,
Thanks.
This article is a great read: http://blogs.perl.org/users/ovid/2010/08/what-to-know-before-debating-type-systems.html Cleared up a lot of things for me when researching trying to answer a similar question, hope others find it useful too.
Strong and Weak Typing:
Probably the most common way type systems are classified is "strong"
or "weak." This is unfortunate, since these words have nearly no
meaning at all. It is, to a limited extent, possible to compare two
languages with very similar type systems, and designate one as having
the stronger of those two systems. Beyond that, the words mean nothing
at all.
Static and Dynamic Types
This is very nearly the only common classification of type systems
that has real meaning. As a matter of fact, it's significance is
frequently under-estimated [...] Dynamic and static type systems are
two completely different things, whose goals happen to partially
overlap.
A static type system is a mechanism by which a compiler examines
source code and assigns labels (called "types") to pieces of the
syntax, and then uses them to infer something about the program's
behavior. A dynamic type system is a mechanism by which a compiler
generates code to keep track of the sort of data (coincidentally, also
called its "type") used by the program. The use of the same word
"type" in each of these two systems is, of course, not really entirely
coincidental; yet it is best understood as having a sort of weak
historical significance. Great confusion results from trying to find a
world view in which "type" really means the same thing in both
systems. It doesn't.
Explicit/Implicit Types:
When these terms are used, they refer to the extent to which a
compiler will reason about the static types of parts of a program. All
programming languages have some form of reasoning about types. Some
have more than others. ML and Haskell have implicit types, in that no
(or very few, depending on the language and extensions in use) type
declarations are needed. Java and Ada have very explicit types, and
one is constantly declaring the types of things. All of the above have
(relatively, compared to C and C++, for example) strong static type
systems.
Strong/weak typing in a language is related to how easily you can do type conversions:
For example in Python:
str = 5 + 'a'
# would throw an error since it does not want to cast one type to the other implicitly.
Where as in C language:
int a = 5;
a = 5 + 'c';
/* is fine, because C treats 'c' as an integer in this case */
Thus Python is more strongly typed than C (from this perspective).
May be this can help you to understand Strong and Weak Typing.......
Strong typing: It checks the type of variables as soon as possible, usually at compile time. It prevents mixing operations between mismatched types.
A strong-typed programming language is one in which:
All variables (or data types) are known at compile time
There is strict enforcement of typing rules (a String can't be used
where an Integer would be expected)
All exceptions to typing rules results in a compile time error
Weak Typing: While weak typing is delaying checking the types of the system as late as possible, usually to run-time. In this you can mix types without an explicit conversion.
A "weak-typed" programming language is simply one which is not strong-typed.
which is preferred depends on what you want. for scripts and good stuff you will usually want weak typing, because you want to write as much less code as possible. in big programs, strong typing can reduce errors at compile time.
Weak typing means that you don't specify what type a variable is, and strong typing means you give a strict type to each variable.
Each has its advantages, with weak typing (or dynamic typing, as it is often called), being more flexible and requiring less code from the programmer. Strong typing, on the other hand, requires more work from the developer, but in return it can alert you of many mistakes when compiling your code, before you run it. Dynamic typing may delay the discovery of these simple problems until the code is executed.
Depending on the task at hand, weak typing may be better than strong typing, or vice versa, but it is mostly a matter of taste. Weak typing is commonly used in scripting languages, while strong typing is used in most compiled languages.