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Type Variable
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 language A programming language is a system of notation for writing computer programs. Programming languages are described in terms of their Syntax (programming languages), syntax (form) and semantics (computer science), semantics (meaning), usually def ...s that support parametric polymorphism make use of universally quantified type variables. Languages that support existential types make use of existentially quantified type variables. For example, the following OCaml code defines a polymorphic identity function that has a universally quantified type, which is printed by the interpreter on the second line: # let id x = x;; val id : 'a -> 'a = In mathematical notation, the type of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type Theory
In mathematics and theoretical computer science, a type theory is the formal presentation of a specific type system. Type theory is the academic study of type systems. Some type theories serve as alternatives to set theory as a foundation of mathematics. Two influential type theories that have been proposed as foundations are: * Typed λ-calculus of Alonzo Church * Intuitionistic type theory of Per Martin-Löf Most computerized proof-writing systems use a type theory for their foundation. A common one is Thierry Coquand's Calculus of Inductive Constructions. History Type theory was created to avoid paradoxes in naive set theory and formal logic, such as Russell's paradox which demonstrates that, without proper axioms, it is possible to define the set of all sets that are not members of themselves; this set both contains itself and does not contain itself. Between 1902 and 1908, Bertrand Russell proposed various solutions to this problem. By 1908, Russell arrive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Programming Language
A programming language is a system of notation for writing computer programs. Programming languages are described in terms of their Syntax (programming languages), syntax (form) and semantics (computer science), semantics (meaning), usually defined by a formal language. Languages usually provide features such as a type system, Variable (computer science), variables, and mechanisms for Exception handling (programming), error handling. An Programming language implementation, implementation of a programming language is required in order to Execution (computing), execute programs, namely an Interpreter (computing), interpreter or a compiler. An interpreter directly executes the source code, while a compiler produces an executable program. Computer architecture has strongly influenced the design of programming languages, with the most common type (imperative languages—which implement operations in a specified order) developed to perform well on the popular von Neumann architecture. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variable (mathematics)
In mathematics, a variable (from Latin language, Latin ) is a Mathematical symbol, symbol, typically a letter, that refers to an unspecified mathematical object. One says colloquially that the variable ''represents'' or ''denotes'' the object, and that any valid candidate for the object is the value (mathematics), value of the variable. The values a variable can take are usually of the same kind, often numbers. More specifically, the values involved may form a Set (mathematics), set, such as the set of real numbers. The object may not always exist, or it might be uncertain whether any valid candidate exists or not. For example, one could represent two integers by the variables and and require that the value of the square of is twice the square of , which in algebraic notation can be written . A definitive proof that this relationship is impossible to satisfy when and are restricted to integer numbers isn't obvious, but it has been known since ancient times and has had a big ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Types
In computer science and computer programming, a data type (or simply type) is a collection or grouping of data values, usually specified by a set of possible values, a set of allowed operations on these values, and/or a representation of these values as machine types. A data type specification in a program constrains the possible values that an expression, such as a variable or a function call, might take. On literal data, it tells the compiler or interpreter how the programmer intends to use the data. Most programming languages support basic data types of integer numbers (of varying sizes), floating-point numbers (which approximate real numbers), characters and Booleans. Concept A data type may be specified for many reasons: similarity, convenience, or to focus the attention. It is frequently a matter of good organization that aids the understanding of complex definitions. Almost all programming languages explicitly include the notion of data type, though the possible da ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variable (programming)
In computer programming, a variable is an abstract storage location paired with an associated symbol, symbolic name, which contains some known or unknown quantity of Data (computer science), data or Object (computer science), object referred to as a ''value (computer science), value''; or in simpler terms, a variable is a named container for a particular set of bits or Data type, type of data (like Integer (computer science), integer, Floating-point arithmetic, float, String (computer science), string, etc...). A variable can eventually be associated with or identified by a memory address. The variable name is the usual way to Reference (computer science), reference the stored value, in addition to referring to the variable itself, depending on the context. This separation of name and content allows the name to be used independently of the exact information it represents. The identifier in computer source code can be Name binding, bound to a Value (computer science), value during R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Programming Language
A programming language is a system of notation for writing computer programs. Programming languages are described in terms of their Syntax (programming languages), syntax (form) and semantics (computer science), semantics (meaning), usually defined by a formal language. Languages usually provide features such as a type system, Variable (computer science), variables, and mechanisms for Exception handling (programming), error handling. An Programming language implementation, implementation of a programming language is required in order to Execution (computing), execute programs, namely an Interpreter (computing), interpreter or a compiler. An interpreter directly executes the source code, while a compiler produces an executable program. Computer architecture has strongly influenced the design of programming languages, with the most common type (imperative languages—which implement operations in a specified order) developed to perform well on the popular von Neumann architecture. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parametric Polymorphism
In programming languages and type theory, parametric polymorphism allows a single piece of code to be given a "generic" type, using variables in place of actual types, and then instantiated with particular types as needed. Parametrically polymorphic functions and data types are sometimes called generic functions and generic datatypes, respectively, and they form the basis of generic programming. Parametric polymorphism may be contrasted with ad hoc polymorphism. Parametrically polymorphic definitions are ''uniform'': they behave identically regardless of the type they are instantiated at. In contrast, ad hoc polymorphic definitions are given a distinct definition for each type. Thus, ad hoc polymorphism can generally only support a limited number of such distinct types, since a separate implementation has to be provided for each type. Basic definition It is possible to write functions that do not depend on the types of their arguments. For example, the identity function \ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Universally Quantified
In mathematical logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any", "for all", "for every", or "given an arbitrary element". It expresses that a predicate can be satisfied by every member of a domain of discourse. In other words, it is the predication of a property or relation to every member of the domain. It asserts that a predicate within the scope of a universal quantifier is true of every value of a predicate variable. It is usually denoted by the turned A (∀) logical operator symbol, which, when used together with a predicate variable, is called a universal quantifier ("", "", or sometimes by "" alone). Universal quantification is distinct from ''existential'' quantification ("there exists"), which only asserts that the property or relation holds for at least one member of the domain. Quantification in general is covered in the article on quantification (logic). The universal quantifier is encoded ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
