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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. 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] |
Isomorphism
In mathematics, an isomorphism is a structure-preserving mapping or morphism between two structures of the same type that can be reversed by an inverse mapping. Two mathematical structures are isomorphic if an isomorphism exists between them. The word is derived . The interest in isomorphisms lies in the fact that two isomorphic objects have the same properties (excluding further information such as additional structure or names of objects). Thus isomorphic structures cannot be distinguished from the point of view of structure only, and may often be identified. In mathematical jargon, one says that two objects are the same up to an isomorphism. A common example where isomorphic structures cannot be identified is when the structures are substructures of a larger one. For example, all subspaces of dimension one of a vector space are isomorphic and cannot be identified. An automorphism is an isomorphism from a structure to itself. An isomorphism between two structures is a ... [...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), tree data structure. Nodes contain data and also may link to other nodes. Links between nodes are often implemented by Pointer (computer programming), 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. ... [...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. It can be defined in Rocq (previously known as ''Coq'') as follows: 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 enco ... [...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 data type, i.e., a data 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 po ... [...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 is defined by the rules :\begin & 0! = 1. \\ & (n+1)! = (n+1) \cdot n!. \end This definition is valid for each natural number , 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 , starting from and proceeding onwards with etc. The recursion theorem states that such a definition indeed defines a function that is unique. The proof uses mathematic ... [...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 A ''typedef declaration'' follows the same syntax as declaring any other C identifier. The keyword typedef itself is a specifier which means that while it typically appears at the start of the declaration, it can also appear after the type specifiers or between two of them. In the C standard library and in POSIX specifications, the identifier for the typedef definition is often suffixed with , such as in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
OCaml
OCaml ( , formerly Objective Caml) is a General-purpose programming language, general-purpose, High-level programming language, high-level, Comparison of multi-paradigm programming languages, multi-paradigm programming language 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 managerOPAM together with a composable build system for OCamlDune. OCaml was initially developed in the context of automated theorem proving, and is used in static program analysis, static analysis and formal methods software. Beyond these areas, it has found use in systems programming, web development, and specific financial utili ... [...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 language. Turner stated that the benefits of Miranda over Haskell are: "Smaller language, simpler type system, simpler arithmetic". In 2020 a version of Miranda was released as open source under a BSD licence. The code 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). Name The na ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
TypeScript
TypeScript (abbreviated as TS) is a high-level programming language that adds static typing with optional type annotations to JavaScript. It is designed for developing large applications and transpiles to JavaScript. It is developed by Microsoft as free and open-source software released under an Apache License 2.0. TypeScript may be used to develop JavaScript applications for both client-side and server-side execution (as with Node.js, Deno or Bun). Multiple options are available for transpiling. 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 entities. There are third-party header files for popular li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Class (computer Science)
In object-oriented programming, a class defines the shared aspects of objects created from the class. The capabilities of a class differ between programming languages, but generally the shared aspects consist of state ( variables) and behavior ( methods) that are each either associated with a particular object or with all objects of that class. Object state can differ between each instance of the class whereas the class state is shared by all of them. The object methods include access to the object state (via an implicit or explicit parameter that references the object) whereas class methods do not. If the language supports inheritance, a class can be defined based on another class with all of its state and behavior plus additional state and behavior that further specializes the class. The specialized class is a ''sub-class'', and the class it is based on is its ''superclass''. Attributes Object lifecycle As an instance of a class, an object is constructed from a class via '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Object-oriented
Object-oriented programming (OOP) is a programming paradigm based on the concept of '' objects''. Objects can contain data (called fields, attributes or properties) and have actions they can perform (called procedures or methods and implemented in code). In OOP, computer programs are designed by making them out of objects that interact with one another. Many of the most widely used programming languages (such as C++, Java, and Python) support object-oriented programming to a greater or lesser degree, typically as part of multiple paradigms in combination with others such as imperative programming and declarative programming. Significant object-oriented languages include Ada, ActionScript, C++, Common Lisp, C#, Dart, Eiffel, Fortran 2003, Haxe, Java, JavaScript, Kotlin, Logo, MATLAB, Objective-C, Object Pascal, Perl, PHP, Python, R, Raku, Ruby, Scala, SIMSCRIPT, Simula, Smalltalk, Swift, Vala and Visual Basic.NET. History The idea of "objects" in programm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
