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BlooP And FlooP
and (Bounded loop and Free loop) are simple programming languages designed by Douglas Hofstadter to illustrate a point in his book ''Gödel, Escher, Bach''. BlooP is a non-Turing-complete programming language whose main control flow structure is a bounded loop (i.e. recursion is not permitted). All programs in the language must terminate, and this language can only express primitive recursive functions. FlooP is identical to BlooP except that it supports unbounded loops; it is a Turing-complete language and can express all computable functions. For example, it can express the Ackermann function, which (not being primitive recursive) cannot be written in BlooP. Borrowing from standard terminology in mathematical logic,Hofstadter (1979), p. 424. Hofstadter calls FlooP's unbounded loops MU-loops. Like all Turing-complete programming languages, FlooP suffers from the halting problem: programs might not terminate, and it is not possible, in general, to decide which programs do. BlooP ... [...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 implementation that is treated as a 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 languages. Definitions There are many considerations when defini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model Of Computation
In computer science, and more specifically in computability theory and computational complexity theory, a model of computation is a model which describes how an output of a mathematical function is computed given an input. A model describes how units of computations, memories, and communications are organized. The computational complexity of an algorithm can be measured given a model of computation. Using a model allows studying the performance of algorithms independently of the variations that are specific to particular implementations and specific technology. Models Models of computation can be classified into three categories: sequential models, functional models, and concurrent models. Sequential models Sequential models include: * Finite state machines * Post machines (Post–Turing machines and tag machines). * Pushdown automata * Register machines ** Random-access machines * Turing machines * Decision tree model Functional models Functional models include: * Abstract re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Machine That Always Halts
In computability theory, a decider is a Turing machine that halts for every input. A decider is also called a total Turing machineKozen, 1997 as it represents a total function. Because it always halts, such a machine is able to decide whether a given string is a member of a formal language. The class of languages which can be decided by such machines is the set of recursive languages. Given an arbitrary Turing machine, determining whether it is a decider is an undecidable problem. This is a variant of the halting problem, which asks for whether a Turing machine halts on a specific input. Functions computable by total Turing machines In practice, many functions of interest are computable by machines that always halt. A machine that uses only finite memory on any particular input can be forced to halt for every input by restricting its flow control capabilities so that no input will ever cause the machine to enter an infinite loop. As a trivial example, a machine implementin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conditional (programming)
In computer science, conditionals (that is, conditional statements, conditional expressions and conditional constructs,) are programming language commands for handling decisions. Specifically, conditionals perform different computations or actions depending on whether a programmer-defined boolean ''condition'' evaluates to true or false. In terms of control flow, the decision is always achieved by selectively altering the control flow based on some condition (apart from the case of branch predication). Although dynamic dispatch is not usually classified as a conditional construct, it is another way to select between alternatives at runtime. Terminology In imperative programming languages, the term "conditional statement" is usually used, whereas in functional programming, the terms "conditional expression" or "conditional construct" are preferred, because these terms all have distinct meanings. If–then(–else) The if–then construct (sometimes called if–then–els ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gödel Numbering For Sequences
In mathematics, a Gödel numbering for sequences provides an effective way to represent each finite sequence of natural numbers as a single natural number. While a set theoretical embedding is surely possible, the emphasis is on the effectiveness of the functions manipulating such representations of sequences: the operations on sequences (accessing individual members, concatenation) can be "implemented" using total recursive functions, and in fact by primitive recursive functions. It is usually used to build sequential “data types” in arithmetic-based formalizations of some fundamental notions of mathematics. It is a specific case of the more general idea of Gödel numbering. For example, recursive function theory can be regarded as a formalization of the notion of an algorithm, and can be regarded as a programming language to mimic lists by encoding a sequence of natural numbers in a single natural number. Monk 1976: 56–58 Csirmaz 1994: 99–100 (seonline Gödel numbering ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Assignment (computer Science)
In computer programming, an assignment statement sets and/or re-sets the value stored in the storage location(s) denoted by a variable name; in other words, it copies a value into the variable. In most imperative programming languages, the assignment statement (or expression) is a fundamental construct. Today, the most commonly used notation for this operation is ''x'' = ''expr'' (originally Superplan 1949–51, popularized by Fortran 1957 and C). The second most commonly used notation is ''x'' := ''expr'' (originally ALGOL 1958, popularised by Pascal). Many other notations are also in use. In some languages, the symbol used is regarded as an operator (meaning that the assignment statement as a whole returns a value). Other languages define assignment as a statement (meaning that it cannot be used in an expression). Assignments typically allow a variable to hold different values at different times during its life-span and scope. However, some languages (primarily strictly f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operator (programming)
In computer programming, operators are constructs defined within programming languages which behave generally like functions, but which differ syntactically or semantically. Common simple examples include arithmetic (e.g. addition with ), comparison (e.g. "greater than" with >), and logical operations (e.g. AND, also written && in some languages). More involved examples include assignment (usually = or :=), field access in a record or object (usually .), and the scope resolution operator (often :: or .). Languages usually define a set of built-in operators, and in some cases allow users to add new meanings to existing operators or even define completely new operators. Syntax Syntactically operators usually contrast to functions. In most languages, functions may be seen as a special form of prefix operator with fixed precedence level and associativity, often with compulsory parentheses e.g. Func(a) (or (Func a) in Lisp). Most languages support programmer-defined ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shepherdson And Sturgis' Model
Shepherdson is a surname. Notable people with the surname include: *Arunah Shepherdson Abell (1806–1888), American publisher * Ella Shepherdson, missionary in Australia whose name was given to Shepherdson College on Elcho Island, Northern Territory *Guy Shepherdson (born 1982), Australian rugby player *Harold Shepherdson Harold Shepherdson MBE (28 October 1918 – 13 September 1995) was an English football player, coach and manager. Born in Middlesbrough, Shepherdson signed for his hometown club in 1936, but saw his playing career interrupted by the Sec ... (1918–1995), English football player and coach * Jane Shepherdson (born 1961), British businesswoman {{surname ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variable (programming)
In computer programming, a variable is an abstract storage location paired with an associated symbolic name, which contains some known or unknown quantity of information referred to as a ''value''; or in simpler terms, a variable is a named container for a particular set of bits or type of data (like integer, float, string etc...). A variable can eventually be associated with or identified by a memory address. The variable name is the usual way to reference the stored value, in addition to referring to the variable itself, depending on the context. This separation of name and content allows the name to be used independently of the exact information it represents. The identifier in computer source code can be bound to a value during run time, and the value of the variable may thus change during the course of program execution. Variables in programming may not directly correspond to the concept of variables in mathematics. The latter is abstract, having no reference to a physi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Halting Problem
In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running, or continue to run forever. Alan Turing proved in 1936 that a general algorithm to solve the halting problem for all possible program–input pairs cannot exist. For any program that might determine whether programs halt, a "pathological" program , called with some input, can pass its own source and its input to ''f'' and then specifically do the opposite of what ''f'' predicts ''g'' will do. No ''f'' can exist that handles this case. A key part of the proof is a mathematical definition of a computer and program, which is known as a Turing machine; the halting problem is '' undecidable'' over Turing machines. It is one of the first cases of decision problems proven to be unsolvable. This proof is significant to practical computing efforts, defining a class of applications which no programming inventi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Douglas Hofstadter
Douglas Richard Hofstadter (born February 15, 1945) is an American scholar of cognitive science, physics, and comparative literature whose research includes concepts such as the sense of self in relation to the external world, consciousness, analogy-making, artistic creation, literary translation, and discovery in mathematics and physics. His 1979 book '' Gödel, Escher, Bach: An Eternal Golden Braid'' won both the Pulitzer Prize for general nonfiction"General Nonfiction" . ''Past winners and finalists by category''. The Pulitzer Prizes. Retrieved March 17, 2012. and a (at that time called The American Book Award) for Science. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Logic
Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics. Since its inception, mathematical logic has both contributed to and been motivated by the study of foundations of mathematics. This study began in the late 19th century with the development of axiomatic frameworks for geometry, arithmetic, and Mathematical analysis, analysis. In the early 20th century it was shaped by David Hilbert's Hilbert's program, program to prove the consistency of foundational theories. Results of Kurt Gödel, Gerhard Gentzen, and others provided partial resolution to the program, and clarified the issues involved in pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
