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Corecursion
In computer science, corecursion is a type of operation that is Dual (category theory), dual to recursion (computer science), recursion. Whereas recursion works analysis, analytically, starting on data further from a base case and breaking it down into smaller data and repeating until one reaches a base case, corecursion works synthetically, starting from a base case and building it up, iteratively producing data further removed from a base case. Put simply, corecursive algorithms use the data that they themselves produce, bit by bit, as they become available, and needed, to produce further bits of data. A similar but distinct concept is ''Generative recursion#Structural versus generative recursion, generative recursion'', which may lack a definite "direction" inherent in corecursion and recursion. Where recursion allows programs to operate on arbitrarily complex data, so long as they can be reduced to simple data (base cases), corecursion allows programs to produce arbitrarily co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recursion (computer Science)
In computer science, recursion is a method of solving a computational problem where the solution depends on solutions to smaller instances of the same problem. Recursion solves such recursion, recursive problems by using function (computer science), functions that call themselves from within their own code. The approach can be applied to many types of problems, and recursion is one of the central ideas of computer science. Most computer programming languages support recursion by allowing a function to call itself from within its own code. Some functional programming languages (for instance, Clojure) do not define any looping constructs but rely solely on recursion to repeatedly call code. It is proved in computability theory that these recursive-only languages are Turing complete; this means that they are as powerful (they can be used to solve the same problems) as imperative languages based on control structures such as and . Repeatedly calling a function from within itse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generative Recursion
In computer science, recursion is a method of solving a computational problem where the solution depends on solutions to smaller instances of the same problem. Recursion solves such recursive problems by using functions that call themselves from within their own code. The approach can be applied to many types of problems, and recursion is one of the central ideas of computer science. Most computer programming languages support recursion by allowing a function to call itself from within its own code. Some functional programming languages (for instance, Clojure) do not define any looping constructs but rely solely on recursion to repeatedly call code. It is proved in computability theory that these recursive-only languages are Turing complete; this means that they are as powerful (they can be used to solve the same problems) as imperative languages based on control structures such as and . Repeatedly calling a function from within itself may cause the call stack to have a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tree Traversal
In computer science, tree traversal (also known as tree search and walking the tree) is a form of graph traversal and refers to the process of visiting (e.g. retrieving, updating, or deleting) each node in a Tree (data structure), tree data structure, exactly once. Such traversals are classified by the order in which the nodes are visited. The following algorithms are described for a binary tree, but they may be generalized to other trees as well. Types Unlike linked lists, one-dimensional arrays and other List of data structures#Linear data structures, linear data structures, which are canonically traversed in linear order, trees may be traversed in multiple ways. They may be traversed in Depth-first search, depth-first or Breadth-first search, breadth-first order. There are three common ways to traverse them in depth-first order: in-order, pre-order and post-order. Beyond these basic traversals, various more complex or hybrid schemes are possible, such as depth-limited searche ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Total Language
Total functional programming (also known as strong functional programming, to be contrasted with ordinary, or ''weak'' functional programming) is a programming paradigm that restricts the range of programs to those that are provably terminating. Restrictions Termination is guaranteed by the following restrictions: # A restricted form of recursion, which operates only upon 'reduced' forms of its arguments, such as Walther recursion, substructural recursion, or "strongly normalizing" as proven by abstract interpretation of code. # Every function must be a total (as opposed to partial) function. That is, it must have a definition for everything inside its domain. #* There are several possible ways to extend commonly used partial functions such as division to be total: choosing an arbitrary result for inputs on which the function is normally undefined (such as \forall x \in \mathbb. x \div 0 = 0 for division); adding another argument to specify the result for those inputs; or exc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Codata (computer Science)
In computer science, coinduction is a technique for defining and proving properties of systems of concurrent interacting objects. Coinduction is the mathematical dual to structural induction. Coinductively defined data types are known as codata and are typically infinite data structures, such as streams. As a definition or specification, coinduction describes how an object may be "observed", "broken down" or "destructed" into simpler objects. As a proof technique, it may be used to show that an equation is satisfied by all possible implementations of such a specification. To generate and manipulate codata, one typically uses corecursive functions, in conjunction with lazy evaluation. Informally, rather than defining a function by pattern-matching on each of the inductive constructors, one defines each of the "destructors" or "observers" over the function result. In programming, co-logic programming (co-LP for brevity) "is a natural generalization of logic programming and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, applied disciplines (including the design and implementation of Computer architecture, hardware and Software engineering, software). Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and preventing security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iterator
In computer programming, an iterator is an object that progressively provides access to each item of a collection, in order. A collection may provide multiple iterators via its interface that provide items in different orders, such as forwards and backwards. An iterator is often implemented in terms of the structure underlying a collection implementation and is often tightly coupled to the collection to enable the operational semantics of the iterator. An iterator is behaviorally similar to a database cursor. Iterators date to the CLU programming language in 1974. Pattern An iterator provides access to an element of a collection (''element access'') and can change its internal state to provide access to the next element (''element traversal''). It also provides for creation and initialization to a first element and indicates whether all elements have been traversed. In some programming contexts, an iterator provides additional functionality. An iterator allows a consu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Factorial
In mathematics, the factorial of a non-negative denoted is the Product (mathematics), product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial: \begin n! &= n \times (n-1) \times (n-2) \times (n-3) \times \cdots \times 3 \times 2 \times 1 \\ &= n\times(n-1)!\\ \end For example, 5! = 5\times 4! = 5 \times 4 \times 3 \times 2 \times 1 = 120. The value of 0! is 1, according to the convention for an empty product. Factorials have been discovered in several ancient cultures, notably in Indian mathematics in the canonical works of Jain literature, and by Jewish mystics in the Talmudic book ''Sefer Yetzirah''. The factorial operation is encountered in many areas of mathematics, notably in combinatorics, where its most basic use counts the possible distinct sequences – the permutations – of n distinct objects: there In mathematical analysis, factorials are used in power series for the ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Call Stack
In computer science, a call stack is a Stack (abstract data type), stack data structure that stores information about the active subroutines and block (programming), inline blocks of a computer program. This type of stack is also known as an execution stack, program stack, control stack, run-time stack, or machine stack, and is often shortened to simply the "stack". Although maintenance of the call stack is important for the proper functioning of most software, the details are normally hidden and automatic in high-level programming languages. Many computer instruction sets provide special instructions for manipulating stacks. A call stack is used for several related purposes, but the main reason for having one is to keep track of the point to which each active subroutine should return control when it finishes executing. An active subroutine is one that has been called, but is yet to complete execution, after which control should be handed back to the point of call. Such activatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Denotational Semantics
In computer science, denotational semantics (initially known as mathematical semantics or Scott–Strachey semantics) is an approach of formalizing the meanings of programming languages by constructing mathematical objects (called ''denotations'') that describe the meanings of Expression (computer science), expressions from the languages. Other approaches providing formal semantics of programming languages include axiomatic semantics and operational semantics. Broadly speaking, denotational semantics is concerned with finding mathematical objects called domain theory, domains that represent what programs do. For example, programs (or program phrases) might be represented by partial functionsDana S. ScottOutline of a mathematical theory of computation Technical Monograph PRG-2, Oxford University Computing Laboratory, Oxford, England, November 1970.Dana Scott and Christopher Strachey. ''Toward a mathematical semantics for computer languages'' Oxford Programming Research Group Techn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Haskell (programming Language)
Haskell () is a General-purpose programming language, general-purpose, static typing, statically typed, purely functional programming, purely functional programming language with type inference and lazy evaluation. Designed for teaching, research, and industrial applications, Haskell pioneered several programming language #Features, features such as type classes, which enable type safety, type-safe operator overloading, and Monad (functional programming), monadic input/output (IO). It is named after logician Haskell Curry. Haskell's main implementation is the Glasgow Haskell Compiler (GHC). Haskell's Semantics (computer science), semantics are historically based on those of the Miranda (programming language), Miranda programming language, which served to focus the efforts of the initial Haskell working group. The last formal specification of the language was made in July 2010, while the development of GHC continues to expand Haskell via language extensions. Haskell is used in a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Denotational Semantics
In computer science, denotational semantics (initially known as mathematical semantics or Scott–Strachey semantics) is an approach of formalizing the meanings of programming languages by constructing mathematical objects (called ''denotations'') that describe the meanings of Expression (computer science), expressions from the languages. Other approaches providing formal semantics of programming languages include axiomatic semantics and operational semantics. Broadly speaking, denotational semantics is concerned with finding mathematical objects called domain theory, domains that represent what programs do. For example, programs (or program phrases) might be represented by partial functionsDana S. ScottOutline of a mathematical theory of computation Technical Monograph PRG-2, Oxford University Computing Laboratory, Oxford, England, November 1970.Dana Scott and Christopher Strachey. ''Toward a mathematical semantics for computer languages'' Oxford Programming Research Group Techn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
