Type system

In programming languages, a type system is a set of rules that assigns a property called type to the various constructs of a computer program, such as variables, expressions, functions or modules. These types formalize and enforce the otherwise implicit categories the programmer uses for algebraic data types, data structures, or other components (e.g. 'string', 'array of float', 'function returning boolean'). The main purpose of a type system is to reduce possibilities for bugs in computer programs 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 time), dynamically (at run time), or as a combination of static and dynamic checking. Type systems have other purposes as well, such as expressing business rules, enabling certain compiler optimizations, allowing for multiple dispatch, providing a form of documentation, etc.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. In programming languages, a type system is a set of rules that assigns a property called type to the various constructs of a computer program, such as variables, expressions, functions or modules. These types formalize and enforce the otherwise implicit categories the programmer uses for algebraic data types, data structures, or other components (e.g. 'string', 'array of float', 'function returning boolean'). The main purpose of a type system is to reduce possibilities for bugs in computer programs 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 time), dynamically (at run time), or as a combination of static and dynamic checking. Type systems have other purposes as well, such as expressing business rules, enabling certain compiler optimizations, allowing for multiple dispatch, providing 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 exactly what constitutes a type error, but in general the aim is to 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 the interpreters and compilers for them; although the type system of a language can be extended by optional tools that perform added kinds of 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 of variables that hold values to pass to it. During execution, the values are placed into temporary storage, 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 value, then the wrong result will be computed by the invoked function. The C compiler checks the type declared for each variable sent, against the type declared for each variable in the interface of the invoked function. 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 type, for example, is represented in 32 bits, in 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. 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 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: Assigning a data type, termed typing, gives 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 to discriminate between for example a memory address and an instruction code, or between a character, an integer, or a floating-point number, because it makes no intrinsic distinction between any of the possible values that a sequence of bits might mean. Associating a sequence of bits with a type conveys that meaning to the programmable hardware to form a symbolic system composed of that hardware and some program. 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 objects, modules, communication channels, and dependencies can become associated with a type. Even a type can become associated with a type. An implementation of a type system could in theory associate identifications called data type (a type of a value), class (a type of an object), and kind (a type of a type, or 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 undecidable, and 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.