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🔗 Computing

Lambda lifting is a meta-process that restructures a computer program so that functions are defined independently of each other in a global scope. An individual "lift" transforms a local function into a global function. It is a two step process, consisting of;

• Eliminating free variables in the function by adding parameters.
• Moving functions from a restricted scope to broader or global scope.

The term "lambda lifting" was first introduced by Thomas Johnsson around 1982 and was historically considered as a mechanism for implementing functional programming languages. It is used in conjunction with other techniques in some modern compilers.

Lambda lifting is not the same as closure conversion. It requires all call sites to be adjusted (adding extra arguments to calls) and does not introduce a closure for the lifted lambda expression. In contrast, closure conversion does not require call sites to be adjusted but does introduce a closure for the lambda expression mapping free variables to values.

The technique may be used on individual functions, in code refactoring, to make a function usable outside the scope in which it was written. Lambda lifts may also be repeated, in order to transform the program. Repeated lifts may be used to convert a program written in lambda calculus into a set of recursive functions, without lambdas. This demonstrates the equivalence of programs written in lambda calculus and programs written as functions. However it does not demonstrate the soundness of lambda calculus for deduction, as the eta reduction used in lambda lifting is the step that introduces cardinality problems into the lambda calculus, because it removes the value from the variable, without first checking that there is only one value that satisfies the conditions on the variable (see Curry's paradox).

Lambda lifting is expensive on processing time for the compiler. An efficient implementation of lambda lifting is ${\displaystyle O(n^{2})}$ on processing time for the compiler.

In the untyped lambda calculus, where the basic types are functions, lifting may change the result of beta reduction of a lambda expression. The resulting functions will have the same meaning, in a mathematical sense, but are not regarded as the same function in the untyped lambda calculus. See also intensional versus extensional equality.

The reverse operation to lambda lifting is lambda dropping.

Lambda dropping may make the compilation of programs quicker for the compiler, and may also increase the efficiency of the resulting program, by reducing the number of parameters, and reducing the size of stack frames. However it makes a function harder to re-use. A dropped function is tied to its context, and can only be used in a different context if it is first lifted.

🔗 Mathematics

Legendre's constant is a mathematical constant occurring in a formula conjectured by Adrien-Marie Legendre to capture the asymptotic behavior of the prime-counting function ${\displaystyle \pi (x)}$. Its value is now known to be exactly 1.

Examination of available numerical evidence for known primes led Legendre to suspect that ${\displaystyle \pi (x)}$ satisfies an approximate formula.

Legendre conjectured in 1808 that

${\displaystyle \pi (x)={\frac {x}{\ln(x)-B(x)}}}$

where ${\displaystyle \lim _{x\to \infty }B(x)=1.08366}$....OEIS: A228211

Or similarly,

${\displaystyle \lim _{n\to \infty }\left(\ln(n)-{n \over \pi (n)}\right)=B}$

where B is Legendre's constant. He guessed B to be about 1.08366, but regardless of its exact value, the existence of B implies the prime number theorem.

Pafnuty Chebyshev proved in 1849 that if the limit B exists, it must be equal to 1. An easier proof was given by Pintz in 1980.

It is an immediate consequence of the prime number theorem, under the precise form with an explicit estimate of the error term

${\displaystyle \pi (x)={\rm {Li}}(x)+O\left(xe^{-a{\sqrt {\ln x}}}\right)\quad {\text{as }}x\to \infty }$

(for some positive constant a, where O(…) is the big O notation), as proved in 1899 by Charles de La Vallée Poussin, that B indeed is equal to 1. (The prime number theorem had been proved in 1896, independently by Jacques Hadamard and La Vallée Poussin, but without any estimate of the involved error term).

Being evaluated to such a simple number has made the term Legendre's constant mostly only of historical value, with it often (technically incorrectly) being used to refer to Legendre's first guess 1.08366... instead.

Pierre Dusart proved in 2010

${\displaystyle {\frac {x}{\ln x-1}}<\pi (x)}$ for ${\displaystyle x\geq 5393}$, and

${\displaystyle \pi (x)<{\frac {x}{\ln x-1.1}}}$ for ${\displaystyle x\geq 60184}$. This is of the same form as

${\displaystyle \pi (x)={\frac {x}{\ln(x)-B(x)}}}$ with ${\displaystyle 1<B(x)<1.1}$.

🔗 Australia 🔗 Portugal 🔗 Australia/Australian maritime history 🔗 Australia/History of exploration

The theory of Portuguese discovery of Australia claims that early Portuguese navigators were the first Europeans to sight Australia between 1521 and 1524, well before the arrival of Dutch navigator Willem Janszoon in 1606 on board the Duyfken who is generally considered to be the first European discoverer. This is based on the following elements:

• The Dieppe maps, a group of 16th-century French world maps, which depict a large landmass between Indonesia and Antarctica. Labelled as Java la Grande, this land mass carries French, Portuguese, and Gallicized Portuguese placenames, and has been interpreted by some as corresponding to Australia's northwestern and eastern coasts.
• The presence of Portuguese colonies in Southeast Asia from the early 16th century, particularly Portuguese Timor – approximately 650 kilometres from the Australian coast – c. 1513–1516.
• Various antiquities found on Australian coastlines, claimed to be relics of early Portuguese voyages to Australia, which are more commonly regarded as evidence of Makassan visit of Northern Australia.

Precedence of Australia's discovery has also been claimed for China (Admiral Zheng), France, Spain, and even Phoenicia.

🔗 Military history 🔗 Military history/World War II 🔗 Scottish Islands

Operation Vegetarian was a British military plan in 1942 to disseminate linseed cakes infected with anthrax spores onto the fields of Germany. These cakes would have been eaten by the cattle, which would then be consumed by the civilian population, causing the deaths of millions of German citizens. Furthermore, it would have wiped out the majority of Germany's cattle, creating a massive food shortage for the rest of the population that remained uninfected. Preparations were not complete until early 1944. Operation Vegetarian was only to be used in the event of a German anthrax attack on the United Kingdom.

The cakes themselves were tested on Gruinard Island, just off the coast of Scotland. Because of the widespread contamination from the anthrax spores, the land remained quarantined until 1990. The five million cakes made to be disseminated in Germany were eventually destroyed in an incinerator shortly after the end of World War II.

In his novel The Impossible Dead (2011), author Ian Rankin mentions the clandestine events surrounding the removal of contaminated soils from Guinard Island by a protest group, the Dark Harvest Commando, and the island's removal from maps by the British Government. The island also features as the principal setting for the 1985 novel El año de gracia, by Cristina Fernández Cubas, in which the protagonist spends a winter shipwrecked on the island.

🔗 Architecture

The Frankfurt kitchen was a milestone in domestic architecture, considered the forerunner of modern fitted kitchens, for it realised for the first time a kitchen built after a unified concept, designed to enable efficient work and to be built at low cost. It was designed in 1926 by Austrian architect Margarete Schütte-Lihotzky for architect Ernst May's social housing project New Frankfurt in Frankfurt, Germany. Some 10,000 units were built in the late 1920s in Frankfurt.

🔗 Biography 🔗 Chicago 🔗 Biography/Actors and Filmmakers 🔗 College Basketball

John Michael Crichton (; October 23, 1942 – November 4, 2008) was an American author, screenwriter, film director, and film producer. His books have sold over 200 million copies worldwide, and over a dozen have been adapted into films. His literary works are usually within the science fiction, techno-thriller, and medical fiction genres, and heavily feature technology. His novels often explore technology and failures of human interaction with it, especially resulting in catastrophes with biotechnology. Many of his novels have medical or scientific underpinnings, reflecting his medical training and scientific background. He wrote, among other works, The Andromeda Strain (1969), The Great Train Robbery (1975), Congo (1980), Sphere (1987), Jurassic Park (1990), Rising Sun (1992), Disclosure (1994), The Lost World (1995), Airframe (1996), Timeline (1999), Prey (2002), State of Fear (2004), and Next (2006). Films he wrote and directed included Westworld (1973), Coma (1978), The Great Train Robbery (1979), Looker (1981), and Runaway (1984).

🔗 Mathematics

Bellman's lost-in-a-forest problem is an unsolved minimization problem in geometry, originating in 1955 by the American applied mathematician Richard E. Bellman. The problem is often stated as follows: "A hiker is lost in a forest whose shape and dimensions are precisely known to him. What is the best path for him to follow to escape from the forest?" It is usually assumed that the hiker does not know the starting point or direction he is facing. The best path is taken to be the one that minimizes the worst-case distance to travel before reaching the edge of the forest. Other variations of the problem have been studied.

A proven solution is only known for a few shapes or classes of shape. A general solution would be in the form of a geometric algorithm which takes the shape of the forest as input and returns the optimal escape path as the output. Although real world applications are not apparent, the problem falls into a class of geometric optimization problems including search strategies that are of practical importance. A bigger motivation for study has been the connection to Moser's worm problem. It was included in a list of 12 problems described by the mathematician Scott W. Williams as "million buck problems" because he believed that the techniques involved in their resolution will be worth at least a million dollars to mathematics.

🔗 Military history 🔗 Military history/Military science, technology, and theory 🔗 Military history/Weaponry

Improvised firearms (sometimes called zip guns or pipe guns) are firearms manufactured other than by a firearms manufacturer or a gunsmith, and are typically constructed by adapting existing materials to the purpose. They range in quality from crude weapons that are as much a danger to the user as the target to high-quality arms produced by cottage industries using salvaged and repurposed materials.

Improvised firearms are commonly used as tools by criminals and insurgents and are often associated with such groups; other uses include self-defense in lawless areas and hunting game in poor rural areas.

🔗 France 🔗 Atheism

The Cult of Reason (French: Culte de la Raison) was France's first established state-sponsored atheistic religion, intended as a replacement for Catholicism during the French Revolution. After holding sway for barely a year, in 1794 it was officially replaced by the rival Cult of the Supreme Being, promoted by Robespierre. Both cults were officially banned in 1802 by Napoleon Bonaparte with his Law on Cults of 18 Germinal, Year X.

🔗 Military history 🔗 Military history/North American military history 🔗 Military history/United States military history 🔗 Military history/Military science, technology, and theory 🔗 Military history/Weaponry 🔗 Military history/Cold War 🔗 Pritzker Military Library 🔗 Firearms

The M-28 or M-29 Davy Crockett Weapon System was the tactical nuclear recoilless gun (smoothbore) for firing the M-388 nuclear projectile that was deployed by the United States during the Cold War. It was one of the smallest nuclear weapon systems ever built, with a yield between 10 and 20 tons TNT equivalent (40–80 gigajoules). It is named after American folk hero, soldier, and congressman Davy Crockett.