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Recursive Data Type
In computer programming languages, a recursive data type (also known as a recursively-defined, inductively-defined or inductive data type) is a data type for values that may contain other values of the same type. Data of recursive types are usually viewed as directed graphs. An important application of recursion in computer science is in defining dynamic data structures such as Lists and Trees. Recursive data structures can dynamically grow to an arbitrarily large size in response to runtime requirements; in contrast, a static array's size requirements must be set at compile time. Sometimes the term "inductive data type" is used for algebraic data types which are not necessarily recursive. Example An example is the list type, in Haskell: data List a = Nil , Cons a (List a) This indicates that a list of a's is either an empty list or a cons cell containing an 'a' (the "head" of the list) and another list (the "tail"). Another example is a similar singly linked type in Jav ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Programming Language
A programming language is a system of notation for writing computer programs. Most programming languages are text-based formal languages, but they may also be graphical. They are a kind of computer language. The description of a programming language is usually split into the two components of syntax (form) and semantics (meaning), which are usually defined by a formal language. Some languages are defined by a specification document (for example, the C programming language is specified by an ISO Standard) while other languages (such as Perl) have a dominant Programming language implementation, implementation that is treated as a reference implementation, reference. Some languages have both, with the basic language defined by a standard and extensions taken from the dominant implementation being common. Programming language theory is the subfield of computer science that studies the design, implementation, analysis, characterization, and classification of programming lan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inverse Function
In mathematics, the inverse function of a function (also called the inverse of ) is a function that undoes the operation of . The inverse of exists if and only if is bijective, and if it exists, is denoted by f^ . For a function f\colon X\to Y, its inverse f^\colon Y\to X admits an explicit description: it sends each element y\in Y to the unique element x\in X such that . As an example, consider the real-valued function of a real variable given by . One can think of as the function which multiplies its input by 5 then subtracts 7 from the result. To undo this, one adds 7 to the input, then divides the result by 5. Therefore, the inverse of is the function f^\colon \R\to\R defined by f^(y) = \frac . Definitions Let be a function whose domain is the set , and whose codomain is the set . Then is ''invertible'' if there exists a function from to such that g(f(x))=x for all x\in X and f(g(y))=y for all y\in Y. If is invertible, then there is exactly one function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Node (computer Science)
A node is a basic unit of a data structure, such as a linked list or tree data structure. Nodes contain data and also may link to other nodes. Links between nodes are often implemented by pointers. Nodes and Trees Nodes are often arranged into tree structures. A node represents the information contained in a single data structure. These nodes may contain a value or condition, or possibly serve as another independent data structure. Nodes are represented by a single parent node. The highest point on a tree structure is called a root node, which does not have a parent node, but serves as the parent or 'grandparent' of all of the nodes below it in the tree. The height of a node is determined by the total number of edges on the path from that node to the furthest leaf node, and the height of the tree is equal to the height of the root node. Node depth is determined by the distance between that particular node and the root node. The root node is said to have a depth of zero. Data ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inductive Type
In type theory, a system has inductive types if it has facilities for creating a new type from constants and functions that create terms of that type. The feature serves a role similar to data structures in a programming language and allows a type theory to add concepts like numbers, relations, and trees. As the name suggests, inductive types can be self-referential, but usually only in a way that permits structural recursion. The standard example is encoding the natural numbers using Peano's encoding. Inductive nat : Type := , 0 : nat , S : nat -> nat. Here, a natural number is created either from the constant "0" or by applying the function "S" to another natural number. "S" is the successor function which represents adding 1 to a number. Thus, "0" is zero, "S 0" is one, "S (S 0)" is two, "S (S (S 0))" is three, and so on. Since their introduction, inductive types have been extended to encode more and more structures, while still being predicative and suppor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Data Type
In computer programming, especially functional programming and type theory, an algebraic data type (ADT) is a kind of composite type, i.e., a type formed by combining other types. Two common classes of algebraic types are product types (i.e., tuples and records) and sum types (i.e., tagged or disjoint unions, coproduct types or ''variant types''). The values of a product type typically contain several values, called ''fields''. All values of that type have the same combination of field types. The set of all possible values of a product type is the set-theoretic product, i.e., the Cartesian product, of the sets of all possible values of its field types. The values of a sum type are typically grouped into several classes, called ''variants''. A value of a variant type is usually created with a quasi-functional entity called a ''constructor''. Each variant has its own constructor, which takes a specified number of arguments with specified types. The set of all possibl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recursive Definition
In mathematics and computer science, a recursive definition, or inductive definition, is used to define the elements in a set in terms of other elements in the set ( Aczel 1977:740ff). Some examples of recursively-definable objects include factorials, natural numbers, Fibonacci numbers, and the Cantor ternary set. A recursive definition of a function defines values of the function for some inputs in terms of the values of the same function for other (usually smaller) inputs. For example, the factorial function ''n''! is defined by the rules :0! = 1. :(''n'' + 1)! = (''n'' + 1)·''n''!. This definition is valid for each natural number ''n'', because the recursion eventually reaches the base case of 0. The definition may also be thought of as giving a procedure for computing the value of the function ''n''!, starting from ''n'' = 0 and proceeding onwards with ''n'' = 1, ''n'' = 2, ''n'' = 3 etc. The recursion theorem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Typedef
typedef is a reserved keyword in the programming languages C, C++, and Objective-C. It is used to create an additional name (''alias'') for another data type, but does not create a new type, except in the obscure case of a qualified typedef of an array type where the typedef qualifiers are transferred to the array element type. As such, it is often used to simplify the syntax of declaring complex data structures consisting of struct and union types, although it is also commonly used to provide specific descriptive type names for integer data types of varying sizes. Syntax The syntax of the typedef declaration is: ; ''type-declaration''; The name of the new type alias follows the same syntax as declaring any other C identifier, therefore, in more detailed form: ; ''type-definition'' ''identifier;'' In the C standard library and in POSIX specifications, the identifier for the typedef definition is often suffixed with , such as in size_t and time_t. This is practiced in o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
OCaml
OCaml ( , formerly Objective Caml) is a general-purpose, multi-paradigm programming language Programming paradigms are a way to classify programming languages based on their features. Languages can be classified into multiple paradigms. Some paradigms are concerned mainly with implications for the execution model of the language, suc ... which extends the Caml dialect of ML (programming language), ML with object-oriented programming, object-oriented features. OCaml was created in 1996 by Xavier Leroy, Jérôme Vouillon, Damien Doligez, Didier Rémy, Ascánder Suárez, and others. The OCaml toolchain includes an interactive top-level Interpreter (computing), interpreter, a bytecode compiler, an optimizing native code compiler, a reversible debugger, and a package manager (OPAM). OCaml was initially developed in the context of automated theorem proving, and has an outsize presence in static program analysis, static analysis and formal methods software. Beyond these areas, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Miranda Programming Language
Miranda is a lazy, purely functional programming language designed by David Turner as a successor to his earlier programming languages SASL and KRC, using some concepts from ML and Hope. It was produced by Research Software Ltd. of England (which holds a trademark on the name ''Miranda'') and was the first purely functional language to be commercially supported. Miranda was first released in 1985 as a fast interpreter in C for Unix-flavour operating systems, with subsequent releases in 1987 and 1989. It had a strong influence on the later Haskell programming language. In 2020 a version of Miranda was released as open source under a BSD licence. The codebase has been updated to conform to modern C standards (C11/ C18) and to generate 64-bit binaries. This has been tested on operating systems including Debian, Ubuntu, WSL/Ubuntu, and MacOS ( Catalina). Overview Miranda is a lazy, purely functional programming language. That is, it lacks side effects and imperative pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
TypeScript
TypeScript is a free and open source programming language developed and maintained by Microsoft. It is a strict syntactical superset of JavaScript and adds optional static typing to the language. It is designed for the development of large applications and transpiles to JavaScript. As it is a superset of JavaScript, existing JavaScript programs are also valid TypeScript programs. TypeScript may be used to develop JavaScript applications for both client-side and server-side execution (as with Node.js or Deno). Multiple options are available for transpilation. The default TypeScript Compiler can be used, or the Babel compiler can be invoked to convert TypeScript to JavaScript. TypeScript supports definition files that can contain type information of existing JavaScript libraries, much like C++ header files can describe the structure of existing object files. This enables other programs to use the values defined in the files as if they were statically typed TypeScript entitie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Class (computer Science)
In object-oriented programming, a class is an extensible program-code-template for creating objects, providing initial values for state (member variables) and implementations of behavior (member functions or methods). In many languages, the class name is used as the name for the class (the template itself), the name for the default constructor of the class (a subroutine that creates objects), and as the type of objects generated by instantiating the class; these distinct concepts are easily conflated. Although, to the point of conflation, one could argue that is a feature inherent in a language because of its polymorphic nature and why these languages are so powerful, dynamic and adaptable for use compared to languages without polymorphism present. Thus they can model dynamic systems (i.e. the real world, machine learning, AI) more easily. When an object is created by a constructor of the class, the resulting object is called an instance of the class, and the member variable ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Object-oriented
Object-oriented programming (OOP) is a programming paradigm based on the concept of " objects", which can contain data and code. The data is in the form of fields (often known as attributes or ''properties''), and the code is in the form of procedures (often known as '' methods''). A common feature of objects is that procedures (or methods) are attached to them and can access and modify the object's data fields. In this brand of OOP, there is usually a special name such as or used to refer to the current object. In OOP, computer programs are designed by making them out of objects that interact with one another. OOP languages are diverse, but the most popular ones are class-based, meaning that objects are instances of classes, which also determine their types. Many of the most widely used programming languages (such as C++, Java, Python, etc.) are multi-paradigm and they support object-oriented programming to a greater or lesser degree, typically in combination with i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
