James Lindsay (actor)
James Lindsay (18691928) was a British actor.
Selected filmography
References
External links
Retrieved from : http://en.wikipedia.org/w/index.php?title=James_Lindsay_(actor)&oldid=458852251
James Lindsay (18691928) was a British actor.
Yevadu  

Directed by  Vamsi Paidipally 
Produced by  Dil Raju 
Written by  Vamsi Paidipally Abburi Ravi 
Screenplay by  Vakkantham Vamsi 
Story by  Vamsi Paidipally 
Starring  Ram Charan Teja Samantha Allu Arjun(guest) Saikumar 
Music by  Devi Sri Prasad 
Cinematography  Chota K. Naidu 
Studio  Sri Venkateswara Creations 
Distributed by  Sri Venkateswara Creations 
Release date(s)  2012 
Country  India 
Language  Telugu 
Yevadu is an upcoming Telugu film written and directed by Vamsi. The film stars Ram Charan Teja and Samantha Ruth Prabhu in lead roles.Allu Arjun will be doing an important role in the movie. Music composed by Devi Sri Prasad. The movie launched on December 9.
The film is being produced by Dil Raju under Sri Venkateswara Creations Banner.
Lucy Beall Candler Owens Heinz Leide (18821962) was the only daughter of CocaCola cofounder Asa Griggs Candler.
In 1903, Lucy married her first husband William Davies Owens, who would become an assistant cashier (i.e. manager) at Central Bank and Trust, the bank that Asa Candler started in 1905. At first they lived together in her parents’ home, , at 61 Elizabeth Street in Inman Park. In 1910 they moved to a newlybuilt home in Druid Hills which would become known as "The Goose". It was located at what is now 1449 South Ponce de Leon Avenue. In 1968 the home would become the Mother Goose day care center, and later classroom space for The Paideia School until it burned down in 2009. William Owens died of influenza and a heart attack in the house in 1914.
Lucy then married Henry Heinz, capitalist, banker and president of Kiwanis International. Heinz was shot by a burglar at their home, Rainbow Terrace, in 1943. A black railroad worker confessed to the crime but rumours persisted that a relative murdered Heinz.
Lucy then married Enrico Leide (18871970), a concert cellist and orchestra conductor, conducting the first Atlanta Symphony Orchestra from 1920 to 1930. He was the brother of violinist and composer Manoah LeideTedesco.
Lucy died aboard the RMS Caronia in 1962.
Namibia observes daylight saving time, it uses UTC+01:00 in winter and UTC+02:00 in summer.
Until March 1903, at that time called German SouthWest Africa, it used UTC+01:30.
The tz database zone for Namibia is Africa/Windhoek.
Books of the New Testament 

Gospels 
Matthew · Mark · Luke · John 
Acts 
Acts of the Apostles 
Epistles 
Romans 1 Corinthians · 2 Corinthians Galatians · Ephesians Philippians · Colossians 1 Thessalonians · 2 Thessalonians 1 Timothy · 2 Timothy Titus · Philemon Hebrews · James 1 Peter · 2 Peter 1 John · 2 John · 3 John Jude 
Apocalypse 
Revelation 
New Testament manuscripts 
The First Epistle of Paul to Timothy, usually referred to simply as First Timothy and often written 1 Timothy, is one of three letters in the New Testament of the Bible often grouped together as the Pastoral Epistles, the others being Second Timothy and Titus. The letter, traditionally attributed to Saint Paul, consists mainly of counsels to his younger colleague and delegate Timothy regarding his ministry in Ephesus (1:3). These include instructions on the forms of worship and organization of the Church, the responsibilities resting on its several members, including episkopoi (overseers or bishops) and diakonoi ("deacons"); and secondly of exhortation to faithfulness in maintaining the truth amid surrounding errors (iv.iff), presented as a prophecy of erring teachers to come.
The author of First Timothy has been traditionally identified as the Apostle Paul. He is named as the author of the letter in the text (1:1). In modern times, scholars have become divided over the issue of authenticity, with many suggesting that First Timothy, along with Second Timothy and Titus, are not original to Paul, but rather an unknown Christian writing some time in the latefirsttomid2nd century. Despite the challenge to Pauline authorship, the traditional view is still held by many New Testament scholars.
The genuineness of Pauline authorship was accepted by Church orthodoxy as early as c. 180 AD, as evidenced by the surviving testimony of Irenaeus and the author of the Muratorian fragment. Possible allusions are found in the letters from Clement of Rome to the Corinthians (c. 95), Ignatius of Antioch to the Ephesians (c. 110) and Polycarp to the Philippians (c. 130), though it is difficult to determine the nature of any such literary relationships. Modern scholars who support Pauline authorship nevertheless stress their importance regarding the question of authenticity: I.H. Marshall and P.H. Towner wrote that 'the key witness is Polycarp, where there is a high probability that 1 and 2 Tim were known to him'. Similarly M.W. Holmes argued that it is 'virtually certain or highly probable' that Polycarp used 1 and 2 Timothy.
Late in the 2nd century there are a number of quotations from all three Pastoral Epistles in Irenaeus' work Against Heresies. The Muratorian Canon (c. 170180) lists the books of the NT and ascribes all three Pastoral Epistles to Paul. Eusebius (c. 330) calls it, along with the other thirteen canonical Pauline Epistles, "undisputed", despite the fact that Eusebius wrote in the 4th century with little to no knowledge of the complex social structures which line the books of the New Testament. Exceptions to this positive witness include Tatian, a disciple of Justin Martyr turned heretic, as well as the Gnostic Basilides.
Marcion, an orthodox Bishop later excommunicated for heresy, formed a Gnostic canon of Scripture c. 140 around ten of the canonical Pauline epistles, excluding 12 Timothy, Titus and Hebrews. The reasons for these exclusions are unknown, and so speculation abounds, including the hypotheses that they were not written until after Marcion's time, or that he knew of them, but regarded them as inauthentic. Proponents of Pauline authorship argue that he had theological grounds for rejecting the Pastorals, namely their teaching about the goodness of creation (cf. 1 Tim 4:1 ff.). The question is indeed curious whether Marcion knew these three letters and rejected them as Tertullian says, since in 1 Timothy 6:20 "false opposing arguments" are referred to, with the word for "opposing arguments" being "antithesis", the name of Marcion's work, and so whether it is a subtle hint of Marcion's heresy. However, the structure of the Church presupposed which is less developed than the one Ignatius presupposes (who wrote c.110), as well as the fact that not only is "antithesis" itself a Greek word which simply means "opposing arguments" but as it has been noted, the attack on the heretics is not central to the three letters.
The modern challenge to Pauline authorship began with the work of German theologians F.D.E. Schleiermacher in 1807 and J.G Eichorn in 1812. (Eichorn extended Schleirmacher's critique of 1 Timothy to all three Pastoral letters.) This was argued in further detail by F.C. Baur in 1835. Following these arguments, a large number of modern scholars continue to reject Pauline authorship, citing various and serious problems in associating it therewith. For example, Norman Perrin analyzed the Greek used by the author or authors of the Pastoral Epistles, finding that over 1/3 of their vocabulary is not used anywhere else in the Pauline epistles; more than 1/5 is not used anywhere else in the New Testament, while 2/3 of the nonPauline vocabulary are used by 2nd century Christian writers. Richard Heard, in 1950, had this to say: "The evidence of teaching as of style and vocabulary is strongly against Paul’s authorship, nor are these arguments seriously weakened by any supposition that the epistles were written late in Paul’s lifetime and to meet a new type of situation. The three epistles show such a unity of thought and expression that they must be the work of one man, but for the author we must look rather to one of Paul’s admirers than to Paul himself." Robert Grant noted the aforementioned parallels to Polycarp's Epistles and suggested he might be the author.
The dating of 1 Timothy depends very much on the question of authorship. Those who accept the epistle's authenticity believe it was most likely written toward the end of Paul's ministry, c.6267 CE. Other historians generally place its composition some time in the late 1st century or first half of the 2nd century CE, with a wide margin of uncertainty. The text seems to be contending against nascent Gnosticism(1 Tim 1:4, 1 Tim 4:3)(see Encratism), which would suggest a later date due to Gnosticism developing primarily in the latter 1st century. The term Gnosis("knowledge") itself occurs in 1 Timothy 6:20. If the parallels between 1 Timothy and Polycarp's epistle are understood as a literary dependence by the latter on the former, as is generally accepted, this would constitute a terminus ante quem of 130155 CE. However, Irenaeus (writing c. 180 CE) is the earliest author to clearly and unequivocally describe the Pastorals.
This historical relationship between Paul and Timothy is one of mentorship. Timothy is first mentioned in Acts 16:1. His mother Eunice, and his grandmother, Lois, are mentioned in 2 Tim. 1:5. All that we know of his father is that he was a Greek not a Jew (Acts 16:1).
Paul's second visit to Lystra is when Timothy first connected with Paul (1 Timothy 1:2; 2 Timothy 3:11). Paul not only brought Timothy into the faith but he was Timothy’s main mentor in Christian leadership (Acts 16:3), having done church planting and missionary journeys together. Timothy would have received his authority to preach in churches directly from Paul who of course was the greater known and accepted of the two and an apostle. Timothy’s official position in the church was one of an evangelist (1 Timothy 4:14) and he worked with Paul in Phrygia, Galatia, and Mysia, Troa, Philippi and Berea (Acts 17:14) and continued on to do even more work in Athens, and Thessalonica for the church (Acts 17:15; 1 Thessalonians 3:2) not to mention his work in Corinth, Macedonia, Ephesus and greater Asia. Timothy was also noted for coming to Paul’s aid when Paul fell into prison (Philippians 1:1, 2 Timothy 4:13). It is noteworthy that despite not being required due the ruling of the Jerusalem council; Timothy took circumcision himself to be a better witness among the Jews. According to church tradition he was loyal to Paul’s wishes and stayed and worked in Ephesus until he finally suffered the Martyr's death himself.
If, however, "… the pastorals are best understood against the background of the second century, the evidence in the letters relative to church order ... clearly reflect a time when apostle and prophet have been succeeded by bishop (and archbishop?) and/or elder in a stabilized church organization fully committed to an authorized succession of ordained ministers. The local churches are no longer lay churches, nor are their needs now taken care of simply by itinerant missionaries. There is obviously hierarchical organization both in the local and ecumenical church. The chief function of the bishop (or archbishop?) is to transmit and maintain the true faith" TIB 1955 XI p. 346
Regardless of whether this epistle is seen as a 4th missionary journey not recorded in Acts or as being written at some other point of Paul’s life, its intent seems clear that Paul is writing to encourage Timothy on his own ministry. Timothy is now pastoring in the Ephesus Church and Paul writes him to tell him to stay there and continue his good work there. Paul had planted the Ephesus church himself putting over 3 years of his blood and tears in to the effort (Acts 19:10; 20:31) and he is well pleased his former student is currently taking the post there. This is most likely a letter written in Paul’s late life and can be seen as being among his departing advice to his former student who has risen up in the ranks of church leadership himself. As Paul becomes more aware of his impending end, soon to be at the hands of Nero, he is setting things in order for the next generation.
If, however, I Timothy is post Paul, then Timothy represents all the "Timothies" of the church whom the writer is exhorting to preserve Pauline Christianity against incipient heresies.
The themes in this book circulate around church structure more than any other issue in the letter. Paul gives an example warning to Timothy not to let false doctrine such as Encratism take hold.
The structure for the role of women in the Church at Ephesus is laid out as well as a detailed list of qualifications for who can and cannot serve as Elders and Deacons in the church. It is a notably a hotly debated issue in the church as to what Paul meant in this book in regard to the women’s role in the church. What provoked this reversion from Paul’s revelation, in Galatians, that in Christ Jesus there is no male or female, to this banal legalism? Had the women, having been led to expect an imminent end of the world, begun to abandon their “wifely duties”? "Some feel he clearly teaches that women are not to have authority over men in the church structure (1 Timothy 2:12) and that this is why he clearly excludes them from the roles of Elder/Bishop and Deacon in chapter three. People who hold to this stance point out that Paul’s use of the phrase “Husband of one wife” is gender specific and excludes women from that role. They would point out that in the Greek text it literally reads "Man of one woman". "μιασ γυναικοσ ανδρα"(1 Timothy 3:2) However, more liberal scholars debate this, arguing that this is a product of the time in which Paul lived and it is a cultural reference not meant to be eternally binding on the church. Many churches have now embraced the ordination of women based on this modern outlook. The treatment of this issue has also been pointed to as evidence that I Timothy is not Pauline, noting "the freedom granted [women] in the aspostolic age to exercise the gifts of the Spirit, [and] Paul's insistence that in Christ there is neither male nor female, [which] had brought them into quick and widespread public activity." TIB 1955 XI p. 349. TNJBC also points out that the reasoning in I Timothy (the fall was Eve's fault) is nonPauline: “Paul himself prefers to assign blame to Adam (as a counterpart to Christ – see Rom [Romans] 5:1221; I Cor [Corinthians] 15: 4549…)” TNJBC 1990 p. 897
The treatment of widows, elders, masters, youth, and church members are spelled out; as well as a healthy warning against greed being given to the rich.
Key words and phrases in this book include; “fight the good fight”, “This is a faithful saying”,” let no one despise your youth”, doctrine, elder/bishop, deacon, fables, guard.
I. Salutation (1:12)
II. Negative Instructions: Stop the False Teachers (1:320)
III. Positive Instructions: Repair the Church (2:1–6:10)
IV. Personal Instructions: Pursue Godliness (6:1121)
Orthodox  

Castra of Bădeni  

Retrieved from : http://en.wikipedia.org/w/index.php?title=Castra_of_B%C4%83deni&oldid=458839030 Preston Field HousePrestonfield House
Prestonfield House is a fivestar boutique hotel located in Prestonfield, Edinburgh. It was originally built in 1687 by architect Sir William Bruce, and was once a wealthy rural estate, but in recent decades has come to serve as a hotel. Though it is but a small establishment, having only 23 rooms, Prestonfield House is well renowned by critics. Situated on extensive grounds at the foot of Arthur's Seat, Prestonfield House also owns a large roundhouse, which was previously used for keeping horses. The nowconverted stables are used to host large functions, one example being the Taste of Scotland festival. Otherwise, the Hotel maintains a small dedicated restaurant named 'Rhubarb', which serves gourmet food. HistoryOriginally known as Priestfield, the site was once a wealthy monastery, founded in 1150 by Henry, Earl of Northumbria. Over the subsequent centuries, the estate changed hands many times, until when newly in the possession of the Catholic Dick family, the monastery was in the 1670s burned down by Protestant students. The Family quickly enlisted William Bruce to design a replacement building, which was renamed Prestonfield. The new estate remained in the family's possession for many generations, who played host to many great thinkers of their times, including David Hume, Benjamin Franklin, Dr Samuel Johnson, and Allan Ramsay. The Dick family continued to modify and improve the estate, adding paintings, a grand new staircase with reception rooms, and a portecochère. Most notably, the stable house was built in the 19th century, as designed by James Gillespie Graham. As later generations of the family spent less and less time at the estate, no further remodelling took place, preserving the decor to the modern day. The estate was converted for use as hotel in the 1960s, and has since played host to Sandie Shaw, Winston Churchill, Margaret Thatcher, Sean Connery, Elton John, Catherine Zeta Jones, and Oliver Reed. In 2003, the hotel was bought by restaurateur James Thomson, who also maintains the acclaimed The Witchery by the Castle. ReferencesExternal LinksCoordinates: 55°56′11″N 3°09′27″W / 55.936426°N 3.157475°W Retrieved from : http://en.wikipedia.org/w/index.php?title=Prestonfield_House&oldid=459968085 Y CombinatorFixedpoint combinator "Y combinator" redirects here. For the technology venture capital firm, see Y Combinator (company). In computer science, a fixedpoint combinator (or fixpoint combinator ) is a higherorder function that computes a fixed point of other functions. A fixed point of a function f is a value x such that x = f(x). For example, 0 and 1 are fixed points of the function f(x) = x, because 0 = 0 and 1 = 1. Whereas a fixedpoint of a firstorder function (a function on "simple" values such as integers) is a firstorder value, a fixed point of a higherorder function f is another function p such that p = f(p). A fixedpoint combinator, then, is a function g which produces such a fixed point p for any function f:
or, alternatively:
Because fixedpoint combinators are higherorder functions, their history is intimately related to the development of lambda calculus. One wellknown fixedpoint combinator in the untyped lambda calculus is Haskell Curry's Y = λf·(λx·f (x x)) (λx·f (x x)). The name of this combinator is sometimes incorrectly used to refer to any fixedpoint combinator. The untyped lambda calculus however, contains an infinitude of fixedpoint combinators. Fixedpoint combinators do not necessarily exist in more restrictive models of computation. For instance, they do not exist in simply typed lambda calculus. In programming languages that support anonymous functions, fixedpoint combinators allow the definition and use of anonymous recursive functions, i.e. without having to bind such functions to identifiers. In this setting, the use of fixedpoint combinators is sometimes called anonymous recursion. How it worksIgnoring for now the question whether fixedpoint combinators even exist (to be addressed in the next section), we illustrate how a function satisfying the fixedpoint combinator equation works. To easily trace the computation steps, we choose untyped lambda calculus as our programming language. The (computational) equality from the equation that defines a fixedpoint combinator corresponds to beta reduction in lambda calculus. As a concrete example of a fixedpoint combinator applied to a function, we use the standard recursive mathematical equation that defines the factorial function
We can express a single step of this recursion in lambda calculus as the lambda abstraction F = λf. λn. IFTHENELSE (ISZERO n) 1 (MULT n (f (PRED n))) using the usual encoding for booleans, and Church encoding for numerals. The functions in CAPITALS above can all be defined as lambda abstractions with their intuitive meaning; see lambda calculus for their precise definitions. Intuitively, f in F is a placeholder argument for the factorial function itself. We now investigate what happens when a fixedpoint combinator FIX is applied to F and the resulting abstraction, which we hope would be the factorial function, is in turn applied to a (Churchencoded) numeral. (FIX F) n = (F (FIX F)) n  expanded the defining equation of FIX = (λx. IFTHENELSE (ISZERO x) 1 (MULT x ((FIX F) (PRED x)))) n  expanded the first F = IFTHENELSE (ISZERO n) 1 (MULT n ((FIX F) (PRED n)))  applied abstraction to n. If we now abbreviate FIX F as FACT, we recognize that any application of the abstraction FACT to a Church numeral calculates its factorial FACT n = IFTHENELSE (ISZERO n) 1 (MULT n (FACT (PRED n))). Recall that in lambda calculus all abstractions are anonymous, and that the names we give to some of them are only syntactic sugar. Therefore, it's meaningless in this context to contrast FACT as a recursive function with F as somehow being "not recursive". What fixed point operators really buy us here is the ability to solve recursive equations. That is, we can ask the question in reverse: does there exist a lambda abstraction that satisfies the equation of FACT? The answer is yes, and we have a "mechanical" procedure for producing such an abstraction: simply define F as above, and then use any fixed point combinator FIX to obtain FACT as FIX F. In the practice of programming, substituting FACT at a call site by the expression FIX F is sometimes called anonymous recursion. In the lambda abstraction F, FACT is represented by the bound variable f, which corresponds to an argument in a programming language, therefore F need not be bound to an identifier. F however is a higherorder function because the argument f is itself called as a function, so the programming language must allow passing functions as arguments. It must also allow function literals because FIX F is an expression rather than an identifier. In practice, there are further limitations imposed on FIX, depending on the evaluation strategy employed by the programming environment and the type checker. These are described in the implementation section. Existence of fixedpoint combinatorsIn certain mathematical formalizations of computation, such as the untyped lambda calculus and combinatory logic, every expression can be considered a higherorder function. In these formalizations, the existence of a fixedpoint combinator means that every function has at least one fixed point; a function may have more than one distinct fixed point. In some other systems, for example in the simply typed lambda calculus, a welltyped fixedpoint combinator cannot be written. In those systems any support for recursion must be explicitly added to the language. In still others, such as the simplytyped lambda calculus extended with recursive types, fixedpoint operators can be written, but the type of a "useful" fixedpoint operator (one whose application always returns) may be restricted. In polymorphic lambda calculus (System F) a polymorphic fixedpoint combinator has type ∀a.(a→a)→a, where a is a type variable. Y combinatorOne wellknown (and perhaps the simplest) fixedpoint combinator in the untyped lambda calculus is called the Y combinator. It was discovered by Haskell B. Curry, and is defined as:
We can see that this function acts as a fixedpoint combinator by applying it to an example function g and rewriting:
In programming practice, the Y combinator is useful only in those languages that provide a callbyname evaluation strategy, since (Y g) diverges (for any g) in callbyvalue settings. Example in Scheme(define Y (lambda (f) ((lambda (recur) (f (lambda arg (apply (recur recur) arg)))) (lambda (recur) (f (lambda arg (apply (recur recur) arg))))))) Factorial definition using Y Combinator (define fact (Y (lambda (f) (lambda (n) (if (<= n 0) 1 (* n (f ( n 1)))))))) Example in Common Lisp(defun y (func) ((lambda (x) (funcall x x)) (lambda (y) (funcall func (lambda (&rest args) (apply (funcall y y) args)))))) Factorial program using the Y combinator (funcall (y (lambda (f) (lambda (x) (if (<= x 1) 1 (* x (funcall f (1 x))))))) 5) => 120 Other fixedpoint combinatorsIn untyped lambda calculus fixedpoint combinators are not especially rare. In fact there are infinitely many of them. In 2005 Mayer Goldberg showed that the set of fixedpoint combinators of untyped lambda calculus is recursively enumerable. A version of the Y combinator that can be used in callbyvalue (applicativeorder) evaluation is given by ηexpansion of part of the ordinary Y combinator:
Here is an example of this in Python: >>> Z = lambda f: (lambda x: f(lambda *args: x(x)(*args)))(lambda x: f(lambda *args: x(x)(*args))) >>> fact = lambda f: lambda x: 1 if x == 0 else x * f(x1) >>> Z(fact)(5) 120 The Y combinator can be expressed in the SKIcalculus as
which corresponds to the lambda expression
This fixedpoint combinator is simpler than the Y combinator, and βreduces into the Y combinator; it is sometimes cited as the Y combinator itself:
Another common fixed point combinator is the Turing fixedpoint combinator (named after its discoverer, Alan Turing):
It also has a simple callbyvalue form:
Some fixed point combinators, such as this one (constructed by Jan Willem Klop) are useful chiefly for amusement:
where:
Strictly nonstandard fixedpoint combinatorsIn untyped lambda calculus there are terms that have the same Böhm tree as a fixedpoint combinator, that is they have the same infinite extension λx.x(x(x ... )). These are called nonstandard fixedpoint combinators. Evidently, any fixedpoint combinator is also a nonstandard one, but not all nonstandard fixedpoint combinators are fixedpoint combinators because some of them fail to satisfy the equation that defines the "standard" ones. These strange combinators are called strictly nonstandard fixedpoint combinators; an example is the following combinator N = BM(B(BM)B), where B = λxyz.x(yz) and M = λx.xx. The set of nonstandard fixedpoint combinators is not recursively enumerable. Implementing fixedpoint combinatorsIn a language that supports lazy evaluation, like in Haskell, it is possible to define a fixedpoint combinator using the defining equation of the fixedpoint combinator. A programming language of this kind effectively solves the fixedpoint combinator equation by means of its own (lazy) recursion mechanism. This implementation of a fixedpoint combinator in Haskell is sometimes referred to as defining the Y combinator in Haskell. This is incorrect because the actual Y combinator is rejected by the Haskell type checker (but see the following section for a small modification of Y using a recursive type which works). The listing below shows the implementation of a fixedpoint combinator in Haskell that exploits Haskell's ability to solve the fixedpoint combinator equation. This fixedpoint combinator is traditionally called fix :: (a > a) > a fix f = f (fix f) fix (const 9)  const is a function that returns its first parameter and ignores the second;  this evaluates to 9 factabs fact 0 = 1  factabs is F from our lambda calculus example factabs fact x = x * fact (x1) (fix factabs) 5  evaluates to 120 In the example above, the application of In a strict language like OCaml, we can avoid the infinite recursion problem by forcing the use of a closure. The strict version of let rec fix f x = f (fix f) x (* note the extra x *) let factabs fact = function (* factabs now has extra level of lambda abstraction *) 0 > 1  x > x * fact (x1) let _ = (fix factabs) 5 (* evaluates to "120" *) The same idea can be used to implement a (monomorphic) fixed combinator in strict languages that support inner classes inside methods (called local inner classes in Java), which are used as 'poor man's closures' in this case. Even when such classes may be anonymous, as in the case of Java, the syntax is still cumbersome. Java code. Function objects, e.g. in C++, simplify the calling syntax, but they still have to be generated, preferably using a helper function such as boost::bind. C++ code. Example of encoding via recursive typesIn programming languages that support recursive types (see System F_{ω}), it is possible to type the Y combinator by appropriately accounting for the recursion at the type level. The need to selfapply the variable x can be managed using a type (Rec a), which is defined so as to be isomorphic to (Rec a > a). For example, in the following Haskell code, we have In and out being the names of the two directions of the isomorphism, with types: In :: (Rec a > a) > Rec a out :: Rec a > (Rec a > a) which lets us write: newtype Rec a = In { out :: Rec a > a } y :: (a > a) > a y = \f > (\x > f (out x x)) (In (\x > f (out x x))) Or equivalently in OCaml: type 'a recc = In of ('a recc > 'a) let out (In x) = x let y f = (fun x a > f (out x x) a) (In (fun x a > f (out x x) a)) Anonymous recursion by other meansAlthough fixed point combinators are the standard solution for allowing a function not bound to an identifier to call itself, some languages like JavaScript provide a syntactical construct which allows anonymous functions to refer to themselves. For example, in Javascript one can write the following, although it has been removed in the strict mode of the latest standard edition. function(x) { return x === 0 ? 1 : x * arguments.callee(x1); } See alsoNotesReferences
ReferencesExternal links
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