类型系统的属性：
1、结构属性；
2、规则属性；类型系统定义了一套规则（内部数据的访问规则、函数的访问规则、类型的比较与转化规则），以供编译和运行时进行检查。
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.[1] These types formalize and enforce the otherwise implicit categories the programmer uses for data structures and 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[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 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.
Type checking[edit]
The process of verifying and enforcing the constraints of types—type checking—may occur either at compile-time (a static check) or at run-time. 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 usually used in a strict sense.
Static type checking[edit]
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 safety), and 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-typed), then it must be incomplete (meaning there are correct programs, which are also rejected, even though they do not encounter runtime errors).[6] For example, consider a program containing the code:
if <complex test> then <do something> else <generate type error>
Even if the expression <complex test> always evaluates to true at run-time, most type checkers will reject the program as ill-typed, because it is difficult (if not impossible) for a static analyzer to determine that the else branch will not be taken.[7] Conversely, a static type checker will quickly detect type errors in rarely used code paths. Without static type checking, even code coverage 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.
A number of useful and common programming language features cannot be checked statically, 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 example, 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 C, programmers can freely cast a value between any two types that have the same size.
For a list of languages with static type checking, see the category for statically typed languages.
Dynamic type checking and runtime type information[edit]
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.e., a reference to a type) containing its type information. This runtime type information (RTTI) can also be used to implement dynamic dispatch, late binding, downcasting, reflection, and similar features.
Most type-safe languages include some form of dynamic type checking, even if they also have a static type checker.[citation needed] The reason for this is that many useful features or properties are difficult or impossible to verify statically. For example, 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 downcasting, then 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, 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.
https://en.wikipedia.org/wiki/Type_system