|
Binary Combinatory Logic
Binary combinatory logic (BCL) is a computer programming language that uses binary terms 0 and 1 to create a complete formulation of combinatory logic using only the symbols 0 and 1.. Using the S and K combinators, complex boolean algebra functions can be made. BCL has applications in the theory of program-size complexity ( Kolmogorov complexity). Definition S-K Basis Utilizing K and S combinators of the Combinatory logic, logical functions can be represented in as functions of combinators: Syntax Backus–Naur form: ::= 00 , 01 , 1 Semantics The denotational semantics of BCL may be specified as follows: * 00 ''K'' * 01 ''S'' * <term2> ">1 <term1> <term2> ( ">lt;term1> ">lt;term2>) where " ../code>" abbreviates "the meaning of ...". Here ''K'' and ''S'' are the ''KS''-basis combinators, and ( ) is the ''application'' operation, of combinatory logic. (The prefix 1 corresponds to a left parenthesis, right parentheses being unnecessary for dis ... [...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] |
Parsing
Parsing, syntax analysis, or syntactic analysis is a process of analyzing a String (computer science), string of Symbol (formal), symbols, either in natural language, computer languages or data structures, conforming to the rules of a formal grammar by breaking it into parts. The term ''parsing'' comes from Latin ''pars'' (''orationis''), meaning Part of speech, part (of speech). The term has slightly different meanings in different branches of linguistics and computer science. Traditional Sentence (linguistics), sentence parsing is often performed as a method of understanding the exact meaning of a sentence or word, sometimes with the aid of devices such as sentence diagrams. It usually emphasizes the importance of grammatical divisions such as subject (grammar), subject and predicate (grammar), predicate. Within computational linguistics the term is used to refer to the formal analysis by a computer of a sentence or other string of words into its constituents, resulting in a par ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
YouTube
YouTube is an American social media and online video sharing platform owned by Google. YouTube was founded on February 14, 2005, by Steve Chen, Chad Hurley, and Jawed Karim who were three former employees of PayPal. Headquartered in San Bruno, California, it is the second-most-visited website in the world, after Google Search. In January 2024, YouTube had more than 2.7billion monthly active users, who collectively watched more than one billion hours of videos every day. , videos were being uploaded to the platform at a rate of more than 500 hours of content per minute, and , there were approximately 14.8billion videos in total. On November 13, 2006, YouTube was purchased by Google for $1.65 billion (equivalent to $ billion in ). Google expanded YouTube's business model of generating revenue from advertisements alone, to offering paid content such as movies and exclusive content produced by and for YouTube. It also offers YouTube Premium, a paid subs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iota And Jot
In formal language theory and computer science, Iota and Jot (from Greek iota ι, Hebrew yodh י, the smallest letters in those two alphabets) are languages, extremely minimalist formal systems, designed to be even simpler than other more popular alternatives, such as lambda calculus and SKI combinator calculus. Thus, they can also be considered minimalist computer programming languages, or Turing tarpits, esoteric programming languages designed to be as small as possible but still Turing-complete. Both systems use only two symbols and involve only two operations. Both were created by professor of linguistics Chris Barker in 2001. Zot (2002) is a successor to Iota that supports input and output. Note that this article uses Backus-Naur form to describe syntax. Universal iota Chris Barker's universal iota combinator has the very simple λf.fSK structure defined here, using denotational semantics in terms of the lambda calculus, From this, one can recover the usual SKI ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turing Completeness
In computability theory, a system of data-manipulation rules (such as a model of computation, a computer's instruction set, a programming language, or a cellular automaton) is said to be Turing-complete or computationally universal if it can be used to simulate any Turing machine (devised by English mathematician and computer scientist Alan Turing). This means that this system is able to recognize or decode other data-manipulation rule sets. Turing completeness is used as a way to express the power of such a data-manipulation rule set. Virtually all programming languages today are Turing-complete. A related concept is that of Turing equivalence two computers P and Q are called equivalent if P can simulate Q and Q can simulate P. The Church–Turing thesis conjectures that any function whose values can be computed by an algorithm can be computed by a Turing machine, and therefore that if any real-world computer can simulate a Turing machine, it is Turing equivalent to a Turing m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cellular Automaton
A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays. Cellular automata have found application in various areas, including physics, theoretical biology and microstructure modeling. A cellular automaton consists of a regular grid of ''cells'', each in one of a finite number of ''State (computer science), states'', such as ''on'' and ''off'' (in contrast to a coupled map lattice). The grid can be in any finite number of dimensions. For each cell, a set of cells called its ''neighborhood'' is defined relative to the specified cell. An initial state (time ''t'' = 0) is selected by assigning a state for each cell. A new ''generation'' is created (advancing ''t'' by 1), according to some fixed ''rule'' (generally, a mathematical function) that dete ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turing Machine
A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer algorithm. The machine operates on an infinite memory tape divided into discrete mathematics, discrete cells, each of which can hold a single symbol drawn from a finite set of symbols called the Alphabet (formal languages), alphabet of the machine. It has a "head" that, at any point in the machine's operation, is positioned over one of these cells, and a "state" selected from a finite set of states. At each step of its operation, the head reads the symbol in its cell. Then, based on the symbol and the machine's own present state, the machine writes a symbol into the same cell, and moves the head one step to the left or the right, or halts the computation. The choice of which replacement symbol to write, which direction to move the head, and whet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rule 110 SK Basis
Rule or ruling may refer to: Human activity * The exercise of political or personal control by someone with authority or power * Business rule, a rule pertaining to the structure or behavior internal to a business * School rule, a rule that is part of school discipline * Sport rule, a rule that defines how a sport is played * Game rule, a rule that defines how a game is played * Morality, a rule or element of a moral code for guiding choices in human behavior * Norm (philosophy), a kind of sentence or a reason to act, feel or believe * Social norm, explicit or implicit rules used within society or by a group * Rule of thumb, a principle with broad application that is not intended to be strictly accurate or reliable for every situation * Unspoken rule, an assumed rule of human behavior that is not voiced or written down Science * Ruler or "rule"; a distance measuring device * Slide rule, a mechanical analog computer * Rule of inference or transformation rule, a term in lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rewriting
In mathematics, computer science, and logic, rewriting covers a wide range of methods of replacing subterms of a formula with other terms. Such methods may be achieved by rewriting systems (also known as rewrite systems, rewrite engines, or reduction systems). In their most basic form, they consist of a set of objects, plus relations on how to transform those objects. Rewriting can be non-deterministic. One rule to rewrite a term could be applied in many different ways to that term, or more than one rule could be applicable. Rewriting systems then do not provide an algorithm for changing one term to another, but a set of possible rule applications. When combined with an appropriate algorithm, however, rewrite systems can be viewed as computer programs, and several theorem provers and declarative programming languages are based on term rewriting. Example cases Logic In logic, the procedure for obtaining the conjunctive normal form (CNF) of a formula can be implemented as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatory Logic
Combinatory logic is a notation to eliminate the need for quantified variables in mathematical logic. It was introduced by Moses Schönfinkel and Haskell Curry, and has more recently been used in computer science as a theoretical model of computation and also as a basis for the design of functional programming languages. It is based on combinators, which were introduced by Schönfinkel in 1920 with the idea of providing an analogous way to build up functions—and to remove any mention of variables—particularly in predicate logic. A combinator is a higher-order function that uses only function application and earlier defined combinators to define a result from its arguments. In mathematics Combinatory logic was originally intended as a 'pre-logic' that would clarify the role of quantified variables in logic, essentially by eliminating them. Another way of eliminating quantified variables is Quine's predicate functor logic. While the expressive power of combinatory log ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turing-complete
In computability theory, a system of data-manipulation rules (such as a model of computation, a computer's instruction set, a programming language, or a cellular automaton) is said to be Turing-complete or computationally universal if it can be used to simulate any Turing machine (devised by English mathematician and computer scientist Alan Turing). This means that this system is able to recognize or decode other data-manipulation rule sets. Turing completeness is used as a way to express the power of such a data-manipulation rule set. Virtually all programming languages today are Turing-complete. A related concept is that of Turing equivalence two computers P and Q are called equivalent if P can simulate Q and Q can simulate P. The Church–Turing thesis conjectures that any function whose values can be computed by an algorithm can be computed by a Turing machine, and therefore that if any real-world computer can simulate a Turing machine, it is Turing equivalent to a Turing ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operational Semantics
Operational semantics is a category of formal programming language semantics in which certain desired properties of a program, such as correctness, safety or security, are verified by constructing proofs from logical statements about its execution and procedures, rather than by attaching mathematical meanings to its terms (denotational semantics). Operational semantics are classified in two categories: structural operational semantics (or small-step semantics) formally describe how the ''individual steps'' of a computation take place in a computer-based system; by opposition natural semantics (or big-step semantics) describe how the ''overall results'' of the executions are obtained. Other approaches to providing a formal semantics of programming languages include axiomatic semantics and denotational semantics. The operational semantics for a programming language describes how a valid program is interpreted as sequences of computational steps. These sequences then ''are'' the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
