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Continuation

In computer science, a continuation is an abstract representation of the control state of a computer program. A continuation implements (reifies) the program control state, i.e. the continuation is a data structure that represents the computational process at a given point in the process's execution; the created data structure can be accessed by the programming language, instead of being hidden in the runtime environment. Continuations are useful for encoding other control mechanisms in programming languages such as exceptions, generators, coroutines, and so on.

The "current continuation" or "continuation of the computation step" is the continuation that, from the perspective of running code, would be derived from the current point in a program's execution. The term continuations can also be used to refer to first-class continuations, which are constructs that give a programming language the ability to save the execution state at any point and return to that point at a later point in the program, possibly multiple times.

History
The earliest description of continuations was made by Adriaan van Wijngaarden in September 1964. Wijngaarden spoke at the IFIP Working Conference on Formal Language Description Languages held in Baden bei Wien, Austria. As part of a formulation for an Algol 60 preprocessor, he called for a transformation of proper procedures into continuation-passing style, though he did not use this name, and his intention was to simplify a program and thus make its result more clear.

Christopher Strachey, Christopher P. Wadsworth and John C. Reynolds brought the term continuation into prominence in their work in the field of denotational semantics that makes extensive use of continuations to allow sequential programs to be analysed in terms of functional programming semantics.

Steve Russell invented the continuation in his second Lisp implementation for the IBM 704, though he did not name it.

gives a complete history of the discovery of continuations.

First-class continuations
First-class continuations are a language's ability to completely control the execution order of instructions. They can be used to jump to a function that produced the call to the current function, or to a function that has previously exited. One can think of a first-class continuation as saving the execution state of the program. True first-class continuations do not save program data – unlike a process image – only the execution context. This is illustrated by the "continuation sandwich" description:

''Say you're in the kitchen in front of the refrigerator, thinking about a sandwich. You take a continuation right there and stick it in your pocket. Then you get some turkey and bread out of the refrigerator and make yourself a sandwich, which is now sitting on the counter. You invoke the continuation in your pocket, and you find yourself standing in front of the refrigerator again, thinking about a sandwich. But fortunately, there's a sandwich on the counter, and all the materials used to make it are gone. So you eat it. :-)''

In this description, the sandwich is part of the program data (e.g., an object on the heap), and rather than calling a "make sandwich" routine and then returning, the person called a "make sandwich with current continuation" routine, which creates the sandwich and then continues where execution left off.

Scheme was the first full production system providing first "catch" and then call/cc. Bruce Duba introduced call/cc into SML.

Continuations are also used in models of computation including denotational semantics, the actor model, process calculi, and lambda calculus. These models rely on programmers or semantics engineers to write mathematical functions in the so-called continuation-passing style. This means that each function consumes a function that represents the rest of the computation relative to this function call. To return a value, the function calls this "continuation function" with a return value; to abort the computation it returns a value.

Functional programmers who write their programs in continuation-passing style gain the expressive power to manipulate the flow of control in arbitrary ways. The cost is that they must maintain the invariants of control and continuations by hand, which can be a highly complex undertaking (but see 'continuation-passing style' below).

Uses
Continuations simplify and clarify the implementation of several common design patterns, including coroutines/green threads and exception handling, by providing the basic, low-level primitive which unifies these seemingly unconnected patterns. Continuations can provide elegant solutions to some difficult high-level problems, like programming a web server that supports multiple pages, accessed by the use of the forward and back buttons and by following links. The Smalltalk Seaside web framework uses continuations to great effect, allowing one to program the web server in procedural style, by switching continuations when switching pages.

More complex constructs for which "continuations provide an elegant description" also exist. For example, in C, longjmp can be used to jump from the middle of one function to another, provided the second function lies deeper in the stack (if it is waiting for the first function to return, possibly among others). Other more complex examples include coroutines in Simula 67, Lua, and Perl; tasklets in Stackless Python; generators in Icon and Python; continuations in Scala (starting in 2.8); fibers in Ruby (starting in 1.9.1); the backtracking mechanism in Prolog; monads in functional programming; and threads.

Examples
The Scheme programming language includes the control operator call-with-current-continuation (abbreviated as: call/cc) with which a Scheme program can manipulate the flow of control:

Using the above, the following code block defines a function  that sets   to the future execution state of itself:

For a gentler introduction to this mechanism, see call-with-current-continuation.

Coroutines
This example shows a possible usage of continuations to implement coroutines as separate threads.

The functions defined above allow for defining and executing threads through cooperative multitasking, i.e. threads that yield control to the next one in a queue:

The previous code will produce this output: This is AAA 0 Hello from BBB 0 This is AAA 1 Hello from BBB 1 This is AAA 2 Hello from BBB 2 ...

Implementation
A program must allocate space in memory for the variables its functions use. Most programming languages use a call stack for storing the variables needed because it allows for fast and simple allocating and automatic deallocation of memory. Other programming languages use a heap for this, which allows for flexibility at a higher cost for allocating and deallocating memory. Both of these implementations have benefits and drawbacks in the context of continuations.

Programming language support
Many programming languages exhibit first-class continuations under various names; specifically:
 * Common Lisp: cl-cont. One can also use custom macros
 * C# / VB.NET:  and  : "sign up the rest of method as the continuation, and then return to your caller immediately; the task will invoke the continuation when it completes." Asynchronous Programming for C#
 * Factor:  and
 * Haskell: The Continuation monad in
 * Haxe: haxe-continuation
 * Icon, Unicon :  operator: coexpressions
 * Java: Lightwolf javaflow (requires bytecode manipulation at runtime or compile time)
 * Kotlin :
 * JavaScript Rhino :
 * Parrot:  PMC; uses continuation-passing style for all control flow
 * Perl: Coro and Continuity
 * Pico:  and
 * Python: PyPy's
 * Racket:  (commonly shortened to  )
 * Ruby:
 * Scala:  provides  /
 * Scheme:  (commonly shortened to  )
 * Smalltalk: ; in most modern Smalltalk environments continuations can be implemented without additional VM support.
 * Standard ML of New Jersey:
 * Unlambda:, the flow control operation for call with current continuation

In any language which supports closures and proper tail calls, it is possible to write programs in continuation-passing style and manually implement call/cc. (In continuation-passing style, call/cc becomes a simple function that can be written with lambda.) This is a particularly common strategy in Haskell, where it is easy to construct a "continuation-passing monad" (for example, the   monad and   monad transformer in the   library). The support for proper tail calls is needed because in continuation-passing style no function ever returns; all calls are tail calls.

In Web development
One area that has seen practical use of continuations is in Web programming. The use of continuations shields the programmer from the stateless nature of the HTTP protocol. In the traditional model of web programming, the lack of state is reflected in the program's structure, leading to code constructed around a model that lends itself very poorly to expressing computational problems. Thus continuations enable code that has the useful properties associated with inversion of control, while avoiding its problems. "Inverting back the inversion of control or, Continuations versus page-centric programming" is a paper that provides a good introduction to continuations applied to web programming.

Kinds
Support for continuations varies widely. A programming language supports re-invocable continuations if a continuation may be invoked repeatedly (even after it has already returned). Re-invocable continuations were introduced by Peter J. Landin using his J (for Jump) operator that could transfer the flow of control back into the middle of a procedure invocation. Re-invocable continuations have also been called "re-entrant" in the Racket language. However this use of the term "re-entrant" can be easily confused with its use in discussions of multithreading.

A more limited kind is the escape continuation that may be used to escape the current context to a surrounding one. Many languages which do not explicitly support continuations support exception handling, which is equivalent to escape continuations and can be used for the same purposes. C's  are also equivalent: they can only be used to unwind the stack. Escape continuations can also be used to implement tail call elimination.

One generalization of continuations are delimited continuations. Continuation operators like  capture the entire remaining computation at a given point in the program and provide no way of delimiting this capture. Delimited continuation operators address this by providing two separate control mechanisms: a prompt that delimits a continuation operation and a reification operator such as  or. Continuations captured using delimited operators thus only represent a slice of the program context.

Disadvantages
Continuations are the functional expression of the GOTO statement, and the same caveats apply. While they are a sensible option in some special cases such as web programming, use of continuations can result in code that is difficult to follow. In fact, the esoteric programming language Unlambda includes call-with-current-continuation as one of its features solely because expressions involving it "tend to be hopelessly difficult to track down." The external links below illustrate the concept in more detail.

Linguistics
In "Continuations and the nature of quantification", Chris Barker introduced the "continuation hypothesis", that some linguistic expressions (in particular, QNPs [quantificational noun phrases]) have denotations that manipulate their own continuations. Barker argued that this hypothesis could be used to explain phenomena such as duality of NP meaning (e.g., the fact that the QNP "everyone" behaves very differently from the non-quantificational noun phrase "Bob" in contributing towards the meaning of a sentence like "Alice sees [Bob/everyone]"), scope displacement (e.g., that "a raindrop fell on every car" is interpreted typically as $$\forall c \exists r, \mbox{fell}(r,c)$$ rather than as $$\exists r \forall c, \mbox{fell}(r,c)$$), and scope ambiguity (that a sentence like "someone saw everyone" may be ambiguous between $$\exists x \forall y, \mbox{saw}(x,y)$$ and $$\forall y \exists x, \mbox{saw}(x,y)$$). He also observed that this idea is in a way just a natural extension of Richard Montague's approach in "The Proper Treatment of Quantification in Ordinary English" (PTQ), writing that "with the benefit of hindsight, a limited form of continuation-passing is clearly discernible at the core of Montague’s (1973) PTQ treatment of NPs as generalized quantifiers".

The extent to which continuations can be used to explain other general phenomena in natural language is a topic of current research.

title: Continuation


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User:Maarten~enwiki

Born November, 6th, 1978 in Amsterdam, the Netherlands. Currently living in Amstelveen (small town on the outskirts of Amsterdam). Social status: married. Education: M.Sc. in biomolecular Chemistry at the University of Amsterdam Occupation: teaching high school level Chemistry, Biology and Physics. Spending free time mainly consists of troubleshooting PC problems (using my alter ego Dr. Piepie... ;)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: User:Maarten~enwiki


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Talk:Robert Hyland

Untitled
Comments that are "below-the-vote" that don't need to be there anymore in WP:VfD:

 * Do you just google for someone with the same name who is somewhat famous in order to get a page kept? I can't imagine that you listened to him in the 1950s but it's possible. - Texture 21:38, 4 Mar 2004 (UTC)
 * That time I did. Isn't that a good thing? Anthony DiPierro 21:56, 4 Mar 2004 (UTC)
 * I didn't say that it was and I didn't say that it was not. I'm still deciding.  Regardless, it was inappropriate to spring that in and throw "legendary" to confuse both people who have voted and those who haven't.  Next time maybe explain the change of target so it can be reevaluated. - Texture 21:59, 4 Mar 2004 (UTC)
 * Next time I suggest you do a little research before spouting out "delete, vanity." Anthony DiPierro 22:04, 4 Mar 2004 (UTC)
 * The original listed was indeed vanity. What's the problem? - Texture 22:06, 4 Mar 2004 (UTC)
 * How can you know it's vanity without doing any research? Anthony DiPierro 22:16, 4 Mar 2004 (UTC)
 * If you read the article and research shows that there are no programmers of fame as that identified then it is a vanity posting. - Texture 22:25, 4 Mar 2004 (UTC)
 * So you did do reasearch, but just didn't run across this legendary individual? Anthony DiPierro 22:40, 4 Mar 2004 (UTC)
 * I did not run into any legendary programmers. Did you? or are you assuming that the programmer is also a dead radio personality? - Texture 23:21, 4 Mar 2004 (UTC)
 * Anthony- the next time you completely change the target of an article, can you make a note of that in your comment, as well as in your argument to keep the page here? It's extremely confusing to other voters. - DropDeadGorgias (talk) 21:46, Mar 4, 2004 (UTC)
 * I changed it after I made my vote. Anthony DiPierro 21:56, 4 Mar 2004 (UTC)
 * I'm confused- you thought the other guy (the attorney) was "Legendary", or you voted, with the intent of changing the target? In either case, both a more descriptive comment and an announcement of your intention with the page here would have been in order. - DropDeadGorgias (talk) 21:59, Mar 4, 2004 (UTC)
 * No, I changed my vote reason after making the change. Anthony DiPierro 22:04, 4 Mar 2004 (UTC)
 * The person was changed from a programmer of no fame to this somewhat famous individual - Texture 21:38, 4 Mar 2004 (UTC)
 * I think "legendary" individual would be a more appropriate description than "somewhat famous". Anthony DiPierro 22:05, 4 Mar 2004 (UTC)
 * You didn't even know who he was until you googled him. Not very "legendary" - Texture 22:15, 4 Mar 2004 (UTC)
 * We better change http://en.wikipedia.org/wiki/Talk_radio then. Anthony DiPierro 22:17, 4 Mar 2004 (UTC)

You criticize me for not explaining the change I made and then you move the explanation of the change to another page? Anthony DiPierro 22:21, 4 Mar 2004 (UTC)

 * You indicated that it was changed in your vote. Your vote remains. - Texture 22:24, 4 Mar 2004 (UTC)

 * Still chuckling, texture? - DropDeadGorgias (talk)

 * Only when his humour makes a point... ;) - Texture 22:32, 4 Mar 2004 (UTC)

 * I didn't indicate anything in my vote. Anthony DiPierro 22:40, 4 Mar 2004 (UTC)

title: Talk:Robert Hyland


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Green Bullfrog

Green Bullfrog is a blues album recorded by an ad hoc band and produced by Derek Lawrence. The bulk of the album was recorded over two sessions at De Lane Lea Studios, London in 1970, with later string and brass overdubs. It was originally released in 1971, with reissues in 1980 and 1991.

The album listed pseudonyms in the credits for contractual reasons and was commercially unsuccessful. The musicians were eventually confirmed as including Deep Purple's Ritchie Blackmore and Ian Paice, Procol Harum's Matthew Fisher, Chas & Dave's Chas Hodges and session guitarists Albert Lee and Big Jim Sullivan.

Background
Green Bullfrog was the idea of producer Derek Lawrence, who assembled a group of musicians with whom he had worked in the 1960s. Guitarist Albert Lee had been working with Lawrence as a session player, and the original idea had been to record with former Screaming Lord Sutch bassist Tony Dangerfield. However, the sessions did not work out, so the pair decided to invite other session musicians and Sutch alumni and record a studio jam.

The backing tracks were recorded in two overnight sessions on 20 April and 23 May 1970 at De Lane Lea Studios, London, starting at 11pm. It was recorded live into four track tape. Deep Purple and former Sutch guitarist Ritchie Blackmore had previously worked with Lawrence and brought along their drummer Ian Paice. According to Lee, Blackmore and Paice arrived at the studio directly from Deep Purple gigs on both occasions. Session guitarist Big Jim Sullivan was invited as he had originally taught Blackmore how to play guitar and was greatly admired by him. Guitarist Rod Alexander was friends with Blackmore and worked in a music shop on Charing Cross Road. He arrived at the session to deliver some guitar strings and was persuaded to stay. All the musicians had wanted to play together for some time, but were too busy with touring or session work to do so. Singer Earl Jordan had been recording with the Les Humphries Singers. He put down guide vocals during the main session, then re-recorded all his parts after everyone else had left. Strings and brass overdubs were added on 4 January 1971.

A few originals (penned by Lawrence) were played, as well as many blues-inflected cover versions. Sullivan rearranged Lawrence's "Lovin' You (Is Good for Me Baby)" in compound time to make it more interesting to play. The guitar workout instrumental "Bullfrog" is a Deep Purple song "Jam Stew", which had been previously recorded at a BBC Radio 1 session. Blackmore played the main riff once to Sullivan and Lee, who both immediately created guitar harmonies around it. The track also features Tony Ashton on Hammond organ. The sessions also included a cover of the Creation's "Makin' Time", which Blackmore and Lawrence had both wanted to record. Lawrence selected all the other songs for everyone to record.

For contractual reasons, the musicians were billed under pseudonyms. Lee was called "Pinta" after an in-joke where he would say "I'm only delivering the milk!" when a second take of a song was requested. Ashton was called "Bevy" because he liked to keep bottles of light ale under his organ. Bassist Chas Hodges (who previously played with Blackmore in the Outlaws and would later be one half of Chas & Dave) took the name "Sleepy" due to his habit of falling asleep at sessions. Blackmore was called "Boots" because he frequently wore suede cowboy boots, while Sullivan was nicknamed "The Boss" due to his respect from the others as one of the best session players. Procol Harum's Matthew Fisher, who played piano on the album, was named "Sorry" after his reputation of apologising if another take was required. Alexander was called "The Vicar" after Lawrence's habit of saying "hello, vicar" to him, while Paice was nicknamed "Speedy" owing to his fast playing style. Despite rumours at the time, Roger Glover and Jon Lord did not attend any of the sessions.

Release
The title Green Bullfrog was chosen by Lawrence. Hodges later said it was because Lawrence wanted to name every project after a colour. The first release of the session was on 19 March 1971 in the US by Decca Records, as well as a single coupling the tracks "My Baby Left Me" and "Lovin' You Is Good for Me, Baby". It was issued in the UK by MCA Records in March 1972 after Lawrence played some tracks to company president Mike Maitland. However, Maitland had left the company by the time the album was released, so it had little promotion and was commercially unsuccessful.

The album was re-released in 1980 under ECY Street Records in the US. The reissue had additional sleeve notes written by Ed Chapero. The front cover had a quote from Blackmore taken from an interview with Guitar Player magazine in September 1978, which correctly identified himself, Paice, Lee and Sullivan on the album but mistakenly credited Glover. Both Blackmore and Glover were unimpressed with the front cover quotation. It was remixed at Abbey Road Studios, London in 1991 by Lawrence and engineer Peter Vince and reissued on LP and CD. The re-release contained extra tracks not on the original release, and additional information and sleeve notes including an interview with Lawrence. It was the first release that properly credited all the musicians. Four tracks recorded by Green Bullfrog have been published on the 2005 Blackmore compilation Get Away – Groups and Sessions.

Dave Thompson gave a retrospective review on AllMusic which was mixed, praising the quality of musicians, but felt there was "little [...] to truly engage the attention".

LP
Taken from the sleeve notes

Side one
 * 1) "My Baby Left Me" (Arthur Crudup)
 * 2) "Makin' Time" (Eddie Phillips, Kenny Pickett)
 * 3) "Lawdy Miss Clawdy" (Lloyd Price)
 * 4) "Bullfrog" (Derek Lawrence, Ritchie Blackmore, Ian Paice)

Side two
 * 1) "I Want You" (Tony Joe White)
 * 2) "I'm a Free Man" (Mark "Moogy" Klingman)
 * 3) "Walk a Mile in My Shoes" (Joe South)
 * 4) "Lovin' You Is Good for Me Baby" (Lawrence/Corlett/Hutton)

CD reissue
Tracks marked * are on the original LP.
 * 1) "Ain't Nobody Home" (Jerry Ragovoy)
 * 2) "Bullfrog" (Derek Lawrence, Ritchie Blackmore, Ian Paice)*
 * 3) "Walk a Mile in My Shoes" (Joe South)*
 * 4) "My Baby Left Me" (Arthur Crudup)*
 * 5) "Makin' Time" (Eddie Phillips, Kenny Pickett)*
 * 6) "Lawdy Miss Clawdy" (Lloyd Price)*
 * 7) "I'm a Free Man" (Mark "Moogy" Klingman)*
 * 8) "Lovin' You Is Good for Me Baby" (Lawrence/Corlett/Hutton)*
 * 9) "I Want You" (Tony Joe White)*
 * 10) "Louisiana Man" (Doug Kershaw)
 * 11) "Who Do You Love?" (Ellas McDaniel)

Personnel

 * "Speedy" (Ian Paice) – drums
 * "Sleepy" (Chas Hodges) – bass
 * "Bevy" (Tony Ashton) – piano / organ
 * "Sorry" (Matthew Fisher) – piano
 * "Boots" (Ritchie Blackmore) – guitar
 * "Pinta" (Albert Lee) – guitar
 * "The Boss" (Big Jim Sullivan) – guitar
 * "The Vicar" (Rod Alexander) – guitar
 * "Jordan" (Earl Jordan) – vocals

Production
 * Derek Lawrence – producer
 * Martin Birch – engineer

title: Green Bullfrog


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Portaria

Portaria (Greek: Πορταριά) is a village and a former municipality in Magnesia, Thessaly, Greece. Since the 2011 local government reform it is part of the municipality Volos, of which it is a municipal unit. The municipal unit has an area of 22.754 km2. It is located on Mt. Pelion, facing the Pagasetic Gulf, north of Volos and its suburbs. The majority of the buildings are typical examples of Pelion architecture with their windows and doors decorated with a variety of colors. The mountaintop of Pelion is to the north. Portaria every year holds a traditional wedding in the main square of the village and many people from Volos and the surrounding villages drop by to learn how weddings were traditionally done in these villages.

Sister cities

 * 🇫🇷 Tourtour, France

title: Portaria


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Battle Creek (Milk River tributary)

Battle Creek is a river that begins in the south-eastern region of the Canadian province of Alberta, near the border with Saskatchewan, in the Cypress Hills Interprovincial Park. From Alberta, Battle Creek flows east and across the border into Saskatchewan. It flows south out of Saskatchewan across the Canada–United States border into Montana, where it joins the Milk River in Blaine County, Montana.

Description
Battle Creek begins in the Cypress Hills and Palliser's Triangle region of Alberta, is 203 km long, has a drainage area of 2600 km2, and flows through Alberta, Saskatchewan, and Montana en route to its mouth at the Milk River. The landscape it runs though is semi-arid with rolling hills, deep-cut valleys, coulees, badlands, and grasslands. Due to the semi-arid climate, the area is prone to drought so several dams and irrigation projects have been built in its watershed. In the 1930s, two notable dam projects were built to help regulate the river's water levels. Near the headwaters of Battle Creek, a dam was built along Adams Creek – a tributary of Battle Creek – that created Adams Lake (49.6582°N, -109.8455°W). During the dry months, water can be released from Adams Lake to help prevent Battle Creek from dying up, which allows for irrigation throughout the growing season. Another project involved the building of two dams that created Cypress Lake. Cypress Lake, while not along the course of Battle Creek, is supplied by Battle Creek plus other nearby creeks. Cypress Lake is an interbasin transfer reservoir as it is the source of the Frenchman River and can re-supply Battle Creek during dry years.

Battle Creek and the other tributaries of the Milk River watershed in Alberta and Saskatchewan, is one of only three watersheds in Canada where the water ultimately flows into the Gulf of Mexico. The other two watersheds are Poplar River and Big Muddy Creek.

Near the community of Nashlyn in Saskatchewan, Battle Creek flows through a portion of the Govenlock-Nashlyn-Battle Creek Grasslands Important Bird Area (IBA) of Canada.

Fort Walsh was established on the river on the Saskatchewan side of Cypress Hills Interprovincial Park.

Fish species
Fish species commonly found in the river include northern pike, rainbow trout, brook trout, brown trout, burbot, common carp, white sucker, and shorthead redhorse. The Battle Creek, along with Lake Diefenbaker, are the only two bodies of water in Saskatchewan that support a reproducing population of rainbow trout. There is concern that Asian carp, particularly silver carp, may spread up the river and to the other south flowing rivers that drain into the Milk River, such as the Frenchman River.

title: Battle Creek (Milk River tributary)


text:
Klinger

Klinger may refer to:

 * Klinger (surname), a list of people with the surname
 * Corporal Klinger, a character from M*A*S*H
 * Klinger (horse), owned by the US Army
 * Klinger (band), an Australia band from 1996 to 2003
 * Klinger Ridge, Marie Byrd Land, Antarctica
 * Klinger Lake, near Klingers, Michigan, United States
 * 22369 Klinger, a main-belt asteroid

title: Klinger


text:
Max Klinger

Max Klinger (18 February 1857 – 5 July 1920) was a German artist who produced significant work in painting, sculpture, prints and graphics, as well as writing a treatise articulating his ideas on art and the role of graphic arts and printmaking in relation to painting. He is associated with symbolism, the Vienna Secession, and Jugendstil (Youth Style) the German manifestation of Art Nouveau. He is best known today for his many prints, particularly a series entitled Paraphrase on the Finding of a Glove and his monumental sculptural installation in homage to Beethoven at the Vienna Secession in 1902.

Life
Klinger was born in Leipzig, Kingdom of Saxony to a wealthy and prominent family. He enrolled in the Academy of Fine Arts in Karlsruhe in 1874 where he was a pupil of Karl (or Carl) Gussow. When Gussow left Karlsruhe to become the Director of the Academy of Fine Arts in Berlin, Klinger moved to Berlin as well to complete his studies there. Klinger shared a studio with Christian Krohg and the two had a mutual admiration for French naturalist authors like Émile Zola and Gustave Flaubert, who explored the shadowy aspects of urban life and the hypocrisy of society and the bourgeoisie in their novels. At that time realism was the prevailing style in Germany and Arnold Böcklin was one of the few artist active there that Klinger felt a close affinity to. Klinger graduated from the Academy in 1877. He was drawn to and studied the etchings and prints of many masters that were more aligned with his sensibilities including Dürer, Rembrandt, Goya, Runge, Menzel, and Rops. He began an apprenticeship studying engraving under Hermann Sagert and soon became a skilled and imaginative engraver in his own right. Klinger visited Brussels for a time in 1879, and the following year he spent time in Munich. He was achieving some notoriety with his pen and ink drawings and prints when in 1881 he published two sets of etchings, including Paraphrase on the Finding of a Glove, which was an immediate success and established his reputation.

With a receptive audience developing in Paris, where the Franco-Uruguayan poet and art critic Jules Laforgue had been celebrating and advocating his prints, Klinger moved to Paris in 1883 where he lived until 1886 or 1887. Klinger first began sculpting about 1883, and sculpture slowly came to dominate his output in his later years. He conceived and started work on his Beethoven sculpture while in Paris but, it was not completed and fully realized until 1902. In 1889 Les XX (The Twenty) invited Klinger to exhibit his work in their annual winter exhibition that year in Brussels. He moved to Rome in 1889, staying until 1893, studying the Italian masters, where the 15th century artists and works from antiquity are said to have been something of a revelation to him. He also intensified his studies of anatomy, the nude, and the representation of mass and volume during this period of his life. It was a productive time in his career. In the 1890s, Klinger continued his gradual shift away from printmaking in favor of sculpting.

Klinger was an accomplished pianist and counted the composer Max Reger among his friends. A friendship with the composer Johannes Brahms developed over a period of 20 years, culminating with Klinger's publication of his print series Brahms Fantasies (1894) and Brahms's dedication of Vier ernste Gesänge (Four Serious Songs), Opus 121, to Klinger in 1896, a year before the composer's death.

In 1906 he founded the Villa Romana Prize. After buying a villa in Florence, complete with 15,000 square meter park, recipients of the prize were given the opportunity to stay for a few months and adsorbed the culture of the city. The first beneficiary of the prize was Gustav Klimt, however Klimt waived his honor and passed it on to Maximilian Kurzweil. Later recipients included Käthe Kollwitz, Max Beckmann, Ernst Barlach and Georg Kolbe.

Elsa Asenijeff (1867-1941) was a writer and poet, as well as a model, muse, and girlfriend of Klinger for about 15 years. They had a daughter Desirée Klinger (1900–1973) but were never married. In 1903 he moved away from Leipzig and bought a vineyard in Großjena [Gross Jena,], near Naumburg, Germany, where he settled in his later years. In 1911 Klinger left Asenijeff, when her mental health begin to show signs of deteriorating, for an 18-year-old model, Gertrud Bock (1893–1932), who he ultimately married a few months before his death in 1920. Klinger left his estate to Gertrud. The sculptor Johannes Hartmann, a friend of Klinger's, served as caretaker of the Klinger estate and designed Klinger's tomb with portraits of Klinger and Gertrud. Johannes Hartmann married Gertrud Klinger in 1922, however, much of the remainder of their lives was spent in litigation with Klinger's daughter, Desirée Klinger over the estate.

Documentary photographs

Art

A significant portion of Klinger’s reputation is associated with his many cycles and series of intaglio prints, which influenced numerous printmakers and artist of the late 19th and early 20th centuries. Klinger would adeptly integrate several intaglio media like aquatint, drypoint, and etching in a single plate, producing remarkable formal and tonal qualities. The subjects range from esoteric symbolism to darker aspects of realism. In the cycle A Life (1884), Klinger is often regarded as the first German artist to deal with prostitution as a social problem and the hypocrisy and injustices regarding societies attitude to the subject. The series follow a middle-class woman's descent into prostitution: impregnated, deserted, then rejected by society, she descends into the depths of urban life, and ridiculed by an apathetic and indifferent genteel society. The series A Love (1887) was dedicated to Arnold Böcklin another symbolist artist Klinger greatly admired.

In the series, Paraphrase on the Finding of a Glove (printed 1881), the pictures were based on images which came to Klinger in dreams after finding a glove at an ice-skating rink. In the leitmotivic device of a glove—belonging to a woman whose face we never see—Klinger anticipated the research of Freud and Krafft-Ebing on fetish objects. In this case, the glove becomes a symbol for the artist's romantic yearnings, finding itself, in each plate, in different dramatic situations, and performing the role that we might expect the figure of the beloved herself to fulfill. Semioticians have also seen in the symbol of the glove an example of a sliding signifier, or signifier without signified—in this case, the identity of the woman which Klinger is careful to conceal. The plates suggest various psychological states or existential crises faced by the artist protagonist (who bears a striking resemblance to the young Klinger).

In Paris he started to draft his polemical text for Painting and Drawing, which was eventually published in 1891, and subsequently reissued a number of times. The manuscript was well circulated and well read, with a number of later artist and historians referencing it, including Giorgio de Chirico who called Klinger the "modern artist par excellence". In it Klinger asserted the idea that prints and the graphic arts should have a new and significant role in the arts, distinct from painting, and were best suited for stylistic and conceptual experimentation. Also that the differences between naturalism (realism) and neo-idealism, as well as form and content, were reconcilable, and both were possible. Concepts of the Gesamtkunstwerk, an all-embracing art form, with unity among the arts (e.g. painting, sculpture, literature, poetry, music, etc.), were also discussed.

Klinger had a lifelong passion for music and musical elements are often reflected and expressed in his art. His print cycles were given opus numbers, typically associated with musical publications. His series Brahms Fantasies (1894) was intended to be an amalgamation of music, poetry, and the visual arts: to be viewed with a performance of the composer’s music, creating Gesamtkunstwerk or "all-embracing art form". Klinger produced sculptures of Beethoven, Brahms, and Liszt as well as the plinth of the Richard Wagner Memorial (1911).

Inspired by recent accounts of archaeological discoveries of antique sculptural remains made from various colored stones, Klinger utilized a variety of materials in many of his sculptures. A mixture of bronze, ivory, alabaster, and several different marbles were used in Beethoven. He studied and took measurements of Beethoven's death mask in Vienna and traveled to Laas in southwestern France to personally select the alabaster, and the Pyrenees and Syra (or Syros), Greece to select marbles. Elsa Asenijeff wrote of the unusually complex and difficult process involved with casting the large bronze throne from wax in her book Max Klinges Beethoven: Eine kunst-technische Studie (Max Klinge's Beethoven: A Practical Artistic Study) published in 1902. The sculpture was exhibited in an earlier stage of development in Paris in 1885 and later rejected from major exhibitions in Berlin 1887 and 1888. It developed something of a cult-like reputation over the years.

Beethoven was the theme of the 14th exhibition of the Vienna Secession in 1902, and Max Klinger's sculpture was brought to Vienna as the centerpiece. The Vienna Secession had hoped to purchase the sculpture but this was not to come to fruition. Headed by Alfred Roller, the artist of the Secession created works on the theme for the galleries and Roller and the architect Josef Hoffmann oversaw the overall installation. Klinger's Beethoven was installed in the central hall with Alfred Roller's mural Night Descending on the wall behind it. Gustav Klimt's seminal Beethoven Frieze was visible in an adjoining room. Even the normally shy and retiring Gustav Mahler was persuaded to transcribe music from Beethoven's Ninth Symphony for trumpets and rehearse the musicians for the opening. The exhibition, presented within the specific architecture, with the sculpture, paintings, and music was in part, offered in the context of the Gesamtkunstwerk, comparative to a contemporary installation. The exhibition received extensive press, and generated a scandal. Most of the hostile and negative reviews were directed at Gustav Klimt and his murals. However, Klinger's sculpture received its criticism as well, some dismissing it as kitsch, while others were offended by seeing Beethoven represented nude. Auguste Rodin attended the exhibition and was reported to have walked past Klinger's sculpture without comment, although at a later time he said it had nothing to do with sculpture.

Klinger was cited by many artists (notably Giorgio de Chirico) as being a major link between the symbolist movement of the 19th century and the start of the metaphysical movement. His work was also admired and a formative influence on later artist such as Max Ernst and other surrealist artist. The historian Holger Jacob-Friesen illustrates and discusses in detail the influence of Klinger's prints on artist such as Franz von Stuck, Käthe Kollwitz, Edvard Munch, Lovis Corinth, Otto Greiner, Alfred Kubin, Max Slevogt, Paul Klee, Richard Müller, Oskar Kokoschka, Max Beckmann, Horst Janssen, as well as De Chirico and Ernst.

Print series published by Max Klinger
 * 1879. Radierte Skizzen (Etched Sketches), Opus I, nos. 1-8.
 * 1879. Rettungen Ovidischer Opper (Deliverances of Ovidian Victims) Opus II, nos. 1-13.
 * 1880. Eva und die Zukunft (Eva and the Future), Opus III, nos. 1-6.
 * 1880, Amor und Psyche (Cupid and Psyche), Opus V, book with 46 etchings
 * 1881. Intermezzi (Intermezzi), Opus IV, nos. 1-12.
 * 1881. Paraphrase über den Fund eines Handschuhs (Paraphrase on the Finding of a Glove), Opus VI, nos. 1-10.
 * 1883. Vier Landschaften (Four Landscapes), Opus VII, nos. 1-4.
 * 1883. Dramen (Dramas), Opus IX, nos. 1-10.
 * 1884. Ein Leben (A Life) Opus VIII, nos. 1-15.
 * 1887. Eine Liebe (A Love), Opus X, nos. 1-10.
 * 1889. Vom Tode, Erster Theil (On Death, Part One) Opus XI, nos. 1-10.
 * 1894. Brahmsphantasie (Brahms Fantasy), Opus XII, nos. 1-41.
 * 1898-1910. Vom Tode, Zweiter Theil (On Death, Part Two), Opus XIII, nos. 1-12.

In contemporary culture
In Elsa Bernstein's naturalist play Dämmerung, Klinger is mentioned in the third act when Carl talks of being able to afford "etchings by Klinger" for 80 francs.

Inspection Medical Hermeneutics, an infamous Moscow art collective, based their 1991 installation Klinger’s Boxes, on an idea inspired by Klinger's Paraphrase on the Finding of a Glove.

Asteroid 22369 Klinger is named in his honor.

Gallery
Paintings

title: Max Klinger


text:
Register machine

In mathematical logic and theoretical computer science, a register machine is a generic class of abstract machines similar to a Turing machine. All models of register machines are Turing equivalent.

Overview
The register machine gets it's name from it's use of one or more "registers". In contrast to the tape and head used by a Turing machine, the model uses multiple uniquely addressed registers, each of which holds a single non-negative integer.

There are at least four sub-classes found in the literature. In ascending order of complexity:
 * Counter machine – the most primitive and reduced theoretical model of computer hardware. This machine lacks indirect addressing and instructions are in the finite state machine in the manner of the Harvard architecture.
 * Pointer machine – a blend of the counter machine and RAM models with less common and more abstract than either model. Instructions are in the finite state machine in the manner of Harvard architecture.
 * Random-access machine (RAM) – a counter machine with indirect addressing and, usually, an augmented instruction set. Instructions are in the finite state machine in the manner of the Harvard architecture.
 * Random-access stored-program machine model (RASP) – a RAM with instructions in its registers analogous to the Universal Turing machine; making it an example of the von Neumann architecture. But unlike a computer, the model is idealized with effectively infinite registers (and if used, effectively infinite special registers such as accumulators). As compared to a modern computer, however, the instruction set is still reduced in number and complexity.

Any properly defined register machine model is Turing equivalent. Computational speed is very dependent on the model specifics.

In practical computer science, a related concept known as a virtual machine is occasionally employed to reduce reliance on underlying machine architectures. These virtual machines are also utilized in educational settings. In textbooks, the term "register machine" is sometimes used interchangeably to describe a virtual machine.

Formal Definition
A register machine consists of:

 * 1) An unbounded number of labelled, discrete, unbounded registers unbounded in extent (capacity): a finite (or infinite in some models) set of registers $$r_0 \ldots r_n$$ each considered to be of infinite extent and each holding a single non-negative integer (0, 1, 2, ...). The registers may do their own arithmetic, or there may be one or more special registers that do the arithmetic e.g. an "accumulator" and/or "address register". See also Random-access machine.
 * 2) Tally counters or marks: discrete, indistinguishable objects or marks of only one sort suitable for the model. In the most-reduced counter machine model, per each arithmetic operation only one object/mark is either added to or removed from its location/tape. In some counter machine models (e.g. Melzak, Minsky ) and most RAM and RASP models more than one object/mark can be added or removed in one operation with "addition" and usually "subtraction"; sometimes with "multiplication" and/or "division". Some models have control operations such as "copy" (or alternatively: "move", "load", "store") that move "clumps" of objects/marks from register to register in one action.
 * 3) A limited set of instructions: the instructions tend to divide into two classes: arithmetic and control. The instructions are drawn from the two classes to form "instruction sets", such that an instruction set must allow the model to be Turing equivalent (it must be able to compute any partial recursive function).
 * 4) Arithmetic: Arithmetic instructions may operate on all registers or on a specific register, such as an accumulator. Typically, they are selected from the following sets, though exceptions exist: Counter machine: { Increment (r), Decrement (r), Clear-to-zero (r) } Reduced RAM, RASP: { Increment (r), Decrement (r), Clear-to-zero (r), Load-immediate-constant k, Add ($$r_1,r_2$$), Proper-Subtract ($$r_1,r_2$$), Increment accumulator, Decrement accumulator, Clear accumulator, Add the contents of register r to the accumulator, Proper-Subtract the contents of register r from the accumulator }  Augmented RAM, RASP: Includes all of the reduced instructions as well as: { Multiply, Divide, various Boolean bit-wise operations (left-shift, bit test, etc.) }
 * 5) Control: Counter machine models: Optionally include { Copy ($$r_1,r_2$$) }. RAM and RASP models: Most include { Copy ($$r_1,r_2$$) }, or { Load Accumulator from r, Store accumulator into r, Load Accumulator with an immediate constant }.  All models: Include at least one conditional "jump" (branch, goto) following the test of a register, such as { Jump-if-zero, Jump-if-not-zero (i.e., Jump-if-positive), Jump-if-equal, Jump-if-not-equal }.  All models optionally include: { unconditional program jump (goto) }.
 * 6) Register-addressing method:
 * 7) *Counter machine: no indirect addressing, immediate operands possible in highly atomized models
 * 8) *RAM and RASP: indirect addressing available, immediate operands typical
 * 9) Input-output: optional in all models
 * 10) State register: A special Instruction Register (IR), distinct from the registers mentioned earlier, stores the current instruction to be executed along with its address in the instruction table. This register, along with its associated table, is located within the finite state machine. The IR is inaccessible in all models. In the case of RAM and RASP, for determining the "address" of a register, the model can choose either (i) the address specified by the table and temporarily stored in the IR for direct addressing or (ii) the contents of the register specified by the instruction in the IR for indirect addressing. It's important to note that the IR is not the "program counter" (PC) of the RASP (or conventional computer). The PC is merely another register akin to an accumulator but specifically reserved for holding the number of the RASP's current register-based instruction. Thus, a RASP possesses two "instruction/program" registers: (i) the IR (finite state machine's Instruction Register), and (ii) a PC (Program Counter) for the program stored in the registers. Additionally, aside from the PC, a RASP may also dedicate another register to the "Program-Instruction Register" (referred to by various names such as "PIR," "IR," "PR," etc.).
 * 11) List of labelled instructions, usually in sequential order: A finite list of instructions $$I_1 \ldots I_m$$. In the case of the counter machine, random-access machine (RAM), and pointer machine, the instruction store is in the "TABLE" of the finite state machine, thus these models are examples of the Harvard architecture. In the case of the RASP, the program store is in the registers, thus this is an example of the Von Neumann architecture. See also Random-access machine and Random-access stored-program machine. The instructions are usually listed in sequential order, like computer programs, unless a jump is successful. In this case, the default sequence continues in numerical order. An exception to this is the abacus counter machine models—every instruction has at least one "next" instruction identifier "z," and the conditional branch has two.
 * 12) *Observe also that the abacus model combines two instructions, JZ then DEC: e.g. { INC ( r, z ), JZDEC ( r, ztrue, zfalse ) }. See McCarthy Formalism for more about the conditional expression "IF r=0 THEN ztrue ELSE zfalse"

Historical development of the register machine model
Two trends appeared in the early 1950s. The first was to characterize the computer as a Turing machine. The second was to define computer-like models—models with sequential instruction sequences and conditional jumps—with the power of a Turing machine, a so-called Turing equivalence. Need for this work was carried out in the context of two "hard" problems: the unsolvable word problem posed by Emil Post —his problem of "tag"—and the very "hard" problem of Hilbert's problems—the 10th question around Diophantine equations. Researchers were questing for Turing-equivalent models that were less "logical" in nature and more "arithmetic."

The first step towards characterizing computers originated with Hans Hermes (1954), Rózsa Péter (1958), and Heinz Kaphengst(1959), the second step with Hao Wang (1954, 1957 ) and, as noted above, furthered along by Zdzislaw Alexander Melzak (1961), Joachim Lambek (1961) and Marvin Minsky (1961, 1967 ).

The last five names are listed explicitly in that order by Yuri Matiyasevich. He follows up with:
 * "Register machines [some authors use "register machine" synonymous with "counter-machine"] are particularly suitable for constructing Diophantine equations. Like Turing machines, they have very primitive instructions and, in addition, they deal with numbers".

Lambek, Melzak, Minsky, Shepherdson and Sturgis independently discovered the same idea at the same time. See note on precedence below.

The history begins with Wang's model.

Wang's (1954, 1957) model: Post–Turing machine
Wang's work followed from Emil Post's (1936) paper and led Wang to his definition of his Wang B-machine—a two-symbol Post–Turing machine computation model with only four atomic instructions:
 * { LEFT, RIGHT, PRINT, JUMP_if_marked_to_instruction_z }

To these four both Wang (1954, 1957 ) and then C. Y. Lee (1961) added another instruction from the Post set { ERASE }, and then a Post's unconditional jump { JUMP_to_ instruction_z } (or to make things easier, the conditional jump JUMP_IF_blank_to_instruction_z, or both. Lee named this a "W-machine" model:
 * { LEFT, RIGHT, PRINT, ERASE, JUMP_if_marked, [maybe JUMP or JUMP_IF_blank] }

Wang expressed hope that his model would be "a rapprochement" between the theory of Turing machines and the practical world of the computer.

Wang's work was highly influential. We find him referenced by Minsky (1961) and (1967), Melzak (1961), Shepherdson and Sturgis (1963). Indeed, Shepherdson and Sturgis (1963) remark that:
 * "...we have tried to carry a step further the 'rapprochement' between the practical and theoretical aspects of computation suggested by Wang"

Martin Davis eventually evolved this model into the (2-symbol) Post–Turing machine.

Difficulties with the Wang/Post–Turing model:

Except there was a problem: the Wang model (the six instructions of the 7-instruction Post–Turing machine) was still a single-tape Turing-like device, however nice its sequential program instruction-flow might be. Both Melzak (1961) and Shepherdson and Sturgis (1963) observed this (in the context of certain proofs and investigations):

 * "...a Turing machine has a certain opacity... a Turing machine is slow in (hypothetical) operation and, usually, complicated. This makes it rather hard to design it, and even harder to investigate such matters as time or storage optimization or a comparison between the efficiency of two algorithms.

 * "...although not difficult ... proofs are complicated and tedious to follow for two reasons: (1) A Turing machine has only a head so that one is obliged to break down the computation into very small steps of operations on a single digit. (2) It has only one tape so that one has to go to some trouble to find the number one wishes to work on and keep it separate from other numbers"

Indeed, as examples in Turing machine examples, Post–Turing machine and partial functions show, the work can be "complicated". <!-- Example: Multiply a x b = c, for example: 3 x 4 = 12.

The scanned square is indicated by brackets around the mark i.e. [1]. An extra mark serves to indicate the symbol "0".

At the start of a computation, just as Shepherdson–Sturgis and Melzak complain, we see the variables expressed in unary—i.e. the tally marks for a= | | | | and b = | | | | | – "in a line" (concatenated on what Melzak calls a "linear tape"). Space must be available for c at the end of the computation, extending without bounds to the right:

At the end of the computation the multiplier b is 5 marks "in a line" (i.e. concatenated) to left of the 13 marks of product c.

Minsky, Melzak–Lambek and Shepherdson–Sturgis models "cut the tape" into many
Initial thought leads to 'cutting the tape' so each is infinitely long (to accommodate any size integer) but left-ended, and call these three tapes "Post–Turing (i.e. Wang-like) tapes". The individual heads will move left (for decrement) and right (for increment). In one sense the heads indicate "the tops of the stack" of concatenated marks. Or in Minsky (1961) and Hopcroft and Ullman (1979) the tape is always blank except for a mark at the left end—at no time does a head ever print or erase.

Care must be taken to write the instructions so that a test-for-zero and jump occurs before decrementing, otherwise the machine will "fall off the end" or "bump against the end"—creating an instance of a partial function.

Minsky (1961) and Shepherdson–Sturgis (1963) prove that only a few tapes—as few as one—still allow the machine to be Turing equivalent if the data on the tape is represented as a Gödel number (or some other uniquely encodable Encodable-decodable number); this number will evolve as the computation proceeds. In the one tape version with Gödel number encoding the counter machine must be able to (i) multiply the Gödel number by a constant (numbers "2" or "3"), and (ii) divide by a constant (numbers "2" or "3") and jump if the remainder is zero. Minsky (1967) shows that the need for this bizarre instruction set can be relaxed to { INC (r), JZDEC (r, z) } and the convenience instructions { CLR (r), J (r) } if two tapes are available. A simple Gödelization is still required, however. A similar result appears in Elgot–Robinson (1964) with respect to their RASP model.<!-- To do a multiplication algorithm we don't need the extra mark to indicate "0", but we will need an extra "temporary" tape t. And we will need an extra "blank/zero" register (e.g. register #0) for an unconditional jump:

We can write simple Post–Turing "subroutines" to atomize "increment" and "decrement" into Post–Turing instructions. Note that the head stays always just one square to the right of the top-most printed mark, i.e. at the "top of the stack". "r" is a parameter in the instructions that symbolizes the tape-as-register to be moved and printed or erased, and tested:
 * "Increment r" = PRINT_SCANNED_SQUARE_of_TAPE_r, MOVE_TAPE_r_LEFT; i.e. (or: move tape r's head right)
 * X+ r is equivalent to P r; L r
 * "Decrement r" = JUMP_IF_TAPE_r_BLANK(ZERO) TO XXX, ELSE MOVE_TAPE_r_RIGHT, ERASE_SCANNED_SQUARE_of_TAPE_rN; (or: move tape r's head left)
 * X- r is equivalent to J0 r, xxx; R r; E r
 * X- r is equivalent to J0 r, xxx; R r; E r

Indeed this is similar to the approach that Minsky (1961) took. He started with 4 left-ended tape-machine that:
 * "used the basic arithmetic device of the present paper. Then, two of the tapes were eliminated by the prime-factor method".

He then observed that:
 * "we may formulate these results so that the operations act essentially only on the length of the strings"

His first model, "1961" (it had changed by 1967 ) started out with only a single mark at the left end of each tape-as-register. The machine was not allowed to Print any marks, just move Left or Right and test for the mark = "1" in the following example. Thus the conventional Post–Turing-like instruction set went from
 * { R; L; P; E; J0 xxx; J1 xxx, H }

to, for each tape-as-register:
 * { R; L; J1 xxx, H }

where R can be renamed INCrement, R can be renamed DECrement, "J1" can be combined with "DEC" to create a non-atomized instruction, or can be kept separate and renamed Jump if Zero. -->

Melzak's (1961) model is different: clumps of pebbles go into and out of holes
Melzak's (1961) model is significantly different. He took his own model, flipped the tapes vertically, called them "holes in the ground" to be filled with "pebble counters". Unlike Minsky's "increment" and "decrement", Melzak allowed for proper subtraction of any count of pebbles and "adds" of any count of pebbles.

He defines indirect addressing for his model and provides two examples of its use;  his "proof"  that his model is Turing equivalent is so sketchy that the reader cannot tell whether or not he intended the indirect addressing to be a requirement for the proof.

Legacy of Melzak's model is Lambek's simplification and the reappearance of his mnemonic conventions in Cook and Reckhow 1973.

Lambek (1961) atomizes Melzak's model into the Minsky (1961) model: INC and DEC-with-test
Lambek (1961) took Melzak's ternary model and atomized it down to the two unary instructions—X+, X− if possible else jump—exactly the same two that Minsky (1961) had come up with.

However, like the Minsky (1961) model, the Lambek model does execute its instructions in a default-sequential manner—both X+ and X− carry the identifier of the next instruction, and X− also carries the jump-to instruction if the zero-test is successful.

Elgot–Robinson (1964) and the problem of the RASP without indirect addressing
A RASP or random-access stored-program machine begins as a counter machine with its "program of instruction" placed in its "registers". Analogous to, but independent of, the finite state machine's "Instruction Register", at least one of the registers (nicknamed the "program counter" (PC)) and one or more "temporary" registers maintain a record of, and operate on, the current instruction's number. The finite state machine's TABLE of instructions is responsible for (i) fetching the current program instruction from the proper register, (ii) parsing the program instruction, (iii) fetching operands specified by the program  instruction, and (iv) executing the program instruction.

Except there is a problem: If based on the counter machine chassis this computer-like, von Neumann machine will not be Turing equivalent. It cannot compute everything that is computable. Intrinsically the model is bounded by the size of its (very-) finite state machine's instructions. The counter machine based RASP can compute any primitive recursive function (e.g. multiplication) but not all mu recursive functions (e.g. the Ackermann function).

Elgot–Robinson investigate the possibility of allowing their RASP model to "self modify" its program instructions. The idea was an old one, proposed by Burks–Goldstine–von Neumann (1946–1947), and sometimes called "the computed goto." Melzak (1961) specifically mentions the "computed goto" by name but instead provides his model with indirect addressing.

Computed goto: A RASP program of instructions that modifies the "goto address" in a conditional- or unconditional-jump program instruction.

But this does not solve the problem (unless one resorts to Gödel numbers). What is necessary is a method to fetch the address of a program instruction that lies (far) "beyond/above" the upper bound of the finite state machine instruction register and TABLE.

 * Example: A counter machine equipped with only four unbounded registers can e.g. multiply any two numbers ( m, n ) together to yield p—and thus be a primitive recursive function—no matter how large the numbers m and n; moreover, less than 20 instructions are required to do this! e.g. { 1: CLR ( p ), 2: JZ ( m, done ), 3 outer_loop: JZ ( n, done ), 4: CPY ( m, temp ), 5: inner_loop: JZ ( m, outer_loop ), 6: DEC ( m ), 7: INC ( p ), 8: J ( inner_loop ), 9: outer_loop: DEC ( n ), 10 J ( outer_loop ), HALT }

 * However, with only 4 registers, this machine has not nearly big enough to build a RASP that can execute the multiply algorithm as a program. No matter how big we build our finite state machine there will always be a program (including its parameters) which is larger. So by definition the bounded program machine that does not use unbounded encoding tricks such as Gödel numbers cannot be universal.

Minsky (1967) hints at the issue in his investigation of a counter machine (he calls them "program computer models") equipped with the instructions { CLR (r), INC (r), and RPT ("a" times the instructions m to n) }. He doesn't tell us how to fix the problem, but he does observe that:
 * "... the program computer has to have some way to keep track of how many RPT's remain to be done, and this might exhaust any particular amount of storage allowed in the finite part of the computer. RPT operations require infinite registers of their own, in general, and they must be treated differently from the other kinds of operations we have considered."

But Elgot and Robinson solve the problem: They augment their P0 RASP with an indexed set of instructions—a somewhat more complicated (but more flexible) form of indirect addressing. Their P'0 model addresses the registers by adding the contents of the "base" register (specified in the instruction) to the "index" specified explicitly in the instruction (or vice versa, swapping "base" and "index"). Thus the indexing P'0 instructions have one more parameter than the non-indexing P0 instructions:
 * Example: INC ( rbase, index ) ; effective address will be [rbase] + index, where the natural number "index" is derived from the finite-state machine instruction itself.

Hartmanis (1971)
By 1971 Hartmanis has simplified the indexing to indirection for use in his RASP model.

Indirect addressing: A pointer-register supplies the finite state machine with the address of the target register required for the instruction. Said another way: The contents of the pointer-register is the address of the "target" register to be used by the instruction. If the pointer-register is unbounded, the RAM, and a suitable RASP built on its chassis, will be Turing equivalent. The target register can serve either as a source or destination register, as specified by the instruction.

Note that the finite state machine does not have to explicitly specify this target register's address. It just says to the rest of the machine: Get me the contents of the register pointed to by my pointer-register and then do xyz with it. It must specify explicitly by name, via its instruction, this pointer-register (e.g. "N", or "72" or "PC", etc.) but it doesn't have to know what number the pointer-register actually contains (perhaps 279,431).

Cook and Reckhow (1973) describe the RAM
Cook and Reckhow (1973) cite Hartmanis (1971) and simplify his model to what they call a random-access machine (RAM—i.e. a machine with indirection and the Harvard architecture). In a sense we are back to Melzak (1961) but with a much simpler model than Melzak's.

Precedence
Minsky was working at the MIT Lincoln Laboratory and published his work there; his paper was received for publishing in the Annals of Mathematics on 15 August 1960, but not published until November 1961. While receipt occurred a full year before the work of Melzak and Lambek was received and published (received, respectively, May and 15 June 1961, and published side-by-side September 1961). That (i) both were Canadians and published in the Canadian Mathematical Bulletin, (ii) neither would have had reference to Minsky's work because it was not yet published in a peer-reviewed journal, but (iii) Melzak references Wang, and Lambek references Melzak, leads one to hypothesize that their work occurred simultaneously and independently.

Almost exactly the same thing happened to Shepherdson and Sturgis. Their paper was received in December 1961—just a few months after Melzak and Lambek's work was received. Again, they had little (at most 1 month) or no benefit of reviewing the work of Minsky. They were careful to observe in footnotes that papers by Ershov, Kaphengst and Péter had "recently appeared" These were published much earlier but appeared in the German language in German journals so issues of accessibility present themselves.

The final paper of Shepherdson and Sturgis did not appear in a peer-reviewed journal until 1963. And as they note in their Appendix A, the 'systems' of Kaphengst (1959), Ershov (1958), Péter (1958) are all so similar to what results were obtained later as to be indistinguishable to a set of the following:
 * produce 0 i.e. 0 → n
 * increment a number i.e. n+1 → n
 * "i.e. of performing the operations which generate the natural numbers"
 * copy a number i.e. n → m
 * to "change the course of a computation", either comparing two numbers or decrementing until 0

Indeed, Shepherson and Sturgis conclude
 * "The various minimal systems are very similar"

By order of publishing date the work of Kaphengst (1959), Ershov (1958), Péter (1958) were first.

title: Register machine


text:
Argalasti

Argalasti (Αργαλαστή) is a village and a former municipality in Magnesia, Thessaly, Greece. Since the 2011 local government reform it is part of the municipality South Pelion, of which it is the seat and a municipal unit. The municipal unit has an area of 74.820 km2. It is built on a fertile plateau, 40 km southeast of Volos. It is an important commercial and tourism center of the area with a rich cultural tradition. Argalasti is a stopping point for those headed for the nearby beaches of the Pagasetic Gulf (Chorto, Kalamos, Lefokastro) or the Aegean Sea (Potistika, Melani, Paltsi). An example of the architecture of the beginning of the 20th century is the church tower of Sts. Apostles.

Subdivisions
The municipal unit Argalasti is subdivided into the following communities (constituent villages in brackets):
 * Argalasti (Argalasti, Kalamos, Kallithea, Lefokastro, Myriovryti, Paltsi, Paou, Chorto)
 * Metochi
 * Xinovrysi (Xinovrysi, Potistika)

History
This Pelion town is known for its buildings of architectural interest. Embedded into the walls of several buildings in the village are find pieces of Ancient and Medieval buildings. The monastery of Saint Nicolas provides views of the town. Close to the town square, is the church of Saint Apostles Peter and Paul built in 1886, with a marble bell tower built in 1913.

title: Argalasti


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Albert Lee

Albert William Lee (born 21 December 1943) is an English guitarist known for his fingerstyle and hybrid picking technique. Lee has worked, both in the studio and on tour, with many famous musicians from a wide range of genres. He has also maintained a solo career and is a noted composer and musical director.

Early life
Lee was born in Lingen, Herefordshire, but grew up in Blackheath, London, a member of a Romani family. His father was a musician, and Lee studied piano, taking up the instrument at age seven.

During this time, Lee became a fan of Buddy Holly and Jerry Lee Lewis. He took up guitar in 1958 when his parents bought him a second-hand Höfner President which he later traded in for a Czechoslovak Jolana Grazioso, the forerunner of the Futurama. Lee left school at the age of 16 to play full-time.

Early career
Lee was with a variety of bands from 1959 onwards, playing mostly R&B, country music and rock and roll. He was accompanying Richard Kneller, (Dickie Pride), in the Castle Pub, Tooting, the night Russ Conway saw him perform there, two weeks before taking Larry Parnes to see Pride. In addition to Buddy Holly, his early guitar influences included Cliff Gallup, Grady Martin, the Everly Brothers, Scotty Moore, James Burton and Jerry Reed. Lee first experienced commercial success as the lead guitarist with Chris Farlowe and the Thunderbirds. Lee says that he enjoyed playing the Stax-type material, but he really wanted to play country music. Consequently, he left Farlowe and the Thunderbirds in 1968.

During his time playing with Heads Hands & Feet, Lee became a "guitar hero", playing his Fender Telecaster at breakneck speed. Heads Hands & Feet became a popular live band in the UK, making appearances on The Old Grey Whistle Test and also in Europe, where they appeared on the German music programme Beat-Club. In October 1969 Country Fever, an RCA package toured six countries in eleven days, starting at the Nashville Room with the London band the Kingpins.

International success
In 1971, Lee performed with Deep Purple's keyboard player Jon Lord on the studio recording of Lord's Gemini Suite. That opus was a follow-up to Deep Purple's Concerto for Group and Orchestra. Ritchie Blackmore had played guitar at the first live performance of the Gemini Suite in September 1970, but declined the invitation to appear on the studio version, which led to the involvement of Lee. Other performers were Yvonne Elliman, Ian Paice, Roger Glover, Tony Ashton and the London Symphony Orchestra conducted by Sir Malcolm Arnold.

Lee left for Los Angeles in 1974 and, through his friend bassist Ric Grech (of Blind Faith), did some session work on three albums with the Crickets who also at the time included Sonny Curtis and Jerry Allison. One of these releases is titled A Long Way From Lubbock. Lee also received many other offers of session work. In 1976, he was asked to join Emmylou Harris's Hot Band, replacing one of his heroes, James Burton, who was returning to perform with Elvis Presley. The Hot Band featured other musicians including Ricky Skaggs and Rodney Crowell. Starting in 1978, Lee worked for five years with Eric Clapton, which included playing and singing for a live concert recording at the Budokan in Japan.

Lee was responsible for the Everly Brothers' 1983 reunion concert and was its musical director. He played regularly with the Everlys for over twenty years.

In 1987, Lee was invited by Gerry Hogan to headline at a steel guitar festival in Newbury, Berkshire. Lee was at first intimidated by the prospect of having to front a band; however, the gig was successful and he toured as Albert Lee & Hogan’s Heroes on a regular basis until 2015. The lineup of the band included British musicians Peter Baron on drums, Gerry Hogan on guitar and Brian Hodgson on bass. Pete Wingfield was the original keyboard player, before leaving to be replaced by Elio Pace and later Gavin Povey.

They were renowned for attracting celebrities to their gigs. Stars such as Eric Clapton, Tommy Emmanuel, Lonnie Donegan, Dave Edmunds, Nick Lowe, Marty Wilde, Willie Nelson, Nanci Griffith, Don Everly, Emmylou Harris, Sonny Curtis and Rodney Crowell have all jammed with the band at one time or another. In 1988 Lee toured Australia along with Vince Gill, then a comparative unknown, and has returned to tour the country on several subsequent occasions.

In the early 2000s Albert Lee toured with Bill Wyman's Rhythm Kings. In 2002, Lee appeared at the Concert for George [Harrison]. Also in 2002, Lee received a Grammy Award for Best Country Instrumental Performance for "Foggy Mountain Breakdown" from the CD Earl Scruggs and Friends. In September 2006 Lee took part in Primal Twang: The Legacy of the Guitar, a documentary about the history of the guitar. Lee appeared at the 2007 Crossroads Guitar Festival on 28 July and performed with Bill Wyman's Rhythm Kings at the Ahmet Ertegun tribute show at The O2 in London on 10 December. A new album entitled Like This was released in spring 2008 to coincide with their European tour. He lives in Malibu, California.

Awards and legacy
Lee has received many awards as a guitarist, winning five consecutive times Guitar Player magazine's "Best Country Guitarist". Lee is known within the music industry for his speed of playing and his technical virtuosity and yet by the same token, one of the most melodic, playing slower passages approximating the sound of the pedal steel guitar with his Music Man and Telecaster guitars which are equipped with B-Benders.

He is known as "the guitar player's guitar player". Lee is also referred to as "Mr. Telecaster". A long-time Telecaster player, Lee wrote a foreword to A.R. Duchossoir's book detailing the history of the instrument.

Lee's song "Country Boy" helped to redefine country guitar for a whole generation of players, and was later to become a hit for multi-instrumentalist Ricky Skaggs.

Despite positive press from Melody Maker and New Musical Express, Lee has never achieved any great commercial success in terms of record sales during his career, but more as a live performer, session player and sideman, perhaps due to his self-effacing stage presence. Lee has been described by his peers, who include Jimmy Page and Ritchie Blackmore, as a complete gentleman who does not know the meaning of the word ego.

After Gram Parsons' death, Emmylou Harris was told that she could gain the backing of a major record label only if she could assemble a really "hot band". Harris did just that, enlisting guitarist James Burton and pianist Glen Hardin, both of whom had played with Elvis Presley and Parsons; she named the band "The Hot Band". When Burton left to return to Elvis Presley, Lee was his replacement. Harris said of him that Lee is "a brilliant guitar player. His sound is unmistakable—often emulated, never equaled. When Saint Peter asks me to chronicle my time down here on earth, I'll be able to say (with pride if that's allowed) that for a while I played rhythm guitar in a band with Albert Lee."

In 2017, Lee was honoured with the Trailblazer Lifetime Achievement Award at the UK Americana Awards.

Guitar collection
Albert Lee owns around 40 guitars, including Don Everly's Gibson J-200. The Gibson Guitar Corporation made one for Don Everly and the other for Phil. The guitars have an all black, high-gloss lacquered finish and are equipped with twin Everly Brothers white pickguards. The Everly Brothers' manager Wesley Rose had wanted the guitar to be presented to the Country Music Hall of Fame, but Everly informed him that guitars like that should be played, not kept sitting in a glass case. Don Everly presented it to Lee, along with his Gibson Everly Brothers model.

Eric Clapton gave Lee the Gibson Les Paul Custom that he played while with Delaney and Bonnie. Lee also plays his signature Music Man (the guitar shown in the photographs) and a 1950s Telecaster (and has versions of both with custom B-Benders), a 1958 Stratocaster and a Martin 000-28 acoustic.

Despite his being heavily associated with the Fender Telecaster, guitar manufacturer Ernie Ball Music Man makes a signature Albert Lee guitar, which unlike the Telecaster has three single-coil pickups.

Band list

 * Chris Farlowe and the Thunderbirds
 * Country Fever
 * Green Bullfrog
 * Heads Hands & Feet
 * The Crickets
 * Emmylou Harris and the Hot Band
 * Albert Lee & Hogan’s Heroes 1987-2015
 * Bill Wyman's Rhythm Kings
 * Biffbaby's All Stars, featuring: Albert Lee, Eddie Van Halen, Steve Morse and Steve Lukather. In association with Ernie Ball products

Featured appearances

 * Poet and the One Man Band – Poet and the One Man Band LP (1969)
 * Heads Hands & Feet – Heads, Hands & Feet LP (1971)
 * Heads Hands & Feet – Tracks LP (1972)
 * Heads Hands & Feet – Let's Get This Show on the Road!
 * Heads Hands & Feet – Jack Daniels Rare Old No.7
 * Heads Hands & Feet – Old Soldiers Never Die LP (1973)
 * Heads Hands & Feet – Home From Home – The Missing Album LP (1995)
 * Bo Diddley – The London Bo Diddley Sessions
 * Jerry Lee Lewis – The London Sessions
 * Eddie Harris – E.H. in the U.K. (Atlantic, 1973)
 * Herbie Mann - London Underground (Atlantic, 1973), Reggae (Atlantic, 1973), Reggae II (Atlantic, 1973 [1976])
 * Emmylou Harris – Luxury Liner, Blue Kentucky Girl, Roses in the Snow, Evangeline, The Ballad of Sally Rose (Guitars, Mandolin)
 * Eric Clapton – Just One Night, Another Ticket, Money and Cigarettes
 * John Prine – The Missing Years (Guitar, Mandolin, Piano)
 * Rosanne Cash – Seven Year Ache
 * Jon Lord – Gemini Suite
 * Earl Scruggs – Earl Scruggs and Friends
 * Ricky Skaggs - Don't Cheat In Our Hometown
 * Paul Kennerley – The Legend of Jesse James (Guitars, Vocals, Mandolin)
 * The Crickets – Long Way From Lubbock, The Crickets and Their Buddies
 * Joe Cocker – Sting Ray
 * Nicolette Larson – The Very Best of Nicolette Larson
 * Rodney Crowell – The Essential Rodney Crowell
 * Dolly Parton – White Limozeen
 * The Return Of Spinal Tap – DVD (As himself, playing on "Break Like The Wind")
 * John 5 – Death Valley
 * Carlene Carter – I Fell in Love
 * Foster and Lloyd – Version of the Truth
 * Nanci Griffith – I Knew Love
 * Hugh Moffatt – Dance Me Outside
 * Shakin' Stevens – Hot Dog
 * Everly Brothers – Reunion Concert LP (Guitars, Piano, Musical Director) (1983)
 * Everly Brothers – EB '84 LP (Guitars) (1984)
 * Everly Brothers – Born Yesterday LP (Guitars) (1986)
 * Everly Brothers – Some Hearts LP (Guitars) (1988)
 * Don Everly – Sunset Towers
 * The Refreshments – Cover of Chuck Berry's "Let It Rock"
 * Dave Edmunds – "Sweet Little Lisa"
 * Marcel Dadi – Nashville Rendez-vous
 * Bert Jansch – Heartbreak
 * Jerry Scheff – Fire Down Below
 * Brad Paisley – Play
 * Jackson Browne – Under the Falling Sky
 * Jean-Pierre Danel – "Tulsa Time"
 * Arlen Roth -Toolin' Around (1993), Telemasters (2019)
 * Maestro Alex Gregory - Bach on Steroids (2009)
 * Maestro Alex Gregory - Another Millennium (2010)
 * Steve Morse -The Introduction (lead guitar in "General Lee") and Stand Up (vocals and guitar in "Rockin' guitars")
 * The Geoff Everett Band – The Quick and the Dead (2012)
 * Maestro Alex Gregory - Holy Grail of 7 strings (2013)
 * Various Artists - Guitar Heroes: Making History (2015), featuring James Burton, Amos Garrett, Albert Lee & David Wilcox
 * Jericho Summer - ''Night Train' (2015), featuring Richard Fortus, Marco Mendoza

title: Albert Lee


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Iterated function system

In mathematics, iterated function systems (IFSs) are a method of constructing fractals; the resulting fractals are often self-similar. IFS fractals are more related to set theory than fractal geometry. They were introduced in 1981.

IFS fractals, as they are normally called, can be of any number of dimensions, but are commonly computed and drawn in 2D. The fractal is made up of the union of several copies of itself, each copy being transformed by a function (hence "function system"). The canonical example is the Sierpiński triangle. The functions are normally contractive, which means they bring points closer together and make shapes smaller. Hence, the shape of an IFS fractal is made up of several possibly-overlapping smaller copies of itself, each of which is also made up of copies of itself, ad infinitum. This is the source of its self-similar fractal nature.

Definition
Formally, an iterated function system is a finite set of contraction mappings on a complete metric space. Symbolically,
 * $$\{f_i:X\to X\mid i=1,2,\dots,N\},\ N\in\mathbb{N}$$

is an iterated function system if each $$f_i$$ is a contraction on the complete metric space $$X$$.

Properties
Hutchinson showed that, for the metric space $$\mathbb{R}^n$$, or more generally, for a complete metric space $$X$$, such a system of functions has a unique nonempty compact (closed and bounded) fixed set S. One way of constructing a fixed set is to start with an initial nonempty closed and bounded set S0 and iterate the actions of the fi, taking Sn+1 to be the union of the images of Sn under the fi; then taking S to be the closure of the limit $$\lim_{n \rightarrow \infty} S_n$$. Symbolically, the unique fixed (nonempty compact) set $$S\subseteq X$$ has the property
 * $$S = \overline{\bigcup_{i=1}^N f_i(S)}.$$

The set S is thus the fixed set of the Hutchinson operator $$F: 2^X\to 2^X$$ defined for $$A\subseteq X$$ via
 * $$F(A)=\overline{\bigcup_{i=1}^N f_i(A)}.$$

The existence and uniqueness of S is a consequence of the contraction mapping principle, as is the fact that
 * $$\lim_{n\to\infty}F^{n}(A)=S$$

for any nonempty compact set $$A$$ in $$X$$. (For contractive IFS this convergence takes place even for any nonempty closed bounded set $$A$$). Random elements arbitrarily close to S may be obtained by the "chaos game," described below.

Recently it was shown that the IFSs of non-contractive type (i.e. composed of maps that are not contractions with respect to any topologically equivalent metric in X) can yield attractors. These arise naturally in projective spaces, though classical irrational rotation on the circle can be adapted too.

The collection of functions $$f_i$$ generates a monoid under composition. If there are only two such functions, the monoid can be visualized as a binary tree, where, at each node of the tree, one may compose with the one or the other function (i.e. take the left or the right branch). In general, if there are k functions, then one may visualize the monoid as a full k-ary tree, also known as a Cayley tree.

Constructions
Sometimes each function $$f_i$$ is required to be a linear, or more generally an affine, transformation, and hence represented by a matrix. However, IFSs may also be built from non-linear functions, including projective transformations and Möbius transformations. The Fractal flame is an example of an IFS with nonlinear functions.

The most common algorithm to compute IFS fractals is called the "chaos game". It consists of picking a random point in the plane, then iteratively applying one of the functions chosen at random from the function system to transform the point to get a next point. An alternative algorithm is to generate each possible sequence of functions up to a given maximum length, and then to plot the results of applying each of these sequences of functions to an initial point or shape.

Each of these algorithms provides a global construction which generates points distributed across the whole fractal. If a small area of the fractal is being drawn, many of these points will fall outside of the screen boundaries. This makes zooming into an IFS construction drawn in this manner impractical.

Although the theory of IFS requires each function to be contractive, in practice software that implements IFS only require that the whole system be contractive on average.

Partitioned iterated function systems
PIFS (partitioned iterated function systems), also called local iterated function systems, give surprisingly good image compression, even for photographs that don't seem to have the kinds of self-similar structure shown by simple IFS fractals.

The inverse problem
Very fast algorithms exist to generate an image from a set of IFS or PIFS parameters. It is faster and requires much less storage space to store a description of how it was created, transmit that description to a destination device, and regenerate that image anew on the destination device, than to store and transmit the color of each pixel in the image.

The inverse problem is more difficult: given some original arbitrary digital image such as a digital photograph, try to find a set of IFS parameters which, when evaluated by iteration, produces another image visually similar to the original. In 1989, Arnaud Jacquin presented a solution to a restricted form of the inverse problem using only PIFS; the general form of the inverse problem remains unsolved.

As of 1995, all fractal compression software is based on Jacquin's approach.

Examples
The diagram shows the construction on an IFS from two affine functions. The functions are represented by their effect on the bi-unit square (the function transforms the outlined square into the shaded square). The combination of the two functions forms the Hutchinson operator. Three iterations of the operator are shown, and then the final image is of the fixed point, the final fractal.

Early examples of fractals which may be generated by an IFS include the Cantor set, first described in 1884; and de Rham curves, a type of self-similar curve described by Georges de Rham in 1957.

History
IFSs were conceived in their present form by John E. Hutchinson in 1981 and popularized by Michael Barnsley's book Fractals Everywhere.

"IFSs provide models for certain plants, leaves, and ferns, by virtue of the self-similarity which often occurs in branching structures in nature."

- Michael Barnsley et al.

title: Iterated function system