A type system associates a type with each computed value. By examining the flow of these values, a type system attempts to ensure or prove that no type errors can occur. The particular type system in question determines exactly what constitutes a type error, but in general the aim is to prevent operations expecting a certain kind of value being used with values for which that operation does not make sense (logic error
Logic error
In computer programming, a logic error is a bug in a program that causes it to operate incorrectly, but not to terminate abnormally . A logic error produces unintended or undesired output or other behavior, although it may not immediately be recognized as such.Logic errors occur in both compiled...
s); memory errors will also be prevented. Type systems are often specified as part of programming language
Programming language
A programming language is an artificial language designed to communicate instructions to a machine, particularly a computer. Programming languages can be used to create programs that control the behavior of a machine and/or to express algorithms precisely....
s, and built into the interpreters and compilers for them; although they can also be implemented as optional tools
Extended static checking
Extended Static Checking is a collective name for a range of techniques for statically checking the correctness of various program constraints. ESC can be thought of as an extended form of type checking. As with type checking, ESC is performed automatically at compile time...
Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...
, a type system may be defined as "a tractable syntactic framework for classifying phrases according to the kinds of values
Value (computer science)
In computer science, a value is an expression which cannot be evaluated any further . The members of a type are the values of that type. For example, the expression "1 + 2" is not a value as it can be reduced to the expression "3"...
A compiler is a computer program that transforms source code written in a programming language into another computer language...
may also use the static type of a value to optimize the storage it needs and the choice of algorithms for operations on the value. In many C
C (programming language)
C is a general-purpose computer programming language developed between 1969 and 1973 by Dennis Ritchie at the Bell Telephone Laboratories for use with the Unix operating system....
In computer programming, a data type is a classification identifying one of various types of data, such as floating-point, integer, or Boolean, that determines the possible values for that type; the operations that can be done on values of that type; the meaning of the data; and the way values of...
A bit is the basic unit of information in computing and telecommunications; it is the amount of information stored by a digital device or other physical system that exists in one of two possible distinct states...
s, in accord with the IEEE specification for single-precision floating point numbers. They will thus use floating-point-specific microprocessor operations
Instruction set
An instruction set, or instruction set architecture , is the part of the computer architecture related to programming, including the native data types, instructions, registers, addressing modes, memory architecture, interrupt and exception handling, and external I/O...
on those values (floating-point addition, multiplication, etc.).
The depth of type constraints and the manner of their evaluation affect the typing of the language. A programming language
Programming language
A programming language is an artificial language designed to communicate instructions to a machine, particularly a computer. Programming languages can be used to create programs that control the behavior of a machine and/or to express algorithms precisely....
may further associate an operation with varying concrete algorithms on each type in the case of type polymorphism
Type polymorphism
In computer science, polymorphism is a programming language feature that allows values of different data types to be handled using a uniform interface. The concept of parametric polymorphism applies to both data types and functions...
In mathematics, logic and computer science, type theory is any of several formal systems that can serve as alternatives to naive set theory, or the study of such formalisms in general...
is the study of type systems, although the concrete type systems of programming languages originate from practical issues of computer architecture, compiler implementation, and language design.
Fundamentals
Assigning data types (typing) gives meaning to sequences of bit
Bit
A bit is the basic unit of information in computing and telecommunications; it is the amount of information stored by a digital device or other physical system that exists in one of two possible distinct states...
s. Types usually have associations either with values in memory
Computer memory
In computing, memory refers to the physical devices used to store programs or data on a temporary or permanent basis for use in a computer or other digital electronic device. The term primary memory is used for the information in physical systems which are fast In computing, memory refers to the...
In computer science, an object is any entity that can be manipulated by the commands of a programming language, such as a value, variable, function, or data structure...
such as variables. Because any value simply consists of a sequence of bits in a computer
Computer
A computer is a programmable machine designed to sequentially and automatically carry out a sequence of arithmetic or logical operations. The particular sequence of operations can be changed readily, allowing the computer to solve more than one kind of problem...
, hardware makes no intrinsic distinction even between memory address
Memory address
A digital computer's memory, more specifically main memory, consists of many memory locations, each having a memory address, a number, analogous to a street address, at which computer programs store and retrieve, machine code or data. Most application programs do not directly read and write to...
In computer and machine-based telecommunications terminology, a character is a unit of information that roughly corresponds to a grapheme, grapheme-like unit, or symbol, such as in an alphabet or syllabary in the written form of a natural language....
The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...
s and floating-point numbers, being unable to discriminate between them based on bit pattern alone. Associating a sequence of bits and a type informs programs and programmers how that sequence of bits should be understood.
Advantages provided by type systems include:
Abstraction (or modularity) – Types allow programmers to think about programs at a higher level than the bit or byte, not bothering with low-level implementation. For example, programmers can think of a string as a collection of character values instead of as a mere array of bytes. Or, types can allow programmers to express the interface
Interface (computer science)
In the field of computer science, an interface is a tool and concept that refers to a point of interaction between components, and is applicable at the level of both hardware and software...
between two subsystems. This helps localize the definitions required for interoperability of the subsystems and prevents inconsistencies when those subsystems communicate.
Documentation – In more expressive type systems, types can serve as a form of documentation
Documentation
Documentation is a term used in several different ways. Generally, documentation refers to the process of providing evidence.Modules of Documentation are Helpful...
, since they can illustrate the intent of the programmer. For instance, timestamps may be represented as integers—but if a programmer declares a function as returning a timestamp type rather than merely an integer type, this documents part of the meaning of the function.
Optimization – Static type-checking may provide useful compile-time information. For example, if a type requires that a value must align in memory at a multiple of four bytes, the compiler may be able to use more efficient machine instructions.
A compiler is a computer program that transforms source code written in a programming language into another computer language...
to detect meaningless or probably invalid code. For example, we can identify an expression 3 / "Hello, World" as invalid, because the rules of arithmetic
Arithmetic
Arithmetic or arithmetics is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. It involves the study of quantity, especially as the result of combining numbers...
The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...
In formal languages, which are used in mathematical logic and theoretical computer science, a string is a finite sequence of symbols that are chosen from a set or alphabet....
. As discussed below, strong typing offers more safety, but generally does not guarantee complete safety (see type safety
Type safety
In computer science, type safety is the extent to which a programming language discourages or prevents type errors. A type error is erroneous or undesirable program behaviour caused by a discrepancy between differing data types...
for more information).
Strong type systems can also have a downside, particularly with regard to forcing the programmer to engage in the unnecessary "bookkeeping" of making unnecessary explicit conversions in contexts where an implicit conversion would cause no harm. Pascal's type system has been described as "too strong", because the size of an array or string is part of its type, making some programming tasks very difficult.
On the contrary, in some languages, such as Haskell
Haskell
Haskell may refer to:*Haskell , a standardized pure functional programming language with non-strict semantics* Haskell Indian Nations University, a four year degree granting university in Lawrence, Kansas which offers free tuition to members of registered Native American tribes in the United...
, types are automatically inferred, so despite the strong type system, (most) type annotations are unnecessary.
Type safety contributes to program correctness, but cannot guarantee it unless the type checking itself becomes an undecidable problem
Undecidable problem
In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is impossible to construct a single algorithm that always leads to a correct yes-or-no answer....
. Depending on the specific type system, a program may give the wrong result and be safely typed, producing no compiler errors. For instance, division by zero
Division by zero
In mathematics, division by zero is division where the divisor is zero. Such a division can be formally expressed as a / 0 where a is the dividend . Whether this expression can be assigned a well-defined value depends upon the mathematical setting...
is not caught by the type checker in most programming languages; instead it is a runtime error. To prove the absence of more general defects, other kinds of formal methods, collectively known as program analyses
Program analysis (computer science)
In computer science, program analysis is the process of automatically analysing the behavior of computer programs. Two main approaches in program analysis are static program analysis and dynamic program analysis...
Software testing is an investigation conducted to provide stakeholders with information about the quality of the product or service under test. Software testing can also provide an objective, independent view of the software to allow the business to appreciate and understand the risks of software...
The word empirical denotes information gained by means of observation or experimentation. Empirical data are data produced by an experiment or observation....
method for finding errors that the type checker cannot detect.
A program typically associates each value with one particular type (although a type may have more than one subtype
Subtype
In programming language theory, subtyping or subtype polymorphism is a form of type polymorphism in which a subtype is a datatype that is related to another datatype by some notion of substitutability, meaning that program constructs, typically subroutines or functions, written to operate on...
In computer science, an object is any entity that can be manipulated by the commands of a programming language, such as a value, variable, function, or data structure...
, modules, communication channels, dependencies, or even types themselves, can become associated with a type. Some implementations might make the following identifications (though these are technically different concepts):
In object-oriented programming, a class is a construct that is used as a blueprint to create instances of itself – referred to as class instances, class objects, instance objects or simply objects. A class defines constituent members which enable these class instances to have state and behavior...
In computer programming, a data type is a classification identifying one of various types of data, such as floating-point, integer, or Boolean, that determines the possible values for that type; the operations that can be done on values of that type; the meaning of the data; and the way values of...
In the area of mathematical logic and computer science known as type theory, a kind is the type of a type constructor or, less commonly, the type of a higher-order type operator...
– a type of a type
A type system, specified for each programming language, controls the ways typed programs may behave, and makes behavior outside these rules illegal. An effect system
Effect system
An effect system is a formal system which describes the computational effects of computer programs, such as side effects. An effect system can be used to provide a compile-time checking of the possible effects of the program....
typically provides more fine-grained control than does a type system.
In mathematics, logic and computer science, type theory is any of several formal systems that can serve as alternatives to naive set theory, or the study of such formalisms in general...
studies type systems. More elaborate type systems (such as dependent type
Dependent type
In computer science and logic, a dependent type is a type that depends on a value. Dependent types play a central role in intuitionistic type theory and in the design of functional programming languages like ATS, Agda and Epigram....
s) allow for finer-grained program specifications to be verified by a type checker, but this comes at a price, as type inference and other properties generally become undecidable
Undecidable problem
In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is impossible to construct a single algorithm that always leads to a correct yes-or-no answer....
, and type checking itself is dependent on user-supplied proofs. It is challenging to find a sufficiently expressive type system that satisfies all programming practices in type safe manner. As Mark Manasse concisely put it:
Type checking
The process of verifying and enforcing the constraints of types – type checking – may occur either at compile-time (a static check) or run-time (a dynamic check). If a language specification requires its typing rules strongly (i.e., more or less allowing only those automatic type conversions that do not lose information), one can refer to the process as strongly typed, if not, as weakly typed. The terms are not used in a strict sense.
Static typing
A programming language is said to use static typing when type checking is performed during compile-time as opposed to run-time. Statically typed languages include ActionScript
ActionScript
ActionScript is an object-oriented language originally developed by Macromedia Inc. . It is a dialect of ECMAScript , and is used primarily for the development of websites and software targeting the Adobe Flash Player platform, used on Web pages in the form of...
Ada is a structured, statically typed, imperative, wide-spectrum, and object-oriented high-level computer programming language, extended from Pascal and other languages...
C is a general-purpose computer programming language developed between 1969 and 1973 by Dennis Ritchie at the Bell Telephone Laboratories for use with the Unix operating system....
The D programming language is an object-oriented, imperative, multi-paradigm, system programming language created by Walter Bright of Digital Mars. It originated as a re-engineering of C++, but even though it is mainly influenced by that language, it is not a variant of C++...
Eiffel is an ISO-standardized, object-oriented programming language designed by Bertrand Meyer and Eiffel Software. The design of the language is closely connected with the Eiffel programming method...
Go is a compiled, garbage-collected, concurrent programming language developed by Google Inc.The initial design of Go was started in September 2007 by Robert Griesemer, Rob Pike, and Ken Thompson. Go was officially announced in November 2009. In May 2010, Rob Pike publicly stated that Go was being...
Haskell is a standardized, general-purpose purely functional programming language, with non-strict semantics and strong static typing. It is named after logician Haskell Curry. In Haskell, "a function is a first-class citizen" of the programming language. As a functional programming language, the...
Java is a programming language originally developed by James Gosling at Sun Microsystems and released in 1995 as a core component of Sun Microsystems' Java platform. The language derives much of its syntax from C and C++ but has a simpler object model and fewer low-level facilities...
Objective-C is a reflective, object-oriented programming language that adds Smalltalk-style messaging to the C programming language.Today, it is used primarily on Apple's Mac OS X and iOS: two environments derived from the OpenStep standard, though not compliant with it...
OCaml , originally known as Objective Caml, is the main implementation of the Caml programming language, created by Xavier Leroy, Jérôme Vouillon, Damien Doligez, Didier Rémy and others in 1996...
Pascal is an influential imperative and procedural programming language, designed in 1968/9 and published in 1970 by Niklaus Wirth as a small and efficient language intended to encourage good programming practices using structured programming and data structuring.A derivative known as Object Pascal...
C++ is a statically typed, free-form, multi-paradigm, compiled, general-purpose programming language. It is regarded as an intermediate-level language, as it comprises a combination of both high-level and low-level language features. It was developed by Bjarne Stroustrup starting in 1979 at Bell...
In programming, RTTI refers to a C++ system that makes information about an object's data type available at runtime. Run-time type information can apply to simple data types, such as integers and characters, or to generic objects...
system. The C# type system performs static-like compile-time type checking, but also includes full runtime type checking. Perl
Perl
Perl is a high-level, general-purpose, interpreted, dynamic programming language. Perl was originally developed by Larry Wall in 1987 as a general-purpose Unix scripting language to make report processing easier. Since then, it has undergone many changes and revisions and become widely popular...
is statically typed with respect to distinguishing arrays, hashes, scalars, and subroutines.
Static typing is a limited form of program verification (see type safety
Type safety
In computer science, type safety is the extent to which a programming language discourages or prevents type errors. A type error is erroneous or undesirable program behaviour caused by a discrepancy between differing data types...
): accordingly, it allows many type errors to be caught early
Fail-fast
Fail-fast is a property of a system or module with respect to its response to failures. A fail-fast system is designed to immediately report at its interface any failure or condition that is likely to lead to failure. Fail-fast systems are usually designed to stop normal operation rather than...
in the development cycle. Static type checkers evaluate only the type information that can be determined at compile time, but are able to verify that the checked conditions hold for all possible executions of the program, which eliminates the need to repeat type checks every time the program is executed. Program execution may also be made more efficient (i.e. faster or taking reduced memory) by omitting runtime type checks and enabling other optimizations.
Because they evaluate type information during compilation and therefore lack type information that is only available at run-time, static type checkers are conservative. They will reject some programs that may be well-behaved at run-time, but that cannot be statically determined to be well-typed. For example, even if an expression always evaluates to true at run-time, a program containing the code
if then 42 else
will be rejected as ill-typed, because a static analysis cannot determine that the else branch won't be taken. The conservative behaviour of static type checkers is advantageous when evaluates to false infrequently: A static type checker can detect type errors in rarely used code paths. Without static type checking, even code coverage
Code coverage
Code coverage is a measure used in software testing. It describes the degree to which the source code of a program has been tested. It is a form of testing that inspects the code directly and is therefore a form of white box testing....
tests with 100% coverage may be unable to find such type errors. The tests may fail to detect such type errors, because the combination of all places where values are created and all places where a certain value is used must be taken into account.
TIOBE programming community index is an ordered list of programming languages, sorted by the frequency of web search using the name of the language as the keyword. The index covers searches in Google, Google Blogs, MSN, Yahoo!, Wikipedia and YouTube. The index is updated once a month. The current...
statically typed languages are not formally type safe
Type safety
In computer science, type safety is the extent to which a programming language discourages or prevents type errors. A type error is erroneous or undesirable program behaviour caused by a discrepancy between differing data types...
In computing, a programming language specification is an artifact that defines a programming language so that users and implementors can agree on what programs in that language mean....
enabling programmers to write code that circumvents the verification performed by a static type checker and so address a wider range of problems. For example, most C-style languages have type punning
Type punning
In computer science, type punning is a common term for any programming technique that subverts or circumvents the type system of a programming language in order to achieve an effect that would be difficult or impossible to achieve within the bounds of the formal language.In C and C++, constructs...
, and Haskell has such features as unsafePerformIO: such operations may be unsafe at runtime, in that they can cause unwanted behaviour due to incorrect typing of values when the program runs.
Dynamic typing
A programming language is said to be dynamically typed when the majority of its type checking is performed at run-time as opposed to at compile-time. In dynamic typing values have types, but variables do not; that is, a variable can refer to a value of any type. Dynamically typed languages include APL, Clojure
Clojure
Clojure |closure]]") is a recent dialect of the Lisp programming language created by Rich Hickey. It is a general-purpose language supporting interactive development that encourages a functional programming style, and simplifies multithreaded programming....
JavaScript is a prototype-based scripting language that is dynamic, weakly typed and has first-class functions. It is a multi-paradigm language, supporting object-oriented, imperative, and functional programming styles....
Jython, successor of JPython, is an implementation of the Python programming language written in Java.-Overview:Jython programs can seamlessly import and use any Java class. Except for some standard modules, Jython programs use Java classes instead of Python modules...
MATLAB is a numerical computing environment and fourth-generation programming language. Developed by MathWorks, MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages,...
GNU Octave is a high-level language, primarily intended for numerical computations. It provides a convenient command-line interface for solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with MATLAB...
Perl is a high-level, general-purpose, interpreted, dynamic programming language. Perl was originally developed by Larry Wall in 1987 as a general-purpose Unix scripting language to make report processing easier. Since then, it has undergone many changes and revisions and become widely popular...
(for user-defined types, but not built-in types), PHP
PHP
PHP is a general-purpose server-side scripting language originally designed for web development to produce dynamic web pages. For this purpose, PHP code is embedded into the HTML source document and interpreted by a web server with a PHP processor module, which generates the web page document...
Python is a general-purpose, high-level programming language whose design philosophy emphasizes code readability. Python claims to "[combine] remarkable power with very clear syntax", and its standard library is large and comprehensive...
Ruby is a dynamic, reflective, general-purpose object-oriented programming language that combines syntax inspired by Perl with Smalltalk-like features. Ruby originated in Japan during the mid-1990s and was first developed and designed by Yukihiro "Matz" Matsumoto...
Smalltalk is an object-oriented, dynamically typed, reflective programming language. Smalltalk was created as the language to underpin the "new world" of computing exemplified by "human–computer symbiosis." It was designed and created in part for educational use, more so for constructionist...
Tcl is a scripting language created by John Ousterhout. Originally "born out of frustration", according to the author, with programmers devising their own languages intended to be embedded into applications, Tcl gained acceptance on its own...
.
Implementations of dynamically-typed languages generally associate run-time objects with "tags" containing their type information. This run-time classification is then used to implement type checks and dispatch overloaded functions, but can also enable pervasive uses of dynamic dispatch
Dynamic dispatch
In computer science, dynamic dispatch is the process of mapping a message to a specific sequence of code at runtime. This is done to support the cases where the appropriate method can't be determined at compile-time...
Late binding is a computer programming mechanism in which the method being called upon an object is looked up by name at runtime. This is informally known as duck typing or name binding....
and similar idioms that would be cumbersome at best in a statically-typed language, requiring the use of variant type
Variant type
Variant is a data type in certain programming languages, particularly Visual Basic and C++ when using the Component Object Model.In Visual Basic the Variant data type is a tagged union that can be used to represent any other data type except fixed-length string type and...
Dynamic programming language is a term used broadly in computer science to describe a class of high-level programming languages that execute at runtime many common behaviors that other languages might perform during compilation, if at all...
features, such as generating types and functionality based on run-time data. (Nevertheless, dynamically typed languages need not support any or all such features, and some dynamic programming languages are statically typed.) On the other hand, dynamic typing provides fewer a priori guarantees: a dynamically typed language accepts and attempts to execute some programs that would be ruled as invalid by a static type checker, either due to errors in the program or due to static type checking being too conservative.
Dynamic typing may result in runtime type errors—that is, at runtime, a value may have an unexpected type, and an operation nonsensical for that type is applied. Such errors may occur long after the place where the programming mistake was made—that is, the place where the wrong type of data passed into a place it should not have. This may make the bug difficult to locate.
Dynamically typed language systems' run-time checks can potentially be more sophisticated than those of statically typed languages, as they can use dynamic information as well as any information from the source code. On the other hand, runtime checks only assert that conditions hold in a particular execution of the program, and the checks are repeated for every execution of the program.
Development in dynamically typed languages is often supported by programming practices such as unit testing. Testing is a key practice in professional software development, and is particularly important in dynamically typed languages. In practice, the testing done to ensure correct program operation can detect a much wider range of errors than static type-checking, but conversely cannot search as comprehensively for the errors that static type checking is able to detect.
Combinations of dynamic and static typing
The presence of static typing in a programming language does not necessarily imply the absence of all dynamic typing mechanisms. For example, Java and some other ostensibly statically typed languages, support downcasting
Downcasting
In object-oriented programming, downcasting or type refinement is the act of casting a reference of a base class to one of its derived classes....
and other type operations that depend on runtime type checks, a form of dynamic typing. More generally, most programming languages include mechanisms for dispatching over different 'kinds' of data, such as disjoint union
Disjoint union
In mathematics, the term disjoint union may refer to one of two different concepts:* In set theory, a disjoint union is a modified union operation that indexes the elements according to which set they originated in; disjoint sets have no element in common.* In probability theory , a disjoint union...
Subtype polymorphism, almost universally called just polymorphism in the context of object-oriented programming, is the ability to create a variable, a function, or an object that has more than one form. The word derives from the Greek "πολυμορφισμός" meaning "having multiple forms"...
Variant is a data type in certain programming languages, particularly Visual Basic and C++ when using the Component Object Model.In Visual Basic the Variant data type is a tagged union that can be used to represent any other data type except fixed-length string type and...
s: Even when not interacting with type annotations or type checking, such mechanisms are materially similar to dynamic typing implementations. See programming language
Programming language
A programming language is an artificial language designed to communicate instructions to a machine, particularly a computer. Programming languages can be used to create programs that control the behavior of a machine and/or to express algorithms precisely....
for more discussion of the interactions between static and dynamic typing.
Clojure |closure]]") is a recent dialect of the Lisp programming language created by Rich Hickey. It is a general-purpose language supporting interactive development that encourages a functional programming style, and simplifies multithreaded programming....
Cython is a programming language to simplify writing C and C++ extension modules for the CPython Python runtime. Strictly speaking, Cython syntax is a superset of Python syntax additionally supporting:...
, are dynamically typed by default, but allow this behaviour to be overridden through the use of explicit type hints that result in static typing. One reason to use such hints would be to achieve the performance benefits of static typing in performance-sensitive parts of code.
As of the 4.0 Release, the .NET Framework supports a variant of dynamic typing via the System.Dynamic namespace whereby a static object of type 'dynamic' is a placeholder for the .NET runtime to interrogate its dynamic facilities to resolve the object reference.
Static and dynamic type checking in practice
The choice between static and dynamic typing requires trade-off
Trade-off
A trade-off is a situation that involves losing one quality or aspect of something in return for gaining another quality or aspect...
s.
Static typing can find type errors reliably at compile time. This should increase the reliability of the delivered program. However, programmers disagree over how commonly type errors occur, and thus disagree over the proportion of those bugs that are coded that would be caught by appropriately representing the designed types in code. Static typing advocates believe programs are more reliable when they have been well type-checked, while dynamic typing advocates point to distributed code that has proven reliable and to small bug databases. The value of static typing, then, presumably increases as the strength of the type system is increased. Advocates of dependently typed languages
Dependent type
In computer science and logic, a dependent type is a type that depends on a value. Dependent types play a central role in intuitionistic type theory and in the design of functional programming languages like ATS, Agda and Epigram....
Dependent ML is an experimental functional programming language proposed by Hongwei Xi and Frank Pfenning. Dependent ML extends ML by a restricted notion of dependent types: types may be dependent on static indices of type Nat...
and Epigram have suggested that almost all bugs can be considered type errors, if the types used in a program are properly declared by the programmer or correctly inferred by the compiler.
Static typing usually results in compiled code that executes more quickly. When the compiler knows the exact data types that are in use, it can produce optimized machine code. Further, compilers for statically typed languages can find assembler shortcuts more easily. Some dynamically typed languages such as Common Lisp
Common Lisp
Common Lisp, commonly abbreviated CL, is a dialect of the Lisp programming language, published in ANSI standard document ANSI INCITS 226-1994 , . From the ANSI Common Lisp standard the Common Lisp HyperSpec has been derived for use with web browsers...
allow optional type declarations for optimization for this very reason. Static typing makes this pervasive. See optimization
Optimization (computer science)
In computer science, program optimization or software optimization is the process of modifying a software system to make some aspect of it work more efficiently or use fewer resources...
.
By contrast, dynamic typing may allow compilers to run more quickly and allow interpreters to dynamically load new code, since changes to source code in dynamically typed languages may result in less checking to perform and less code to revisit. This too may reduce the edit-compile-test-debug cycle.
Type inference refers to the automatic deduction of the type of an expression in a programming language. If some, but not all, type annotations are already present it is referred to as type reconstruction....
(such as C and Java) require that programmers declare the types they intend a method or function to use. This can serve as additional documentation for the program, which the compiler will not permit the programmer to ignore or permit to drift out of synchronization. However, a language can be statically typed without requiring type declarations (examples include Haskell
Haskell (programming language)
Haskell is a standardized, general-purpose purely functional programming language, with non-strict semantics and strong static typing. It is named after logician Haskell Curry. In Haskell, "a function is a first-class citizen" of the programming language. As a functional programming language, the...
, Scala and to a lesser extent C#), so explicit type declaration is not a necessary requirement for static typing in all languages.
Dynamic typing allows constructs that some static type checking would reject as illegal. For example, eval
Eval
In some programming languages, eval is a function which evaluates a string as though it were an expression and returns a result; in others, it executes multiple lines of code as though they had been included instead of the line including the eval...
functions, which execute arbitrary data as code, become possible. An eval function is possible with static typing, but requires advanced uses of algebraic data types. Furthermore, dynamic typing better accommodates transitional code and prototyping, such as allowing a placeholder data structure (mock object
Mock object
In object-oriented programming, mock objects are simulated objects that mimic the behavior of real objects in controlled ways. A programmer typically creates a mock object to test the behavior of some other object, in much the same way that a car designer uses a crash test dummy to simulate the...
) to be transparently used in place of a full-fledged data structure (usually for the purposes of experimentation and testing).
In computer programming with object-oriented programming languages, duck typing is a style of dynamic typing in which an object's current set of methods and properties determines the valid semantics, rather than its inheritance from a particular class or implementation of a specific interface...
Metaprogramming is the writing of computer programs that write or manipulate other programs as their data, or that do part of the work at compile time that would otherwise be done at runtime...
more effective and easier to use. For example, C++
C++
C++ is a statically typed, free-form, multi-paradigm, compiled, general-purpose programming language. It is regarded as an intermediate-level language, as it comprises a combination of both high-level and low-level language features. It was developed by Bjarne Stroustrup starting in 1979 at Bell...
Templates are a feature of the C++ programming language that allow functions and classes to operate with generic types. This allows a function or class to work on many different data types without being rewritten for each one....
are typically more cumbersome to write than the equivalent Ruby
Ruby (programming language)
Ruby is a dynamic, reflective, general-purpose object-oriented programming language that combines syntax inspired by Perl with Smalltalk-like features. Ruby originated in Japan during the mid-1990s and was first developed and designed by Yukihiro "Matz" Matsumoto...
Python is a general-purpose, high-level programming language whose design philosophy emphasizes code readability. Python claims to "[combine] remarkable power with very clear syntax", and its standard library is large and comprehensive...
code. More advanced run-time constructs such as metaclass
Metaclass
In object-oriented programming, a metaclass is a class whose instances are classes. Just as an ordinary class defines the behavior of certain objects, a metaclass defines the behavior of certain classes and their instances. Not all object-oriented programming languages support metaclasses...
es and introspection are often more difficult to use in statically typed languages. In some languages, such features may also be used e.g. to generate new types and behaviors on the fly, based on run-time data. Such advanced constructs are often provided by dynamic programming language
Dynamic programming language
Dynamic programming language is a term used broadly in computer science to describe a class of high-level programming languages that execute at runtime many common behaviors that other languages might perform during compilation, if at all...
s; many of these are dynamically typed, although dynamic typing need not be related to dynamic programming languages.
Strong and weak typing: Liskov Definition
In 1974 Jones and Liskov describe a strong-typed language as one in which “each type defines a set of primitive operations that are the only direct means for manipulating objects of that type.”
Jackson wrote, “In a strongly typed language each data area will have a distinct type and each process will state its communication requirements in terms of these types.”
Strong and weak typing
A type system is said to feature strong typing when it specifies one or more restrictions on how operations involving values of different data types can be intermixed. A computer language that implements strong typing will prevent the successful execution of an operation on arguments that have the wrong type.
Weak typing means that a language implicitly converts (or casts) types when used. Consider the following example:
var x := 5; // (1) (x is an integer) var y := "37"; // (2) (y is a string)
x + y; // (3) (?)
In a weakly typed language, the result of this operation is unclear. Some languages, such as Visual Basic
Visual Basic
Visual Basic is the third-generation event-driven programming language and integrated development environment from Microsoft for its COM programming model...
, would produce runnable code producing the result 42: the system would convert the string "37" into the number 37 to forcibly make sense of the operation. Other languages like JavaScript
JavaScript
JavaScript is a prototype-based scripting language that is dynamic, weakly typed and has first-class functions. It is a multi-paradigm language, supporting object-oriented, imperative, and functional programming styles....
would produce the result "537": the system would convert the number 5 to the string "5" and then concatenate the two. In both Visual Basic and JavaScript, the resulting type is determined by rules that take both operand
Operand
In mathematics, an operand is the object of a mathematical operation, a quantity on which an operation is performed.-Example :The following arithmetic expression shows an example of operators and operands:3 + 6 = 9\;...
s into consideration. In JavaScript, the order of the operands is not significant (y + x would be "375"). As the use of the "+" operator on a String and a Number (a JavaScript type) results in a String - if the value of y was a String that could not be converted to a Number (e.g. "Hello World") is moot. In some languages, such as AppleScript
AppleScript
AppleScript is a scripting language created by Apple Inc. and built into Macintosh operating systems since System 7. The term "AppleScript" may refer to the scripting system itself, or to particular scripts that are written in the AppleScript language....
, the type of the resulting value is determined by the type of the left-most operand only.
In the same manner, due to JavaScript's dynamic type conversions:
var y = 2 / 0; // y now equals a constant for infinity
y
C is a general-purpose computer programming language developed between 1969 and 1973 by Dennis Ritchie at the Bell Telephone Laboratories for use with the Unix operating system....
In computer science, type conversion, typecasting, and coercion are different ways of, implicitly or explicitly, changing an entity of one data type into another. This is done to take advantage of certain features of type hierarchies or type representations...
gone wrong exemplifies the problem that can occur, if strong typing is absent; if a programmer casts a value from one type to another in C, not only must the compiler allow the code at compile time, but the runtime must allow it as well. This may permit more compact and faster C code, but it can make debugging
Debugging
Debugging is a methodical process of finding and reducing the number of bugs, or defects, in a computer program or a piece of electronic hardware, thus making it behave as expected. Debugging tends to be harder when various subsystems are tightly coupled, as changes in one may cause bugs to emerge...
more difficult.
Safely and unsafely typed systems
A third way of categorizing the type system of a programming language uses the safety of typed operations and conversions. Computer scientists consider a language "type-safe", if it does not allow operations or conversions that lead to erroneous conditions.
Some observers use the term memory-safe language (or just safe language) to describe languages that do not allow undefined operations to occur. For example, a memory-safe language will check array bounds
Bounds checking
In computer programming, bounds checking is any method of detecting whether a variable is within some bounds before its use. It is particularly relevant to a variable used as an index into an array to ensure its value lies within the bounds of the array...
, or else statically guarantee (i.e., at compile time before execution) that array accesses out of the array boundaries will cause compile-time and perhaps runtime errors.
var x := 5; // (1)
var y := "37"; // (2)
var z := x + y; // (3)
Visual Basic is the third-generation event-driven programming language and integrated development environment from Microsoft for its COM programming model...
, variable in the example acquires the value 42. While the programmer may or may not have intended this, the language defines the result specifically, and the program does not crash or assign an ill-defined value to . In this respect, such languages are type-safe; however, in some languages, if the value of was a string that could not be converted to a number (e.g. "Hello World"), the results would be undefined. Such languages are type-safe (in that they will not crash), but can easily produce undesirable results. In other languages like JavaScript
JavaScript
JavaScript is a prototype-based scripting language that is dynamic, weakly typed and has first-class functions. It is a multi-paradigm language, supporting object-oriented, imperative, and functional programming styles....
, the numeric operand would be converted to a string, and then concatenation performed. In this case, the results are not undefined and are predictable.
Now let us look at the same example in C:
int x = 5;
char y[] = "37";
char* z = x + y;
In this example will point to a memory address five characters beyond , equivalent to three characters after the terminating zero character of the string pointed to by . The content of that location is undefined, and might lie outside addressable memory. The mere computation of such a pointer may result in undefined behavior (including the program crashing) according to C standards, and in typical systems dereferencing z at this point could cause the program to crash. We have a well-typed, but not memory-safe program—a condition that cannot occur in a type-safe language.
JavaScript is a prototype-based scripting language that is dynamic, weakly typed and has first-class functions. It is a multi-paradigm language, supporting object-oriented, imperative, and functional programming styles....
, the use of special numeric values and constants allows type-safety for mathematical operations without resulting in runtime errors. For example, when dividing a by a , or a by zero.
var x = 32;
var aString = new String("A");
x = x/aString; // x now equals the constant NaN, meaning Not A Number
isNaN(x); // returns true
typeof(x); // returns "number"
var y = 2 / 0; // y now equals a constant for infinity
y Number.POSITIVE_INFINITY; // returns true
typeof(y); // returns "number"
Variable levels of type checking
Some languages allow different levels of checking to apply to different regions of code. Examples include:-
Perl is a high-level, general-purpose, interpreted, dynamic programming language. Perl was originally developed by Larry Wall in 1987 as a general-purpose Unix scripting language to make report processing easier. Since then, it has undergone many changes and revisions and become widely popular...
PHP is a general-purpose server-side scripting language originally designed for web development to produce dynamic web pages. For this purpose, PHP code is embedded into the HTML source document and interpreted by a web server with a PHP processor module, which generates the web page document...
suppresses some error messages.
The Option Strict On in VB.NET allows the compiler to require a conversion between objects.
Additional tools such as lint and IBM Rational Purify can also be used to achieve a higher level of strictness.
Gilad Bracha is a software engineer, a co-author of the second and third editions of the Java Language Specification, a major contributor to the second edition of the Java Virtual Machine Specification, and the creator of the Newspeak programming language....
, that choice of type system be made independent of choice of language; that a type system should be a module that
can be "plugged" into a language as required. He believes this is advantageous, because what he calls mandatory type systems make languages less expressive and code more fragile. The requirement that types do not affect the semantics of the language is difficult to fulfil: for instance, class based inheritance becomes impossible.
Polymorphism and types
The term "polymorphism" refers to the ability of code (in particular, methods or classes) to act on values of multiple types, or to the ability of different instances of the same data structure to contain elements of different types. Type systems that allow polymorphism generally do so in order to improve the potential for code re-use: in a language with polymorphism, programmers need only implement a data structure such as a list or an associative array
Associative array
In computer science, an associative array is an abstract data type composed of a collection of pairs, such that each possible key appears at most once in the collection....
once, rather than once for each type of element with which they plan to use it. For this reason computer scientists sometimes call the use of certain forms of polymorphism generic programming
Generic programming
In a broad definition, generic programming is a style of computer programming in which algorithms are written in terms of to-be-specified-later types that are then instantiated when needed for specific types provided as parameters...
. The type-theoretic foundations of polymorphism are closely related to those of abstraction
Abstraction (computer science)
In computer science, abstraction is the process by which data and programs are defined with a representation similar to its pictorial meaning as rooted in the more complex realm of human life and language with their higher need of summarization and categorization , while hiding away the...
In programming language theory, subtyping or subtype polymorphism is a form of type polymorphism in which a subtype is a datatype that is related to another datatype by some notion of substitutability, meaning that program constructs, typically subroutines or functions, written to operate on...
In object-oriented programming, a method is a subroutine associated with a class. Methods define the behavior to be exhibited by instances of the associated class at program run time...
m on an object does not rely on the declared type of the object; only that the object, of whatever type, must supply an implementation of the method called, when called, at run-time.
A structural type system is a major class of type system, in which type compatibility and equivalence are determined by the type's structure, and not by other characteristics such as its name or place of declaration. Structural systems are used to determine if types are equivalent and whether a...
in that, if the part (of the whole module structure) needed for a given local computation is present at runtime, the duck type system is satisfied in its type identity analysis. On the other hand, a structural type system would require the analysis of the whole module structure at compile time to determine type identity or type dependence.
In computer science, a nominal or nominative type system is a major class of type system, in which compatibility and equivalence of data types is determined by explicit declarations and/or the name of the types. Nominative systems are used to determine if types are equivalent, as well as if a type...
in a number of aspects. The most prominent ones are that for duck typing, type information is determined at runtime (as contrasted to compile time), and the name of the type is irrelevant to determine type identity or type dependence; only partial structure information is required for that for a given point in the program execution.
Duck typing uses the premise that (referring to a value) "if it walks like a duck, and quacks like a duck, then it is a duck" (this is a reference to the duck test
Duck test
The duck test is a humorous term for a form of inductive reasoning. This is its usual expression:The test implies that a person can identify an unknown subject by observing that subject's habitual characteristics...
James Whitcomb Riley was an American writer, poet, and best selling author. During his lifetime he was known as the Hoosier Poet and Children's Poet for his dialect works and his children's poetry respectively...
Alex Martelli is an Italian computer engineer and member of the Python Software Foundation. Since early 2005, he works as "Über Tech Lead" for Google, Inc. in Mountain View, California...
in a 2000 message to the comp.lang.python newsgroup
Newsgroup
A usenet newsgroup is a repository usually within the Usenet system, for messages posted from many users in different locations. The term may be confusing to some, because it is usually a discussion group. Newsgroups are technically distinct from, but functionally similar to, discussion forums on...
Python is a general-purpose, high-level programming language whose design philosophy emphasizes code readability. Python claims to "[combine] remarkable power with very clear syntax", and its standard library is large and comprehensive...
).
Specialized type systems
Many type systems have been created that are specialized for use in certain environments with certain types of data, or for out-of-band static program analysis. Frequently, these are based on ideas from formal type theory
Type theory
In mathematics, logic and computer science, type theory is any of several formal systems that can serve as alternatives to naive set theory, or the study of such formalisms in general...
and are only available as part of prototype research systems.
In computer science and logic, a dependent type is a type that depends on a value. Dependent types play a central role in intuitionistic type theory and in the design of functional programming languages like ATS, Agda and Epigram....
s are based on the idea of using scalars or values to more precisely describe the type of some other value. For example, might be the type of a 3×3 matrix. We can then define typing rules such as the following rule for matrix multiplication:
where , , are arbitrary positive integer values. A variant of ML called Dependent ML
Dependent ML
Dependent ML is an experimental functional programming language proposed by Hongwei Xi and Frank Pfenning. Dependent ML extends ML by a restricted notion of dependent types: types may be dependent on static indices of type Nat...
has been created based on this type system, but because type checking for conventional dependent types is undecidable, not all programs using them can be type-checked without some kind of limits. Dependent ML limits the sort of equality it can decide to Presburger arithmetic
Presburger arithmetic
Presburger arithmetic is the first-order theory of the natural numbers with addition, named in honor of Mojżesz Presburger, who introduced it in 1929. The signature of Presburger arithmetic contains only the addition operation and equality, omitting the multiplication operation entirely...
. Other languages such as Epigram make the value of all expressions in the language decidable so that type checking can be decidable. It is also possible to make the language Turing-complete at the price of undecidable type checking, as in Cayenne.
Linear logic is a substructural logic proposed by Jean-Yves Girard as a refinement of classical and intuitionistic logic, joining the dualities of the former with many of the constructive properties of the latter...
In computing, a unique type guarantees that an object is used in a single-threaded way, with at most a single reference to it. If a value has a unique type, a function applied to it can be optimized to update the value in-place in the object code. In-place updates improve the efficiency of...
s, are types assigned to values having the property that they have one and only one reference to them at all times. These are valuable for describing large immutable values such as files, strings, and so on, because any operation that simultaneously destroys a linear object and creates a similar object (such as 'str = str + "a"') can be optimized "under the hood" into an in-place mutation. Normally this is not possible, as such mutations could cause side effects on parts of the program holding other references to the object, violating referential transparency. They are also used in the prototype operating system Singularity
Singularity (operating system)
Singularity is an experimental operating system being built by Microsoft Research since 2003. It is intended as a highly-dependable OS in which the kernel, device drivers, and applications are all written in managed code.- Workings :...
for interprocess communication, statically ensuring that processes cannot share objects in shared memory in order to prevent race conditions. The Clean language (a Haskell
Haskell (programming language)
Haskell is a standardized, general-purpose purely functional programming language, with non-strict semantics and strong static typing. It is named after logician Haskell Curry. In Haskell, "a function is a first-class citizen" of the programming language. As a functional programming language, the...
-like language) uses this type system in order to gain a lot of speed while remaining safe.
Intersection types
Intersection types are types describing values that belong to both of two other given types with overlapping value sets. For example, in most implementations of C the signed char has range -128 to 127 and the unsigned char has range 0 to 255, so the intersection type of these two types would have range 0 to 127. Such an intersection type could be safely passed into functions expecting either signed or unsigned chars, because it is compatible with both types.
Intersection types are useful for describing overloaded function types: For example, if " → " is the type of functions taking an integer argument and returning an integer, and " → " is the type of functions taking a float argument and returning a float, then the intersection of these two types can be used to describe functions that do one or the other, based on what type of input they are given. Such a function could be passed into another function expecting an " → " function safely; it simply would not use the " → " functionality.
In a subclassing hierarchy, the intersection of a type and an ancestor type (such as its parent) is the most derived type. The intersection of sibling types is empty.
Forsythe, in business, can mean:* Forsythe Technology, Inc., an American businessForsythe, as a surname, includes the following people:* Abe Forsythe , Australian actor* Bruce Forsythe , British entertainer...
language includes a general implementation of intersection types. A restricted form is refinement types.
Union types
Union types are types describing values that belong to either of two types. For example, in C, the signed char has range -128 to 127, and the unsigned char has range 0 to 255, so the union of these two types would have range -128 to 255. Any function handling this union type would have to deal with integers in this complete range. More generally, the only valid operations on a union type are operations that are valid on both types being unioned. C's "union" concept is similar to union types, but is not typesafe, as it permits operations that are valid on either type, rather than both. Union types are important in program analysis, where they are used to represent symbolic values whose exact nature (e.g., value or type) is not known.
In a subclassing hierarchy, the union of a type and an ancestor type (such as its parent) is the ancestor type. The union of sibling types is a subtype of their common ancestor (that is, all operations permitted on their common ancestor are permitted on the union type, but they may also have other valid operations in common).
Existential types
Existential types are frequently used in connection with record types to represent modules and abstract data type
Abstract data type
In computing, an abstract data type is a mathematical model for a certain class of data structures that have similar behavior; or for certain data types of one or more programming languages that have similar semantics...
s, due to their ability to separate implementation from interface. For example, the type "T = ∃X { a: X; f: (X → int); }" describes a module interface that has a data member of type X and a function that takes a parameter of the same type X and returns an integer. This could be implemented in different ways; for example:
intT = { a: int; f: (int → int); }
floatT = { a: float; f: (float → int); }
These types are both subtypes of the more general existential type T and correspond to concrete implementation types, so any value of one of these types is a value of type T. Given a value "t" of type "T", we know that "t.f(t.a)" is well-typed, regardless of what the abstract type X is. This gives flexibility for choosing types suited to a particular implementation while clients that use only values of the interface type—the existential type—are isolated from these choices.
In general it's impossible for the typechecker to infer which existential type a given module belongs to. In the above example intT { a: int; f: (int → int); } could also have the type ∃X { a: X; f: (int → int); }. The simplest solution is to annotate every module with its intended type, e.g.:
Although abstract data types and modules had been implemented in programming languages for quite some time, it wasn't until 1988 that John C. Mitchell
John C. Mitchell
John Clifford Mitchell is professor of computer science and electrical engineering at Stanford University. He has published in the area of programming language theory and computer security....
Gordon D. Plotkin, FRS, FRSE is a Scottish computer scientist.Gordon Plotkin is best-known for his introduction of structural operational semantics and his work on denotational semantics. In particular, his notes on A Structural Approach to Operational Semantics of 1981 were very influential...
established the formal theory under the slogan: "Abstract [data] types have existential type". The theory is a second-order typed lambda calculus
Typed lambda calculus
A typed lambda calculus is a typed formalism that uses the lambda-symbol to denote anonymous function abstraction. In this context, types are usually objects of a syntactic nature that are assigned to lambda terms; the exact nature of a type depends on the calculus considered...
System F, also known as the polymorphic lambda calculus or the second-order lambda calculus, is a typed lambda calculus that differs from the simply typed lambda calculus by the introduction of a mechanism of universal quantification over types...
, but with existential instead of universal quantification.
Explicit or implicit declaration and inference
Many static type systems, such as those of C and Java, require type declarations: The programmer must explicitly associate each variable with a particular type. Others, such as Haskell's, perform type inference
Type inference
Type inference refers to the automatic deduction of the type of an expression in a programming language. If some, but not all, type annotations are already present it is referred to as type reconstruction....
: The compiler draws conclusions about the types of variables based on how programmers use those variables. For example, given a function that adds and together, the compiler can infer that and must be numbers – since addition is only defined for numbers. Therefore, any call to elsewhere in the program that specifies a non-numeric type (such as a string or list) as an argument would signal an error.
Numerical and string constants and expressions in code can and often do imply type in a particular context. For example, an expression might imply a type of floating-point, while might imply a list of integers – typically an array.
Type inference is in general possible, if it is decidable
Decidability (logic)
In logic, the term decidable refers to the decision problem, the question of the existence of an effective method for determining membership in a set of formulas. Logical systems such as propositional logic are decidable if membership in their set of logically valid formulas can be effectively...
in the type theory in question. Moreover, even if inference is undecidable in general for a given type theory, inference is often possible for a large subset of real-world programs. Haskell's type system, a version of Hindley-Milner, is a restriction of System Fω to so-called rank-1 polymorphic types, in which type inference is decidable. Most Haskell compilers allow arbitrary-rank polymorphism as an extension, but this makes type inference undecidable. (Type checking is decidable, however, and rank-1 programs still have type inference; higher rank polymorphic programs are rejected unless given explicit type annotations.)
Types of types
In the area of mathematical logic and computer science known as type theory, a kind is the type of a type constructor or, less commonly, the type of a higher-order type operator...
In computer science, typeful programming is a programming style identified by widespread use of type information handled through mechanical typechecking techniques. The concept was introduced in a paper of the same name by Luca Cardelli in 1991....
Haskell is a standardized, general-purpose purely functional programming language, with non-strict semantics and strong static typing. It is named after logician Haskell Curry. In Haskell, "a function is a first-class citizen" of the programming language. As a functional programming language, the...
In computer science, primitive data type is either of the following:* a basic type is a data type provided by a programming language as a basic building block...
The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...
and floating-point number
Boolean
Integral types – types of whole numbers; e.g., integers and natural numbers
Floating point types – types of numbers in floating-point representation
In programming language theory, a reference type is a data type that can only be accessed by references. Unlike objects of value types, objects of reference types cannot be directly embedded into composite objects and are always dynamically allocated...
In programming languages and type theory, an option type or maybe type is a polymorphic type that represents encapsulation of an optional value; e.g. it is used as the return type of functions which may or may not return a meaningful value when they're applied...
In computer science, a composite data type is any data type which can be constructed in a program using its programming language's primitive data types and other composite types...
s – types composed of basic types; e.g., arrays or records
Record (computer science)
In computer science, a record is an instance of a product of primitive data types called a tuple. In C it is the compound data in a struct. Records are among the simplest data structures. A record is a value that contains other values, typically in fixed number and sequence and typically indexed...
In computing, an abstract data type is a mathematical model for a certain class of data structures that have similar behavior; or for certain data types of one or more programming languages that have similar semantics...
In programming language theory, subtyping or subtype polymorphism is a form of type polymorphism in which a subtype is a datatype that is related to another datatype by some notion of substitutability, meaning that program constructs, typically subroutines or functions, written to operate on...
In computer science, an object type is a datatype which is used in object-oriented programming to wrap a non-object type to make it look like a dynamic object....
In type theory and programming languages, a type variable is a mathematical variable ranging over types. Even in programming languages that allow mutable variables, a type variable remains an abstraction, in the sense that it does not correspond to some memory locations.Programming languages that...
In computer science, a function type is the type of a variable or parameter to which a function has or can be assigned or the result type of a higher-order function returning a function....
In predicate logic, an existential quantification is the predication of a property or relation to at least one member of the domain. It is denoted by the logical operator symbol ∃ , which is called the existential quantifier...
types, such as modules
Refinement types – types that identify subsets of other types
In computer science and logic, a dependent type is a type that depends on a value. Dependent types play a central role in intuitionistic type theory and in the design of functional programming languages like ATS, Agda and Epigram....
s – types that depend on terms (values)
Ownership types – types that describe or constrain the structure of object-oriented systems
Pre-defined types provided for convenience in real-world applications, such as date, time and money.
Compatibility: equivalence and subtyping
A type-checker for a statically typed language must verify that the type of any expression
Expression (programming)
An expression in a programming language is a combination of explicit values, constants, variables, operators, and functions that are interpreted according to the particular rules of precedence and of association for a particular programming language, which computes and then produces another value...
is consistent with the type expected by the context in which that expression appears. For instance, in an assignment statement of the form x := e,
the inferred type of the expression e must be consistent with the declared or inferred type of the variable x. This notion of consistency, called compatibility, is specific to each programming language.
If the type of e and the type of x are the same and assignment is allowed for that type, then this is a valid expression. In the simplest type systems, therefore, the question of whether two types are compatible reduces to that of whether they are equal}} (or equivalent). Different languages, however, have different criteria for when two type expressions are understood to denote the same type. These different equational theories}} of types vary widely, two extreme cases being structural type system
Structural type system
A structural type system is a major class of type system, in which type compatibility and equivalence are determined by the type's structure, and not by other characteristics such as its name or place of declaration. Structural systems are used to determine if types are equivalent and whether a...
s, in which any two types are equivalent that describe values with the same structure, and nominative type system
Nominative type system
In computer science, a nominal or nominative type system is a major class of type system, in which compatibility and equivalence of data types is determined by explicit declarations and/or the name of the types. Nominative systems are used to determine if types are equivalent, as well as if a type...
s, in which no two syntactically distinct type expressions denote the same type (i.e., types must have the same "name" in order to be equal).
In programming language theory, subtyping or subtype polymorphism is a form of type polymorphism in which a subtype is a datatype that is related to another datatype by some notion of substitutability, meaning that program constructs, typically subroutines or functions, written to operate on...
, the compatibility relation is more complex. In particular, if A is a subtype of B, then a value of type A can be used in a context where one of type B is expected, even if the reverse is not true. Like equivalence, the subtype relation is defined differently for each programming language, with many variations possible. The presence of parametric or ad hoc polymorphism in a language may also have implications for type compatibility.
Programming style
Some programmers prefer statically typed languages; others prefer dynamically typed languages. Statically typed languages alert programmers to type errors during compilation, and they may perform better at runtime. Advocates of dynamically typed languages claim they better support rapid prototyping and that type errors are only a small subset of errors in a program. Likewise, there is often no need to manually declare all types in statically typed languages with type inference; thus, the need for the programmer to explicitly specify types of variables is automatically lowered for such languages; and some dynamic languages have run-time optimisers that can generate fast code approaching the speed of static language compilers, often by using partial type inference.
See also
Within the type system of a programming language, covariance and contravariance refers to the ordering of types from narrower to wider and their interchangeability or equivalence in certain situations ....
In object oriented computer programming, operator overloading—less commonly known as operator ad-hoc polymorphism—is a specific case of polymorphism, where different operators have different implementations depending on their arguments...
Subtype polymorphism, almost universally called just polymorphism in the context of object-oriented programming, is the ability to create a variable, a function, or an object that has more than one form. The word derives from the Greek "πολυμορφισμός" meaning "having multiple forms"...
A programming language is an artificial language designed to communicate instructions to a machine, particularly a computer. Programming languages can be used to create programs that control the behavior of a machine and/or to express algorithms precisely....
In computing, signedness is a property of data types representing numbers in computer programs. A numeric variable is signed if it can represent both positive and negative numbers, and unsigned if it can only represent non-negative numbers .As signed numbers can represent negative numbers, they...
In computer science, a type signature or type annotation defines the inputs and outputs for a function, subroutine or method. A type signature includes at least the function name and the number of its arguments...
In mathematics, logic and computer science, type theory is any of several formal systems that can serve as alternatives to naive set theory, or the study of such formalisms in general...
might be the type of a 3×3 matrix. We can then define typing rules such as the following rule for matrix multiplication:
, 
, 
are arbitrary positive integer values. A variant of ML called Dependent ML