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Referential transparency

Referential transparency and referential opacity are properties of parts of computer programs. An expression is called referentially transparent if it can be replaced with its corresponding value without changing the program's behavior; this requires that the expression be pure, to say the expression value must be the same for the same inputs and its evaluation must have no side effects. An expression, not referentially transparent is called referentially opaque. In mathematics all function applications are referentially transparent, by the definition of what constitutes a mathematical function. However, this is not always the case in programming, where the terms procedure and method are used to avoid misleading connotations. In functional programming only referentially transparent functions are considered; some programming languages provide means to guarantee referential transparency. Some functional programming languages enforce referential transparency for all functions; the importance of referential transparency is that it allows the programmer and the compiler to reason about program behavior as a rewrite system.

This can help in proving correctness, simplifying an algorithm, assisting in modifying code without breaking it, or optimizing code by means of memoization, common subexpression elimination, lazy evaluation, or parallelization. The concept seems to have originated in Alfred North Whitehead and Bertrand Russell's Principia Mathematica, it was adopted in analytical philosophy by Willard Van Orman Quine. In §30 of Word and Object Quine gives this definition: A mode of containment φ is referentially transparent if, whenever an occurrence of a singular term t is purely referential in a term or sentence ψ, it is purely referential in the containing term or sentence φ; the term appeared in its contemporary computer science usage, in the discussion of variables in programming languages, in Christopher Strachey's seminal set of lecture notes Fundamental Concepts in Programming Languages. The lecture notes referenced Object in the bibliography. If all functions involved in the expression are pure functions the expression is referentially transparent.

Consider a function that returns the input from some source. In pseudocode, a call to this function might be GetInput where Source might identify a particular disk file, the keyboard, etc. With identical values of Source, the successive return values will be different. Therefore, function GetInput is neither deterministic nor referentially transparent. A more subtle example is that of a function that has a free variable, i.e. depends on some input, not explicitly passed as a parameter. This is resolved according to name binding rules to a non-local variable, such as a global variable, a variable in the current execution environment, or a variable in a closure. Since this variable can be altered without changing the values passed as parameter, the results of subsequent calls to the function may differ if the parameters are identical. However, in pure functional programming, destructive assignment is not allowed, thus if the free variable is statically bound to a value, the function is still referentially transparent, as neither the non-local variable nor its value can change, due to static binding and immutability, respectively.

Arithmetic operations are referentially transparent: 5 * 5 can be replaced by 25, for instance. In fact, all functions in the mathematical sense are referentially transparent: sin is transparent, since it will always give the same result for each particular x. Assignments are not transparent. For instance, the C expression x = x + 1 changes the value assigned to the variable x. Assuming x has value 10, two consecutive evaluations of the expression yield 11 and 12. Replacing x = x + 1 with either 11 or 12 gives a program with different meaning, so the expression is not referentially transparent. However, calling a function such as int plusone is transparent, as it will not implicitly change the input x and thus has no such side effects. Today is not transparent, as if you evaluate it and replace it by its value, you don't get the same result as you will if you run it tomorrow; this is. In languages with no side-effects, like Haskell, we can substitute equals for equals: i.e. if x=y f = f. This is a property known as indistinguishable identicals, see Identity of indiscernibles.

Such properties need not hold in general for languages with side-effects. So it is important to limit such assertions to so-called judgmental equality, the equality of the terms as tested by the system, not including user defined equivalence for types. For instance, if f:A->B and the type A has overridden the notion of equality, e.g. making all terms equal it is possible to test x==y and yet find f/=f. This is because systems like Haskell do not verify that functions defined on types with user defined equivalence relations be well-defined with respect to that equivalence, thus the referential transparency is limited to types without equivalence relations. To extend referential transparency to user-defined equivalence relations can be done for example with a Martin-Lof Identity Type, but requires a dependently typed system such as in Agda, Coq or Idris. If the substitution of an expression with its value is valid only at a certain point in the execution of the program the expression is not referentially transparent.

The definition and ordering of these sequence points are the theoretical foundation of imperative programming, part of the semantics of an imperative programming language. However, because a referen

Denmark, Maine

Denmark is a town in Oxford County, United States. The population was 1,148 at the 2010 census. A number of ponds and lakes are located within the town; the land was once part of village of the Sokokis Abenaki Indians. Attacked by Captain John Lovewell in 1725 during Dummer's War, the tribe abandoned the area and fled to Canada; the township combined a grant made by the Massachusetts General Court to Fryeburg Academy, Foster's Gore and a strip from Brownfield. Several settlers came from Massachusetts, it was incorporated as Denmark on February 20, 1807, named in a show of solidarity with Denmark. That country's capital, was attacked in 1801 and 1807 by the Royal Navy, which in 1775 had attacked Portland. Farmers found the soil to be stony and sandy, producing fair yields of potatoes and oats, but the town did have excellent water powers at the streams, mills were established to manufacture grain, long lumber, barrel staves, sashes and doors. Denmark Village was established at the foot of Moose Pond, whose outlet, Moose Pond Brook, provided the best water-power site.

Today, the town is site of summer camps. Camp Wyonegonic, founded 1902, is the oldest girls' camp in the country. In Denmark is Camp Walden, established in 1916. Founded in 1994, the Denmark Arts Center is the latest addition to the town's culture. According to the United States Census Bureau, Denmark has a total area of 49.93 square miles, of which 46.12 square miles is land and 3.81 square miles is water. Denmark is drained by the Saco River; the largest of its many ponds is Moose Pond, about 8 miles long. The town is crossed by State Routes 117 and 160, it is bordered by the towns of Bridgton to the northeast, Sebago to the southeast, Hiram to the south, Brownfield to the southwest, Fryeburg to the northwest. As of 2000, the median income for a household in the town was $45,885, the median income for a family was $57,625; the per capita income for the town was $28,563. About 5.4% of families and 7.8% of the population were below the poverty line, including 12.2% of those under age 18 and 6.9% of those age 65 or over.

As of the census of 2010, there were 1,148 people, 479 households, 330 families residing in the town. The population density was 24.9 inhabitants per square mile. There were 1,075 housing units at an average density of 23.3 per square mile. The racial makeup of the town was 98.4% White, 0.4% African American, 0.1% Native American, 0.3% Asian, 0.3% from other races, 0.5% from two or more races. Hispanic or Latino of any race were 0.3% of the population. There were 479 households of which 28.6% had children under the age of 18 living with them, 57.6% were married couples living together, 6.7% had a female householder with no husband present, 4.6% had a male householder with no wife present, 31.1% were non-families. 23.0% of all households were made up of individuals and 8.3% had someone living alone, 65 years of age or older. The average household size was 2.40 and the average family size was 2.80. The median age in the town was 46.6 years. 21.7% of residents were under the age of 18. The gender makeup of the town was 48.0 % female.

Denmark has a Town Meeting-Selectmen-Town Manager form of government and is governed by a municipal charter. The three member Board of Selectmen is elected at large on a non-partisan basis for staggered three-year terms; the Town Manager is appointed by the Board of Selectmen for an initial term of up to two years and may be reappointed in successive terms of up to three years each. Denmark's is seeking a Town Manager as Ephrem Paraschak left the position as of June 0f 2014. Retired Fire Chief and current Road Commissioner Ken Richardson is filling the role of Acting Town Manager until the full-time position is filled; the school system that serves Denmark is known as Maine School Administrative District 72 or MSAD 72. MSAD 72 serves the municipalities of Brownfield, Lovell, Stoneham and Sweden in addition to Denmark. Nathaniel Cobb Deering, US congressman Richard L. Dunn, state legislator Rufus Ingalls, Civil War era general Nancy Masterton, state legislator James W. Milliken, Michigan state senator Hazen S. Pingree, 24th governor of Michigan, mayor of Detroit Ralph Sarty, state legislator Congregational Church Town of Denmark Maine School Administrative District #72 Brownfield-Denmark Elementary School Oxford County Denmark Arts Center

Ingo Walter

Ingo Walter is a professor of finance, corporate governance and ethics as well as Vice Dean of Faculty at New York University's Stern School of Business. Walter researches and consults in the areas of international trade policy, international banking, environmental economics, economics of multinational corporate operations. Professor Walter received his A. B. and M. S. degrees from Lehigh University, his Ph. D. degree in 1966 from New York University. He taught at the University of Missouri - St. Louis from 1965 to 1970 and has been on the faculty at New York University since 1970, he held a joint appointment as Professor of International Management at INSEAD from 1986 to 2005 and remains a Visiting Professor there. He teaches "Sovereign and Reputational Risk" in the Risk Management Open Enrollment program for Stern Executive Education, he teaches for the TRIUM Global Executive MBA Program, an alliance of NYU Stern, the London School of Economics and HEC School of Management. Professor Walter teaches for, is the Academic Director of, both the Master of Science in Global Finance and Master of Science in Risk Management Program for Executives.

MSGF is jointly offered by the Hong Kong University of Science and Technology. MSRM is offered by NYU Stern. Walter is the co-author, or editor of 26 books, including: Walter, Ingo. Governing the Modern Corporation. New York: Oxford University Press. ISBN 0-19-517167-5. Walter, Ingo. Mergers and Acquisitions in Banking and Finance: What Works, What Fails and Why?. New York: Oxford University Press. ISBN 0-19-515900-4. Walter, Ingo. High Finance in the Euro-Zone. London: Prentice Hall. ISBN 0-273-63737-1. Walter, Ingo; the Political Economy of European Financial Integration. Cambridge: MIT Press. ISBN 0-262-69203-1. Walter, Ingo. Street Smarts: Linking Professional Conduct and Shareholder Value in the Securities Industry. Boston: Harvard Business School Press. ISBN 0-87584-653-X. Walter, Ingo; the Secret Money Market: Inside the dark world of Tax Evasion, Financial Fraud, Insider Trading, Money Laundering, Capital Flight. New York, NY: Harper Business. ISBN 0-88730-489-3. NYU Stern Executive Education Ingo Walter's profile at NYU Stern School of Business TRIUM Global Executive MBA Program Master of Science in Global Finance Master of Science in Risk Management Program for Executives

Moses Gomberg

Moses Gomberg was a chemistry professor at the University of Michigan. He was born in Yelisavetgrad, Russian Empire, his parents were the son of Hershko Gomberg and Maryam-Ethel née Reznikova. In 1884, the family emigrated to Chicago to escape the pogroms following the assassination of Czar Alexander II. In Chicago he worked at the Stock Yards. In 1886, Moses entered the University of Michigan, where he obtained his B. Sc. in 1890 and his doctorate in 1894 under the supervision of A. B. Prescott, his thesis, titled "Trimethylxanthine and Some of its Derivatives", dealt with the derivatization of caffeine. Appointed an instructor in 1893, Gomberg worked at the University of Michigan for the duration of his professional academic career, becoming chair of the department of chemistry from 1927 until his retirement in 1936. Dr. Gomberg served as president of the American Chemical Society in 1931. In 1896–1897, he took a year's leave to work as a postdoctoral researcher with Baeyer and Thiele in Munich and with Victor Meyer in Heidelberg, where he prepared the long-elusive tetraphenylmethane.

During attempts to prepare the more sterically congested hydrocarbon hexaphenylethane, he identified the triphenylmethyl radical, the first persistent radical to be discovered, is thus known as the founder of radical chemistry. The work was followed up by Wilhelm Schlenk. Gomberg was a mentor to Werner Emmanuel Bachmann who carried on his work and together they discovered the Gomberg-Bachmann reaction. In 1923, he claimed to have synthesized chlorine tetroxide via the reaction of silver perchlorate with iodine, but was shown to have been mistaken. Gomberg was the first to synthesize tetraphenylmethane; this was accomplished by the thermal decomposition of 1-phenyl-2-trityldiazene to the desired product in 2-5% yield. Seeking to prepare hexaphenylethane, Gomberg attempted a Wurtz coupling of triphenylmethyl chloride. Elemental analysis of the resultant white crystalline solid, uncovered discrepancies with the predicted molecular formula: Hypothesizing that had combined with molecular oxygen to form the peroxide, Gomberg found that treatment of with sodium peroxide was another means of synthesizing.

By performing the reaction of triphenylchloromethane with zinc under an atmosphere of carbon dioxide Gomberg obtained the free radical. This compound reacted with air, chlorine and iodine. On the basis of his experimental evidence Gomberg concluded that he had discovered the first instance of a persistent radical and trivalent carbon; this was a controversial conclusion for many years as molecular weight determinations of found a value, double that of the free radical. Gomberg postulated that some non-tetravalent carbon structure existed in solution because of the observed activity towards oxygen and the halogens. Gomberg and Bachmann found that treatment of "hexaphenylethane" with magnesium resulted in a Grignard reagent, the first instance of the formation of such a compound from a hydrocarbon. Studies of other triarylmethyl compounds gave results similar to Gomberg's, it was hypothesized that existed in equilibrium with its dimer hexaphenylethane; however this structure was disproven in favor of the quinoid dimer.

At the end of his first report of trivalent carbon "On Trivalent Carbon" Gomberg wrote "This work will be continued and I wish to reserve the field for myself." While nineteenth-century chemists respected such claims Gomberg found that the field of chemistry he founded was too rich to reserve for himself. Upon his death in 1947 Moses Gomberg bequeathed his estate to the chemistry department of the University of Michigan for the creation of student fellowships. In 2000, the centennial of his paper "Triphenylmethyl, a Case of Trivalent Carbon", a symposium was held in his memory and a plaque was installed in the Chemistry Building at the University of Michigan designating a National Historic Chemical Landmark. In 1993, the chemistry department of the University of Michigan instituted the Moses Gomberg Lecture series to provide assistant professors an opportunity to invite distinguished scientists to the chemistry department. Gomberg never married. Chemistry Department at the University of Michigan Link National Academy of Sciences Biographical Memoir

Sepia mestus

Sepia mestus known as the reaper cuttlefish or red cuttlefish, is a species of cuttlefish native to the southwestern Pacific Ocean Escape Reef off Queensland to Murrays Beach off Jervis Bay. Reports of this species from China and Vietnam are now known to be misidentifications. S. mestus lives at a depth of between 0 and 22 m. S. mestus exhibits sexual dimorphism. Females grow to a mantle length of 124 mm, while males do not exceed 77 mm ML; the type specimen was collected off the Australian coast and is deposited at The Natural History Museum in London. Cephalopods share many similar anatomical structures and it can be hard to distinguish between different species in certain situations. All cephalopods have a similar basic anatomical plan. Structures include a set of limbs. Major body parts such as reproductive systems, digestive organs and the gills are contained in the mantle at the posterior portion of the animal. Cuttlefish including S. mestus differ from octopuses as they have an additional pair of limbs that octopuses lack.

These limbs are known as feeding tentacles. These tentacles are found between arms four; the feeding tentacles are used for extended to capture prey. S. mestus is referred to as the red cuttlefish. When undisturbed it is recognized by its red colouration and two dark spots on the posterior of the animal. S. mestus propels itself through the water using a technique, seen in many Cephalopods. Water is pushed through a cavity, formed by the mantle; the animal ejects water from the mantle via a tubular funnel. This technique allows the animal to move through the environment using jet propulsion. A relaxed mantle allows for water to fill the mantle cavity. A contracted mantle forces water out through the tubular funnel; the funnel can be pointed in different directions allowing for movement forward and backward away from predators or towards prey. Some common predators of S. mestus include bluefish, summer flounder, black seabass. Common prey of S. mestus and other cuttlefish include different species of shrimp and young fish.

Camoflauge is a distinctive feature of Cephalopods including S. mestus. Camouflage is achieved through changing of the animals texture. Small organs in the skin allow; these chromatophores can be described as small bags of dense pigment that can be expanded or contracted in which a spot of particular colour can be displayed. S. Mestus and most other species of cuttlefish can alter skin texture to blend in with their environment; this is achieved by pushing up flaps of skin to match shapes of rock and seaweed. These flaps are known as papillae. Contracting rings of muscle around the base of these papillae allows for the flaps to rise, changing the appearance of the animal. S. Mestus can bury itself under the sand to avoid predators. To attract a potential mate, a male will perform various displays to catch the attention of a female. Once a male is successful in attracting a mate, the male will insert the hectocotylus into the female’s mantle cavity to fertilize the female; the female will lay her eggs nearby.

After spawning and brooding and female adults die shortly after. Like most members of the class Cephalopoda, S. mestus are gonochoric. After the embryos develop for about two months, they will hatch and remain in a planktonic stage before developing into adults. All cuttlefish including S. mestus disperse their eggs by attachment to the sea floor on or under hard surfaces such as rock and coral. S. mestus is endemic to Australia, ranging along the east coast from northern Queensland to Jervis Bay in New South Wales. S. mestus lives in depths up to 22 m. inhabitating a tropical climateS. Mestus lives on rocky reefs and is seen under ledges. Many of the worlds cuttlefish species are found including S. mestus. It is considered of least concern. Increasing levels of CO2 in the atmosphere causes ocean acidification and is a threat to all cuttlefish. According to studies, high CO2 concentrations, cuttlefishes tend to lay down a denser cuttlebone; this could negatively affect cuttlefish buoyancy regulation.

"CephBase: Sepia mestus". Archived from the original on 2005


SmY ribonucleic acids are a family of small nuclear RNAs found in some species of nematode worms. They are thought to be involved in mRNA trans-splicing. SmY RNAs are about 70–90 nucleotides long and share a common secondary structure, with two stem-loops flanking a consensus binding site for Sm protein. Sm protein is a shared component of spliceosomal snRNPs. SmY RNAs have been found in nematodes of class Chromadorea, which includes the most studied nematodes, but not in the more distantly related Trichinella spiralis in class Dorylaimia; the number of SmY genes in each species varies, with most Caenorhabditis and Pristionchus species having 10–26 related paralogous copies, while other nematodes have 1–5. The first SmY RNA was discovered in 1996 in purified Ascaris lumbricoides spliceosome preparations, as was another called SmX RNA, not detectably homologous to SmY. Twelve SmY homologs were identified computationally in Caenorhabditis elegans, ten in Caenorhabditis briggsae. Several transcripts from these SmY genes were cloned and sequenced in a systematic survey of small non-coding RNA transcripts in C. elegans.

A systematic survey of 2,2,7-trimethylguanosine 5' capped transcripts in C.elegans using anti TMG antibodies identified two TMG capped SmY transcripts. Sequence analysis of the potential Sm binding sites in these transcripts indicated the SmY, U5 snRNA, U3 snoRNA and the spliced leader RNAs transcripts all contain a similar consensus SM binding sequence; the predicted SM binding sites identified in the U1, U2 and U4 snRNA transcripts varied from this consensus. In C. elegans, SmY RNAs copurify with spliceosome and with Sm, SL75p, SL26p proteins, while the better-characterized C. elegans SL1 trans-splicing snRNA copurifies in a complex with Sm, SL75p, SL21p. Loss of function of either SL21p or SL26p individually causes only a weak cold-sensitive phenotype, whereas knockdown of both is lethal, as is a SL75p knockdown. Based on these results, the SmY RNAs are believed to have a function in trans-splicing. Page for SmY spliceosomal RNA at Rfam