I would like to create a type (say, my_vector) that behaves exactly like a Vector, so that I can pass it to all the functions that take Vectors. In addition to that, I want to create special functions exclusively for my_vector, that do not work for generic Vectors.
So, for instance, if A is a Matrix and typeof(b) is my_vector, I want to be able to solve a linear system using A\b, to recover its length with length(b), or to access its elements with b[index].
At the same time, I want to define a specific function that can take objects of type my_vector as parameters, but that does not take objects of type Vector.
How can I do this?
This is not possible in general.
What you can do is define your my_vector type as subtype of AbstractVector. Then all functions accepting AbstractVector will also accept your type. What you need to implement for AbstractVector is listed in https://docs.julialang.org/en/v1/manual/interfaces/#man-interface-array.
Then if you want your my_vector type to also have functionalities that Vector has but AbstractVector does not have you need to implement yourself methods for functions that are specifically defined to only accept Vector. There are 49 such methods in Julia standard installation and you can find their list by writing methodswith(Vector). Most likely you will not need them all but only a small selection of such methods e.g. push! or pop!.
Having said that this will not ensure that everything that accepts Vector will accept your my_vector, as if some package accepts only Vector you will have to perform the same process for functions defined in this package.
In summary - check if AbstractVector is enough for you, as most likely it is and then it is simple. If it is not the case then doing what you want is difficult.
I am writing a language where functions are not typed. Which means I need to infer the return type of a function call in order to do type checking. However when somebody writes a recursive function the type checker goes into an infinite recursion trying to infer the type of the function call inside the function body.
The type checker does something like this:
Infer the types of the function call actual arguments.
Create a mapping of the actual argument types to the formal arguments.
Use the mapping to annotate types on the arguments used inside the function body.
Infer and return the return type of the function body.
Step 4 tries to then infer the type of the function call inside the function body, which calls the same type checker function again, causing an infinite recursion.
An example of a recursive function that gives me this problem:
function factorial(n) = n<1 ? 1 : n*factorial(n-1); // Function definition.
...
assert 24 == factorial(4); // Function call expression usage example.
How can I solve this problem without going in to an infinite recursion loop? Is there a way to infer the type of the recursive function call without having to go into the body again? Or some clean way to infer the type from context?
I know the easy solution might be to add types annotations to functions, this way the problem is trivial, but before doing that I want to know if there is a way to solve this without resorting to that.
I'd also like for the solution to work for mutual recursion.
Type inference can vary a lot depending on the language's type system and on what properties you want to have in terms of when annotations are needed. But whatever your language looks like, I think there's one seminal case you really should read about, which is ML. ML's type inference holds a nice sweet spot where it all fits together in a relatively simple paradigm. No type annotations are needed, and any expression has a single most general type (this property is called principality of typing).
ML's type system is the Hindley-Milner type system, which has parametric polymorphism. The type of an expression is either a specific type, or “any”. More precisely, the type constructor of an expression is either a specific type constructor or “any”, and type constructors can have arguments which themselves either have a specific type constructor or “any”. For example, the empty list has the type “list of any”. Two expressions that can have “any” type in isolation may be constrained to have the same type, whatever it is, so “any” is expressed with variables. For example, function list_of_two(x, y) = [x, y] (in a notation like your language) constrains x and y to have the same type, because they're inserted in the same list, but that type can be any type, so the type of this function is “take any two parameters of the same type α, and return a value of type list of α”.
The basic type inference algorithm for Hindley-Milner is algorithm W. At its core, it works by giving each subexpression a type that's a variable: α₁, α₂, α₃, … Programming language constructions then impose constraints on those variables. For example, if a list contains two elements of types α₁ and α₂ and the list itself has the type α₃, this constraints α₁ = α₂ and α₃ = list of α₁. Putting all these constraints together is a unification problem.
The constraints are based on a purely syntactic reading of the program. If there's a recursive call, you don't need to know the type of the function: it just means that there's a constraint that the variable for the return type of the function is the same as the type at its point of use. That's just one more equation to add to the set of constraints.
I left out an important aspect of ML which is that an expression's type can be generalized: an expression can be used with different types at different places. This is what allows polymorphism. For example,
let empty_list = [] in
(empty_list # [3]), (empty_list # ["hello"])
is a valid program where empty_list is used once with the type “list of integers” and once with the type “list of strings”. The type of empty_list is “for any α, list of α”: that's parametric polymorphism. Generalization adds some complexity to the algorithm, but it also removes complexity elsewhere, because that's what allows principality. Without it, let empty_list = [] in … would be ambiguous: empty_list would have to have some type, but there's no way to know what type without analyzing …, and then when you do analyze the … above you'd need to make a choice between integer and string.
Depending on your language's type system, ML and algorithm W may be directly reusable or may just provide some vague inspiration. But the principle of using variables during the inference, and progressively constraining these variables, is very general.
If a language is type-safe does that mean one could automatically assume that its statically typed since you would have to check types at compile time ?
C, for example, is statically typed and not type safe, while Haskell is statically typed and type safe. Most (all?) dynamically typed languages are type safe, as they have means of checking types at runtime to make sure they're the right thing. Additionally, these languages assume that because you have chosen to incur the performance penalty of including runtime type information, you would want to use that information as effectively as possible, and so generally do not allow interpreting a chunk of memory as the wrong type.
Dynamically typed languages have an additional measure of type safety, which is coercion. For example, if you type [] + [] in javascript, it will see that the operands to + are arrays and cannot be added directly, and so will convert them both to strings, giving the result of "" (the empty string).
Some languages, like javascript, will usually coerce other things to strings, while PHP for example will coerce strings to numbers to compare them.
EDIT: Type safety means not being allowed to interpret a chunk of memory holding something of type A as something of type B. As an example of type unsafety, C++ has the reinterpret_cast operator, which means "convert anything to anything else even if it doesn't make sense to do so." For example,
float a = 6.2;
int b = reinterpret_cast<int>(a);
//b now contains some form of garbage
For a much more complete explanation of type safety, see this answer.
I would hesitate to call a dynamic-typed language type-safe, however rigorously it checks types at runtime, because runtime might be too late to do anything about the error!
You could justifiably call such a language strongly typed, but I wouldn't call it type-safe.
Catching the error at compile time gives you a chance to fix it...
For a good example of a type safe language, look at SPARK.
In SPARK, indexing off the end of an array is a type error (each array has a new type for its index, and you have a value that isn't compatible with that type)
You would normally prove there are no such errors before even compiling the program...
What does "type-safe" mean?
Type safety means that the compiler will validate types while compiling, and throw an error if you try to assign the wrong type to a variable.
Some simple examples:
// Fails, Trying to put an integer in a string
String one = 1;
// Also fails.
int foo = "bar";
This also applies to method arguments, since you are passing explicit types to them:
int AddTwoNumbers(int a, int b)
{
return a + b;
}
If I tried to call that using:
int Sum = AddTwoNumbers(5, "5");
The compiler would throw an error, because I am passing a string ("5"), and it is expecting an integer.
In a loosely typed language, such as javascript, I can do the following:
function AddTwoNumbers(a, b)
{
return a + b;
}
if I call it like this:
Sum = AddTwoNumbers(5, "5");
Javascript automaticly converts the 5 to a string, and returns "55". This is due to javascript using the + sign for string concatenation. To make it type-aware, you would need to do something like:
function AddTwoNumbers(a, b)
{
return Number(a) + Number(b);
}
Or, possibly:
function AddOnlyTwoNumbers(a, b)
{
if (isNaN(a) || isNaN(b))
return false;
return Number(a) + Number(b);
}
if I call it like this:
Sum = AddTwoNumbers(5, " dogs");
Javascript automatically converts the 5 to a string, and appends them, to return "5 dogs".
Not all dynamic languages are as forgiving as javascript (In fact a dynamic language does not implicity imply a loose typed language (see Python)), some of them will actually give you a runtime error on invalid type casting.
While its convenient, it opens you up to a lot of errors that can be easily missed, and only identified by testing the running program. Personally, I prefer to have my compiler tell me if I made that mistake.
Now, back to C#...
C# supports a language feature called covariance, this basically means that you can substitute a base type for a child type and not cause an error, for example:
public class Foo : Bar
{
}
Here, I created a new class (Foo) that subclasses Bar. I can now create a method:
void DoSomething(Bar myBar)
And call it using either a Foo, or a Bar as an argument, both will work without causing an error. This works because C# knows that any child class of Bar will implement the interface of Bar.
However, you cannot do the inverse:
void DoSomething(Foo myFoo)
In this situation, I cannot pass Bar to this method, because the compiler does not know that Bar implements Foo's interface. This is because a child class can (and usually will) be much different than the parent class.
Of course, now I've gone way off the deep end and beyond the scope of the original question, but its all good stuff to know :)
Type-safety should not be confused with static / dynamic typing or strong / weak typing.
A type-safe language is one where the only operations that one can execute on data are the ones that are condoned by the data's type. That is, if your data is of type X and X doesn't support operation y, then the language will not allow you to to execute y(X).
This definition doesn't set rules on when this is checked. It can be at compile time (static typing) or at runtime (dynamic typing), typically through exceptions. It can be a bit of both: some statically typed languages allow you to cast data from one type to another, and the validity of casts must be checked at runtime (imagine that you're trying to cast an Object to a Consumer - the compiler has no way of knowing whether it's acceptable or not).
Type-safety does not necessarily mean strongly typed, either - some languages are notoriously weakly typed, but still arguably type safe. Take Javascript, for example: its type system is as weak as they come, but still strictly defined. It allows automatic casting of data (say, strings to ints), but within well defined rules. There is to my knowledge no case where a Javascript program will behave in an undefined fashion, and if you're clever enough (I'm not), you should be able to predict what will happen when reading Javascript code.
An example of a type-unsafe programming language is C: reading / writing an array value outside of the array's bounds has an undefined behaviour by specification. It's impossible to predict what will happen. C is a language that has a type system, but is not type safe.
Type safety is not just a compile time constraint, but a run time constraint. I feel even after all this time, we can add further clarity to this.
There are 2 main issues related to type safety. Memory** and data type (with its corresponding operations).
Memory**
A char typically requires 1 byte per character, or 8 bits (depends on language, Java and C# store unicode chars which require 16 bits).
An int requires 4 bytes, or 32 bits (usually).
Visually:
char: |-|-|-|-|-|-|-|-|
int : |-|-|-|-|-|-|-|-| |-|-|-|-|-|-|-|-| |-|-|-|-|-|-|-|-| |-|-|-|-|-|-|-|-|
A type safe language does not allow an int to be inserted into a char at run-time (this should throw some kind of class cast or out of memory exception). However, in a type unsafe language, you would overwrite existing data in 3 more adjacent bytes of memory.
int >> char:
|-|-|-|-|-|-|-|-| |?|?|?|?|?|?|?|?| |?|?|?|?|?|?|?|?| |?|?|?|?|?|?|?|?|
In the above case, the 3 bytes to the right are overwritten, so any pointers to that memory (say 3 consecutive chars) which expect to get a predictable char value will now have garbage. This causes undefined behavior in your program (or worse, possibly in other programs depending on how the OS allocates memory - very unlikely these days).
** While this first issue is not technically about data type, type safe languages address it inherently and it visually describes the issue to those unaware of how memory allocation "looks".
Data Type
The more subtle and direct type issue is where two data types use the same memory allocation. Take a int vs an unsigned int. Both are 32 bits. (Just as easily could be a char[4] and an int, but the more common issue is uint vs. int).
|-|-|-|-|-|-|-|-| |-|-|-|-|-|-|-|-| |-|-|-|-|-|-|-|-| |-|-|-|-|-|-|-|-|
|-|-|-|-|-|-|-|-| |-|-|-|-|-|-|-|-| |-|-|-|-|-|-|-|-| |-|-|-|-|-|-|-|-|
A type unsafe language allows the programmer to reference a properly allocated span of 32 bits, but when the value of a unsigned int is read into the space of an int (or vice versa), we again have undefined behavior. Imagine the problems this could cause in a banking program:
"Dude! I overdrafted $30 and now I have $65,506 left!!"
...'course, banking programs use much larger data types. ;) LOL!
As others have already pointed out, the next issue is computational operations on types. That has already been sufficiently covered.
Speed vs Safety
Most programmers today never need to worry about such things unless they are using something like C or C++. Both of these languages allow programmers to easily violate type safety at run time (direct memory referencing) despite the compilers' best efforts to minimize the risk. HOWEVER, this is not all bad.
One reason these languages are so computationally fast is they are not burdened by verifying type compatibility during run time operations like, for example, Java. They assume the developer is a good rational being who won't add a string and an int together and for that, the developer is rewarded with speed/efficiency.
Many answers here conflate type-safety with static-typing and dynamic-typing. A dynamically typed language (like smalltalk) can be type-safe as well.
A short answer: a language is considered type-safe if no operation leads to undefined behavior. Many consider the requirement of explicit type conversions necessary for a language to be strictly typed, as automatic conversions can sometimes leads to well defined but unexpected/unintuitive behaviors.
A programming language that is 'type-safe' means following things:
You can't read from uninitialized variables
You can't index arrays beyond their bounds
You can't perform unchecked type casts
An explanation from a liberal arts major, not a comp sci major:
When people say that a language or language feature is type safe, they mean that the language will help prevent you from, for example, passing something that isn't an integer to some logic that expects an integer.
For example, in C#, I define a function as:
void foo(int arg)
The compiler will then stop me from doing this:
// call foo
foo("hello world")
In other languages, the compiler would not stop me (or there is no compiler...), so the string would be passed to the logic and then probably something bad will happen.
Type safe languages try to catch more at "compile time".
On the down side, with type safe languages, when you have a string like "123" and you want to operate on it like an int, you have to write more code to convert the string to an int, or when you have an int like 123 and want to use it in a message like, "The answer is 123", you have to write more code to convert/cast it to a string.
To get a better understanding do watch the below video which demonstrates code in type safe language (C#) and NOT type safe language ( javascript).
http://www.youtube.com/watch?v=Rlw_njQhkxw
Now for the long text.
Type safety means preventing type errors. Type error occurs when data type of one type is assigned to other type UNKNOWINGLY and we get undesirable results.
For instance JavaScript is a NOT a type safe language. In the below code “num” is a numeric variable and “str” is string. Javascript allows me to do “num + str” , now GUESS will it do arithmetic or concatenation .
Now for the below code the results are “55” but the important point is the confusion created what kind of operation it will do.
This is happening because javascript is not a type safe language. Its allowing to set one type of data to the other type without restrictions.
<script>
var num = 5; // numeric
var str = "5"; // string
var z = num + str; // arthimetic or concat ????
alert(z); // displays “55”
</script>
C# is a type safe language. It does not allow one data type to be assigned to other data type. The below code does not allow “+” operator on different data types.
Concept:
To be very simple Type Safe like the meanings, it makes sure that type of the variable should be safe like
no wrong data type e.g. can't save or initialized a variable of string type with integer
Out of bound indexes are not accessible
Allow only the specific memory location
so it is all about the safety of the types of your storage in terms of variables.
Type-safe means that programmatically, the type of data for a variable, return value, or argument must fit within a certain criteria.
In practice, this means that 7 (an integer type) is different from "7" (a quoted character of string type).
PHP, Javascript and other dynamic scripting languages are usually weakly-typed, in that they will convert a (string) "7" to an (integer) 7 if you try to add "7" + 3, although sometimes you have to do this explicitly (and Javascript uses the "+" character for concatenation).
C/C++/Java will not understand that, or will concatenate the result into "73" instead. Type-safety prevents these types of bugs in code by making the type requirement explicit.
Type-safety is very useful. The solution to the above "7" + 3 would be to type cast (int) "7" + 3 (equals 10).
Try this explanation on...
TypeSafe means that variables are statically checked for appropriate assignment at compile time. For example, consder a string or an integer. These two different data types cannot be cross-assigned (ie, you can't assign an integer to a string nor can you assign a string to an integer).
For non-typesafe behavior, consider this:
object x = 89;
int y;
if you attempt to do this:
y = x;
the compiler throws an error that says it can't convert a System.Object to an Integer. You need to do that explicitly. One way would be:
y = Convert.ToInt32( x );
The assignment above is not typesafe. A typesafe assignement is where the types can directly be assigned to each other.
Non typesafe collections abound in ASP.NET (eg, the application, session, and viewstate collections). The good news about these collections is that (minimizing multiple server state management considerations) you can put pretty much any data type in any of the three collections. The bad news: because these collections aren't typesafe, you'll need to cast the values appropriately when you fetch them back out.
For example:
Session[ "x" ] = 34;
works fine. But to assign the integer value back, you'll need to:
int i = Convert.ToInt32( Session[ "x" ] );
Read about generics for ways that facility helps you easily implement typesafe collections.
C# is a typesafe language but watch for articles about C# 4.0; interesting dynamic possibilities loom (is it a good thing that C# is essentially getting Option Strict: Off... we'll see).
Type-Safe is code that accesses only the memory locations it is authorized to access, and only in well-defined, allowable ways.
Type-safe code cannot perform an operation on an object that is invalid for that object. The C# and VB.NET language compilers always produce type-safe code, which is verified to be type-safe during JIT compilation.
Type-safe means that the set of values that may be assigned to a program variable must fit well-defined and testable criteria. Type-safe variables lead to more robust programs because the algorithms that manipulate the variables can trust that the variable will only take one of a well-defined set of values. Keeping this trust ensures the integrity and quality of the data and the program.
For many variables, the set of values that may be assigned to a variable is defined at the time the program is written. For example, a variable called "colour" may be allowed to take on the values "red", "green", or "blue" and never any other values. For other variables those criteria may change at run-time. For example, a variable called "colour" may only be allowed to take on values in the "name" column of a "Colours" table in a relational database, where "red, "green", and "blue", are three values for "name" in the "Colours" table, but some other part of the computer program may be able to add to that list while the program is running, and the variable can take on the new values after they are added to the Colours table.
Many type-safe languages give the illusion of "type-safety" by insisting on strictly defining types for variables and only allowing a variable to be assigned values of the same "type". There are a couple of problems with this approach. For example, a program may have a variable "yearOfBirth" which is the year a person was born, and it is tempting to type-cast it as a short integer. However, it is not a short integer. This year, it is a number that is less than 2009 and greater than -10000. However, this set grows by 1 every year as the program runs. Making this a "short int" is not adequate. What is needed to make this variable type-safe is a run-time validation function that ensures that the number is always greater than -10000 and less than the next calendar year. There is no compiler that can enforce such criteria because these criteria are always unique characteristics of the problem domain.
Languages that use dynamic typing (or duck-typing, or manifest typing) such as Perl, Python, Ruby, SQLite, and Lua don't have the notion of typed variables. This forces the programmer to write a run-time validation routine for every variable to ensure that it is correct, or endure the consequences of unexplained run-time exceptions. In my experience, programmers in statically typed languages such as C, C++, Java, and C# are often lulled into thinking that statically defined types is all they need to do to get the benefits of type-safety. This is simply not true for many useful computer programs, and it is hard to predict if it is true for any particular computer program.
The long & the short.... Do you want type-safety? If so, then write run-time functions to ensure that when a variable is assigned a value, it conforms to well-defined criteria. The down-side is that it makes domain analysis really difficult for most computer programs because you have to explicitly define the criteria for each program variable.
Type Safety
In modern C++, type safety is very important. Type safety means that you use the types correctly and, therefore, avoid unsafe casts and unions. Every object in C++ is used according to its type and an object needs to be initialized before its use.
Safe Initialization: {}
The compiler protects from information loss during type conversion. For example,
int a{7}; The initialization is OK
int b{7.5} Compiler shows ERROR because of information loss.\
Unsafe Initialization: = or ()
The compiler doesn't protect from information loss during type conversion.
int a = 7 The initialization is OK
int a = 7.5 The initialization is OK, but information loss occurs. The actual value of a will become 7.0
int c(7) The initialization is OK
int c(7.5) The initialization is OK, but information loss occurs. The actual value of a will become 7.0