A programming language may further associate an operation with various resolutions for each type, in the case of type polymorphism. Type theory is the study of type systems. The concrete types of some programming languages, such as integers and strings, depend on practical issues of computer architecture, compiler implementation, and language The Commuter Services Office (CSO) provides transportation and parking assistance to employees and students of Thomas Jefferson University, Thomas Jefferson University Hospital, and Jefferson University Physicians.. A partnership with CSO and those companies providing area transportation and parking results in a savings passed on to you. The benefits include discounts on the following: transit A programming language may further associate an operation with various resolutions for each type, in the case of type polymorphism. Type theory is the study of type systems. The concrete types of some programming languages, such as integers and strings, depend on practical issues of computer architecture, compiler implementation, and language
Type system - Wikipedia
In programming languagesa type system is a logical system comprising a set of rules that assigns a property called a type to the various constructs of a computer programsuch as variablesexpressionsfunctions or modules. The main purpose of a type system is to reduce possibilities for bugs in computer programs [2] by defining interfaces between different parts of a computer program, and then checking that the parts have been connected in a consistent way.
This checking can happen statically at compile timedynamically at run timeor as a combination of both. Type systems have other purposes as well, such as expressing business rules, enabling certain compiler optimizationsallowing for multiple dispatchproviding a form of documentation, etc. A type system associates a type with each computed value and, by examining the flow of these values, attempts to ensure or prove that no type errors can occur.
The given type system in question determines what constitutes a type error, but in general, the aim is jeremy siek phd thesis language generic programming prevent operations expecting a certain kind of value from being used with values for which that operation does not make sense logic errors.
Type systems are often specified as part of programming languages and built into interpreters and compilers, although the type system of a language can be extended by optional tools that perform added checks using the language's original type syntax and grammar. An example of a simple type system is that of the C language. The portions of a C program are the function definitions.
One function is invoked by another function. The interface of a function states the name of the function and a list of values that are passed to the function's code. The code of an invoking function states the name of the invoked, along with the names jeremy siek phd thesis language generic programming variables that hold values to pass to it. During execution, the values are placed into temporary storage, jeremy siek phd thesis language generic programming, then execution jumps to the code of the invoked function.
The invoked function's code accesses the values and makes use of them. If the instructions inside the function are written with the assumption of receiving an integer value, but the calling code passed a floating-point valuethen the wrong result will be computed by the invoked function. The C compiler checks the types of the arguments passed to a function when it is called against the types of the parameters declared in the function's definition.
If the types do not match, the compiler throws a compile-time error. A compiler 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 compilers the float data typefor example, is represented in 32 bitsin accord with the IEEE specification for single-precision floating point numbers.
They will thus use floating-point-specific microprocessor operations 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 may further associate an operation with various resolutions for each type, in the case of type polymorphism. Jeremy siek phd thesis language generic programming theory is the study of type systems.
The concrete types of some programming languages, such as integers and strings, depend on practical issues of computer architecture, compiler implementation, and language design. Formally, type theory studies type systems. A programming language must have occurrence to type check using the type system whether at compile time or runtime, manually annotated or automatically inferred. As Mark Manasse concisely put it: [3]. The fundamental problem addressed by a type theory is to ensure that programs have meaning.
The fundamental problem caused by a type theory is that meaningful programs may not have meanings ascribed to them. The quest for richer type systems results from this tension. Assigning a data type, termed typinggives meaning to a sequence of bits such as a value in memory or some object such as a variable. The hardware of a general purpose computer is unable jeremy siek phd thesis language generic programming discriminate between for example a memory address and an instruction codeor between a character jeremy siek phd thesis language generic programming, an integeror a floating-point numberbecause it makes no intrinsic distinction between any of the possible values that a sequence of bits might mean.
A program associates each value with at least one specific type, but it also can occur that one value is associated with many subtypes. Other entities, such as objectsjeremy siek phd thesis language generic programming, modulescommunication channels, and dependencies can become associated with a type. Even a type can become associated with a type, jeremy siek phd thesis language generic programming.
An implementation of a type system could in theory associate identifications called data type a type of a valueclass a type of an objectand kind a type of a typeor metatype. These are the abstractions that typing can go through, on a hierarchy of levels contained in a system.
When a programming language evolves a more elaborate type system, it gains a more finely grained rule set than basic type checking, but this comes at a price when the type inferences and other properties become undecidableand when more attention must be paid by the programmer to annotate code or to consider computer-related operations and functioning. It is challenging to find a sufficiently expressive type system that satisfies all programming practices in a type safe manner.
The more type restrictions that are imposed by the compiler, the more strongly typed a programming language is. Strongly-typed languages often require the programmer to make explicit conversions in contexts where an implicit conversion would cause no harm.
Pascal's type system has been described as "too strong" because, for example, the size of an array or string is part of its type, making some programming tasks difficult. A programming language compiler can also implement a dependent type or an effect systemwhich enables even more program specifications to be verified by a type checker. Beyond simple value-type pairs, a virtual "region" of code is associated with an "effect" component describing what is being done with whatand enabling for example to "throw" an error report.
Thus the symbolic system may be a type and effect systemwhich endows it with more safety checking than type checking alone. Whether automated by the compiler or specified by a programmer, a type system makes program behavior illegal if outside the type-system rules. Advantages provided by programmer-specified type systems include:. A type error is an unintended condition which might manifest in multiple stages of a program's development. Thus a facility for detection of the error is needed in the type system.
In some languages, such as Haskell, for which type inference is automated, lint might be available to its compiler to aid in the detection of error. Type safety contributes to program correctnessbut might only guarantee correctness at the cost of making the type checking itself an undecidable problem. Division by zero is an unsafe and incorrect operation, but a type checker running at compile time only does not scan for division by zero in most languages, and then it is left as a runtime error.
To prove the absence of these more-general-than-types defects, other kinds of formal methodscollectively known as program analysesare in common use. Alternatively, a sufficiently expressive type system, such as in dependently-typed languages, can prevent these kinds of errors for example, expressing the type of non-zero numbers.
In addition software testing is an empirical method for finding errors that the type checker cannot detect. The process jeremy siek phd thesis language generic programming verifying and enforcing the constraints of types— type checking —may occur either at compile time a static check or at run-time, jeremy siek phd thesis language generic programming.
If a language specification requires its typing rules strongly i. The terms are not usually used in a strict sense. Static type checking is the process of verifying the type safety of a program based on analysis of a program's text source code. If a program passes a static type checker, then the program is guaranteed to satisfy some set of type safety properties for all possible inputs.
Static type checking can be considered a limited form of program verification see type safetyand in a type-safe language, can be considered also an optimization.
If a compiler can prove that a program is well-typed, then it does not need to emit dynamic safety checks, allowing the resulting compiled binary to run faster and to be smaller. Static type checking for Turing-complete languages is inherently conservative. That is, if a type system is both sound meaning that it rejects all incorrect programs and decidable meaning that it is possible to write an algorithm that determines whether a program is well-typedthen it must be incomplete meaning there are correct programs, which are also rejected, even though they do not encounter runtime 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. A number of useful and common programming language features cannot be checked statically, jeremy siek phd thesis language generic programming, such as downcasting. Thus, many languages will have both static and dynamic type checking; the static type checker verifies what it can, and dynamic checks verify the rest.
Many languages with static type checking provide a way to bypass the type checker. Some languages allow programmers to choose between static and dynamic type safety. For jeremy siek phd thesis language generic programming, C distinguishes between statically-typed and dynamically-typed variables. Uses of the former are checked statically, whereas uses of the latter are checked dynamically. Other languages allow writing code that is not type-safe; for example, in Cprogrammers can freely cast a value between any two types that have the same size, effectively subverting the type concept.
For a list of languages with static type checking, see the category for statically-typed languages. Dynamic type checking is the process of verifying the type safety of a program at runtime. Implementations of dynamically type-checked languages generally associate each runtime object with a type tag i.
This runtime type information RTTI can also be used to implement dynamic jeremy siek phd thesis language generic programminglate bindingdowncastingreflectionand similar features. Most type-safe languages include some form of dynamic type checking, even if they also have a static type checker. For example, jeremy siek phd thesis language generic programming, suppose that a program defines two types, A and B, where B is a subtype of A.
If the program tries to convert a value of type A to type B, which is known as downcastingthen the operation is legal only if the value being converted is actually a value of type B.
Thus, a dynamic check is needed to verify that the operation is safe. This requirement is one of the criticisms of downcasting. By definition, jeremy siek phd thesis language generic programming, dynamic type checking may cause a program to fail at runtime. In some programming languages, it is possible to anticipate and recover from these failures. In others, type-checking errors are considered fatal. Programming languages that include dynamic type checking but not static type checking are often called "dynamically-typed programming languages".
For a list of such languages, see the category for dynamically-typed programming languages. Some languages allow both static and dynamic typing. For example, Java and some other ostensibly statically-typed languages support jeremy siek phd thesis language generic programming types to their subtypesquerying an object to discover its dynamic type and other type operations that depend on runtime type information.
More generally, most programming languages include mechanisms for dispatching over different 'kinds' of data, such as disjoint unionsruntime polymorphismand variant types.
Even when not interacting with type annotations or type checking, such mechanisms are materially similar to dynamic typing implementations.
See programming language for more discussion of the interactions between static and dynamic typing. Objects in object-oriented languages are usually accessed by a reference whose static target type or manifest type is equal to either the object's run-time type its latent type or a supertype thereof.
This is conformant with the Liskov substitution principlewhich states that all operations performed on an instance of a given type can also be performed on an instance of a subtype. This concept is also known as subsumption or subtype polymorphism. In some languages subtypes may also possess covariant or contravariant return types and argument types respectively.
Certain languages, for example ClojureCommon Lispor Cython are dynamically type checked by default, but allow programs to opt into static type checking by providing optional annotations. One reason to use such hints would be to optimize the performance of critical sections of a program. This is formalized by gradual typing. The programming environment DrRacketa pedagogic environment based on Lisp, and a precursor of the language Racket is also soft-typed, jeremy siek phd thesis language generic programming.
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A programming language may further associate an operation with various resolutions for each type, in the case of type polymorphism. Type theory is the study of type systems. The concrete types of some programming languages, such as integers and strings, depend on practical issues of computer architecture, compiler implementation, and language The Commuter Services Office (CSO) provides transportation and parking assistance to employees and students of Thomas Jefferson University, Thomas Jefferson University Hospital, and Jefferson University Physicians.. A partnership with CSO and those companies providing area transportation and parking results in a savings passed on to you. The benefits include discounts on the following: transit A programming language may further associate an operation with various resolutions for each type, in the case of type polymorphism. Type theory is the study of type systems. The concrete types of some programming languages, such as integers and strings, depend on practical issues of computer architecture, compiler implementation, and language
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