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Jot (programming Language)
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 expres ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Language
In logic, mathematics, computer science, and linguistics, a formal language is a set of strings whose symbols are taken from a set called "alphabet". The alphabet of a formal language consists of symbols that concatenate into strings (also called "words"). Words that belong to a particular formal language are sometimes called ''well-formed words''. A formal language is often defined by means of a formal grammar such as a regular grammar or context-free grammar. In computer science, formal languages are used, among others, as the basis for defining the grammar of programming languages and formalized versions of subsets of natural languages, in which the words of the language represent concepts that are associated with meanings or semantics. In computational complexity theory, decision problems are typically defined as formal languages, and complexity classes are defined as the sets of the formal languages that can be parsed by machines with limited computational power. In ... [...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] |
Iota
Iota (; uppercase Ι, lowercase ι; ) is the ninth letter of the Greek alphabet. It was derived from the Phoenician letter Yodh. Letters that arose from this letter include the Latin I and J, the Cyrillic І (І, і), Yi (Ї, ї), and Je (Ј, ј), and iotated letters (e.g. Yu (Ю, ю)). In the system of Greek numerals, iota has a value of 10. Iota represents the close front unrounded vowel . In early forms of ancient Greek, it occurred in both long and short versions, but this distinction was lost in Koine Greek. Iota participated as the second element in falling diphthongs, with both long and short vowels as the first element. Where the first element was long, the iota was lost in pronunciation at an early date, and was written in polytonic orthography as iota subscript, in other words as a very small ι under the main vowel. Examples include ᾼ ᾳ ῌ ῃ ῼ ῳ. The former diphthongs became digraphs for simple vowels in Koine Greek.see Koine Greek phonolog ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use Conditional (computer programming), conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning). In contrast, a Heuristic (computer science), heuristic is an approach to solving problems without well-defined correct or optimal results.David A. Grossman, Ophir Frieder, ''Information Retrieval: Algorithms and Heuristics'', 2nd edition, 2004, For example, although social media recommender systems are commonly called "algorithms", they actually rely on heuristics as there is no truly "correct" recommendation. As an e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gödel Numbering
In mathematical logic, a Gödel numbering is a function that assigns to each symbol and well-formed formula of some formal language a unique natural number, called its Gödel number. Kurt Gödel developed the concept for the proof of his incompleteness theorems. A Gödel numbering can be interpreted as an encoding in which a number is assigned to each symbol of a mathematical notation, after which a sequence of natural numbers can then represent a sequence of symbols. These sequences of natural numbers can again be represented by single natural numbers, facilitating their manipulation in formal theories of arithmetic. Since the publishing of Gödel's paper in 1931, the term "Gödel numbering" or "Gödel code" has been used to refer to more general assignments of natural numbers to mathematical objects. Simplified overview Gödel noted that each statement within a system can be represented by a natural number (its ''Gödel number''). The significance of this was that propert ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regular Language
In theoretical computer science and formal language theory, a regular language (also called a rational language) is a formal language that can be defined by a regular expression, in the strict sense in theoretical computer science (as opposed to many modern regular expression engines, which are Regular expression#Patterns for non-regular languages, augmented with features that allow the recognition of non-regular languages). Alternatively, a regular language can be defined as a language recognised by a finite automaton. The equivalence of regular expressions and finite automata is known as Kleene's theorem (after American mathematician Stephen Cole Kleene). In the Chomsky hierarchy, regular languages are the languages generated by regular grammar, Type-3 grammars. Formal definition The collection of regular languages over an Alphabet (formal languages), alphabet Σ is defined recursively as follows: * The empty language ∅ is a regular language. * For each ''a'' ∈ Σ (''a'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function Application
In mathematics, function application is the act of applying a function to an argument from its domain so as to obtain the corresponding value from its range. In this sense, function application can be thought of as the opposite of function abstraction. Representation Function application is usually depicted by juxtaposing the variable representing the function with its argument encompassed in parentheses. For example, the following expression represents the application of the function ''ƒ'' to its argument ''x''. :f(x) In some instances, a different notation is used where the parentheses aren't required, and function application can be expressed just by juxtaposition. For example, the following expression can be considered the same as the previous one: :f\; x The latter notation is especially useful in combination with the currying isomorphism. Given a function f : (X \times Y) \to Z, its application is represented as f(x, y) by the former notation and f\;(x,y) (or f \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cons
In computer programming, ( or ) is a fundamental function in most dialects of the Lisp programming language. ''constructs'' memory objects which hold two values or pointers to two values. These objects are referred to as (cons) cells, conses, non-atomic s-expressions ("NATSes"), or (cons) pairs. In Lisp jargon, the expression "to cons ''x'' onto ''y''" means to construct a new object with (cons ''x'' ''y''). The resulting pair has a left half, referred to as the (the first element, or '' contents of the address part of register''), and a right half, referred to as the (the second element, or '' contents of the decrement part of register''). It is loosely related to the object-oriented notion of a constructor, which creates a new object given arguments, and more closely related to the constructor function of an algebraic data type system. The word "cons" and expressions like "to cons onto" are also part of a more general functional programming jargon. Sometimes operato ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Universal Iota
Universal is the adjective for universe. Universal may also refer to: Companies * NBCUniversal, a media and entertainment company that is a subsidiary of Comcast ** Universal Animation Studios, an American Animation studio, and a subsidiary of NBCUniversal ** Universal TV, a television channel owned by NBCUniversal ** Universal Kids, an American current television channel, formerly known as Sprout, owned by NBCUniversal ** Universal Pictures, an American film studio, and a subsidiary of NBCUniversal ** Universal Television, a television division owned by NBCUniversal Content Studios ** Universal Destinations & Experiences, the theme park unit of NBCUniversal * Universal Airlines (other) * Universal Avionics, a manufacturer of flight control components * Universal Corporation, an American tobacco company * Universal Display Corporation, a manufacturer of displays * Universal Edition, a classical music publishing firm, founded in Vienna in 1901 * Universal Entertainment ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polish Notation
Polish notation (PN), also known as normal Polish notation (NPN), Łukasiewicz notation, Warsaw notation, Polish prefix notation, Eastern Notation or simply prefix notation, is a mathematical notation in which Operation (mathematics), operators ''precede'' their operands, in contrast to the more common infix notation, in which operators are placed ''between'' operands, as well as reverse Polish notation (RPN), in which operators ''follow'' their operands. It does not need any parentheses as long as each operator has a fixed arity, number of operands. The description "Polish" refers to the nationality of logician Jan Łukasiewicz, who invented Polish notation in 1924. The term ''Polish notation'' is sometimes taken (as the opposite of ''infix notation'') to also include reverse Polish notation. When Polish notation is used as a syntax for mathematical expressions by programming language Interpreter (computing), interpreters, it is readily parsed into abstract syntax trees and c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LL Parser
In computer science, an LL parser (left-to-right, leftmost derivation) is a top-down parser for a restricted context-free language. It parses the input from Left to right, performing Leftmost derivation of the sentence. An LL parser is called an LL(''k'') parser if it uses ''k'' tokens of lookahead when parsing a sentence. A grammar is called an LL(''k'') grammar if an LL(''k'') parser can be constructed from it. A formal language is called an LL(''k'') language if it has an LL(''k'') grammar. The set of LL(''k'') languages is properly contained in that of LL(''k''+1) languages, for each ''k'' ≥ 0. A corollary of this is that not all context-free languages can be recognized by an LL(''k'') parser. An LL parser is called LL-regular (LLR) if it parses an LL-regular language. The class of LLR grammars contains every LL(''k'') grammar for every ''k''. For every LLR grammar there exists an LLR parser that parses the grammar in linear time. Two nomenclative outlier p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chaitin's Constant
In the computer science subfield of algorithmic information theory, a Chaitin constant (Chaitin omega number) or halting probability is a real number that, informally speaking, represents the probability that a randomly constructed program will halt. These numbers are formed from a construction due to Gregory Chaitin. Although there are infinitely many halting probabilities, one for each (universal, see below) method of encoding programs, it is common to use the letter to refer to them as if there were only one. Because depends on the program encoding used, it is sometimes called Chaitin's construction when not referring to any specific encoding. Each halting probability is a normal and transcendental real number that is not computable, which means that there is no algorithm to compute its digits. Each halting probability is Martin-Löf random, meaning there is not even any algorithm which can reliably guess its digits. Background The definition of a halting probability ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
