title: LaToya Cantrell

text: During the 2019 session of the Louisiana Legislature, Cantrell negotiated the Fair Share Agreement with Governor John Bel Edwards and city, state, and tourism officials. The agreement secured $50 million in upfront funding for the city's infrastructure needs as well as $26 million in annual recurring revenue for the city. Following the approval of the Fair Share Agreement, New Orleans voters approved 3 of the 4 proposals Cantrell and the City Council put on the ballot in the 2019 general election. Voters approved a $500 million bond sale and a tax on short-term rental properties, as well the establishment of a Human Right Commission under the New Orleans Home Rule Charter.


title: LaToya Cantrell

text: In 2016, Cantrell was given a lifetime achievement award by the presidents of Tulane, Loyola and Xavier universities and the University of New Orleans for her service to the community.


title: LaToya Cantrell

text: Cantrell was re-elected to office by a wide margin in November 2021, securing 65% of the vote. Her campaign focused on the city's status in 2020 as a COVID-19 hotspot and her efforts, which at times were unpopular, to stop the disease's spread. She also stressed the need for higher-paying jobs for city workers, better public health outcomes and new technologies for the future of New Orleans.


title: Louis Cyr

text: Louis Cyr (; born Cyprien-Noé Cyr, October 10, 1863 - November 10, 1912) was a Canadian strongman with a career spanning the late 19th and early 20th centuries. His recorded feats, including lifting (1/4 ton) with one finger and backlifting (2 tons), show Cyr to be, according to former International Federation of BodyBuilding and Fitness chairman Ben Weider as stated in 2000, the strongest man ever.


title: Louis Cyr

text: Cyr was born in Saint-Cyprien-de-Napierville, Quebec, Canada. Coming from a French-Acadian family, he began developing his extraordinary strength at an early age. From the age of twelve Cyr worked in a lumber camp during the winters and on the family's farm the rest of the year. Discovering his exceptional strength at a very young age, he impressed his fellow workers with his feats of strength. After learning of the tale, Cyr attempted to mimic the practice of legendary strongman Milo of Croton, who as a child carried a calf on his shoulders, continuing to carry it as it grew into a full-grown bull and he into a grown man. Cyr's calf, however, bolted one day, kicking him in his back, after which he instead began carrying a sack of grain every day, adding each day. According to one of his biographers, his mother decided "He should let his hair grow, like Samson in the Bible". She curled it regularly.


title: Louis Cyr

text: Louis started his strong man career at the age of 17, after some publicity came about due to an incident when the young Louis was reported to have lifted a farmer's heavily laden wagon out of the mire in which it had become stuck. He was matched in a contest against Michaud of Quebec, who was recognized as Canada's strongest man of the time. Cyr beat him in tests of lifting of heavy stones by hoisting a granite boulder weighing .


title: Louis Cyr

text: In 1878 the Cyr family immigrated to Lowell, Massachusetts in the United States. In Lowell, Cyr changed his name from Cyprien-Noé to Louis, as it was easier to pronounce in English. Again his great strength brought him fame. At 17 years old he weighed . He entered his first strongman contest in Boston at age 22, lifting a horse off the ground; the fully grown male horse was placed on a platform with 2 iron bars attached enabling Cyr to obtain a better grip. The horse weighed at least .


title: Louis Cyr

text: In 1882, while working as a logger, Louis married Melina (née Gilbert dit Comtois). The following year he and his wife returned to Lowell, hoping to capitalize on his fame there. A tour of the Maritimes was organized, and while it may have benefited the organizer, Cyr gained no profit financially. He then began touring Quebec with his family in a show they called "The Troupe Cyr".


title: Louis Cyr

text: Soon proving his immense strength, he was urged by friends to enter the exciting, albeit highly precarious world of professional strong men, lifting mainly crude solid or shot-filled weights.


title: Louis Cyr

text: From 1883 to 1885, Cyr served as a police officer in Montreal, Quebec. Following this, he went on tour with a troupe that included a wrestler, a boxer, and a weightlifter. He entered a strongman competition in March 1886, at Quebec City, against the reigning Canadian strongman, David Michaud. Cyr lifted a barbell with one hand (to Michaud's ) and a weight of on his back, to his opponent's to win the title of strongest man in the country.


title: Louis Cyr

text: With little reward at this early foray into professional weightlifting, Louis was forced to seek other employment. Cyr became a police officer after breaking up a knife fight and carrying both participants to the police station.


title: Louis Cyr

text: Prudent with his earnings, Louis left the police force and purchased a tavern/restaurant in St. Cunégonde, where he also featured a gymnasium that became a mecca for strength athletes and fighters. Cyr was well acquainted with John L. Sullivan, being one of the few to defy Sullivan's commands to drink when he drank. Sullivan was known as The Boston Strong Boy and was very powerful, but not in Cyr's class. Cyr, happy in his own environment, beat all comers when challenged to perform.


title: Louis Cyr

text: Cyr's exploits had been well publicized in the 'Pink Un' or Police Gazette published by Richard K. Fox, the proprietor and promoter of other strength athletes, e.g. Travis, Eugen Sandow, etc. Fox offered a side bet of $5,000 to anyone who could beat Cyr at any of his strength feats. Promoted by Fox, Louis went on tour circa 1885–1891 beating, amongst others: Sebastian Miller, Bienkowski, or Cyclops, August Johnson, and Richard Pennell, plus continually challenging, without success, Eugen Sandow, with a genuine diamond studded belt to be awarded to the winner, should such an event ever take place. It never did. Sandow avoided any such challenges throughout his esteemed career after early mistakes, like the time he was beaten by McCann.


title: Louis Cyr

text: There was no doubt that Cyr was an unusual man regarding size and measurements, the latter often causing debate. Although Dr. Dudley A. Sargent, famous Harvard University physical director recorded measuring Cyr in 1895 when Cyr was 32 years old and weighed . Sargent listed Cyr's height as 5'8.5". Other measurements, most on the conservative side as compared to other biographers, were neck – , biceps – , forearms – , wrists – , chest (normal) – , chest expanded – , waist - , hips – , thighs – , knees – 17", and calves - , far short of the quoted 28", but perhaps a possible 23" later when of higher body weight. Ankle and Shoulder width with calipers ... across the deltoids . The above details were just one set of figures relating to Cyr's size, others being recorded by Willoughby when for example Cyr was 47 years old (in 1910) gave him calf 23", neck 22 3/4", biceps 21 1/2". chest normal 59 1/2" and thighs 33" with other parts to match the increase in weight, being at the time a heavier 365 lbs. Ben Weider, who was privileged to access family archives, was even more generous giving arm size , forearms , and calves, the disputed , following a similar line to Jowett.


title: Louis Cyr

text: While several of Cyr's feats of strength may have been exaggerated over the years, some were documented and remain impressive.


title: Louis Cyr

text: Perhaps his greatest feat occurred in 1895, when he was reported to have lifted on his back in Boston by putting 18 men on a platform and lifting them. One of his most memorable displays of strength occurred in Montreal on 12 October 1891. Louis resisted the pull of four draught horses (two in each hand) as grooms stood cracking their whips to get the horses to pull harder, a feat he again demonstrated in Ottawa with Queen Victoria's team of draught horses during her royal visit. While in Ottawa he volunteered with the police when they took deputies to round up a local gang of miscreants; they turned him away claiming he would be too slow due to his bulk. He challenged the regular officers to a foot race, beating the majority, and they took him on.


title: Louis Cyr

text: He patrolled as a police officer between 1883 and 1885 in Sainte-Cunégonde, known now as Petite-Bourgogne (Little Burgundy) in Montreal. Both the Parc Louis-Cyr and the "Place des Hommes-Forts" ("Strongmen's Square") are named after him. Statues of him are located at "Place des Hommes-Forts" and the "Musée de la Civilisation" in Quebec City. The high school in his hometown of Napierville is also named after him.


title: Louis Cyr

text: Through no fault of his own, many of Cyr's lifts, like his measurements, have been exaggerated or misquoted. In particular, his celebrated back lift done in Boston, of 18 men on a platform, is usually generously estimated at 4,300 lb, which allowing for a very heavy platform of at most 500 lb, meant that each man on average would have weighed approximately 211 lb.


title: Louis Cyr

text: Cyr was also credited with side pressing with "one arm" (the right), a lift witnessed by Britain's great champion Tom Pevier, who described it more like a 'Jerk Press.' The dumbbell, a huge thick-handled one, was lifted to the shoulders with two hands, before the single-handed overhead move. Cyr's dumbbells were often so unwieldy that many respectable strongmen were unable to lift them off the floor, let alone lift them overhead.


title: Louis Cyr

text: One particular dumbbell of Cyr's weighed, when empty, . It was the same bell that had defeated a drove of former strength athletes, and it was exchanged by its owner, 280 lb. police chief Joseph Moquin of Quebec (who could and did bent press the weight) for a modern set of York weights. Thus, it came into the possession of the late Bob Hoffman and Mike Dietz. According to "Strength & Health" magazine, Hoffman, after several attempts, was able to bent press it, as did the much lighter 150 lb. Sig Klein. John Grimek later also bent pressed it, half a dozen times or so one afternoon, when the weight was increased to 269.5 lb, by adding, as it happened, the lead type from Mark Berrys' classic tome Physical Training Simplified. Hence the reason the book was never reprinted.


title: Louis Cyr

text: Cyr was a big man in all ways, both heart and size, being a great trencherman, eating more than four normal men. Up to 6 lb of meat at one meal ... a genuine gourmand, increasing weight enormously in his later years. His lightest bodyweight was when he competed against August Johnson, then just 270 lb, although his normal contest condition was nearer 320 lb. Cyr's wife, Melina, by contrast, never weighed more than 100 lb.


title: Louis Cyr

text: In 1886 Cyr met and defeated Richard Pennell, then Pennell being 40, and Louis just 23. In 1888 on 1 October at Berthierville, Quebec, he lifted 3,536 lb/1, 604 kg of pig iron for his first record in the back lift.


title: Louis Cyr

text: On 1 December 1891 at Sohmer Park in Montreal, before some 10,000 people, Cyr resisted the pull of four draught horses, two on each side, despite grooms cracking their whips to encourage the horses to pull harder and strain their haunches.


title: Louis Cyr

text: In January 1892, Cyr embarked in England with partner Horace Barré, arousing much interest and curiosity at his London debut at the Royal Aquarium, with 5,000 people packing the theater to watch Cyr's act and witness his open challenge to the wide world of strongmen, many celebrities of which were in the audience, with a side wager of £1,000 (Equivalent to about £98,070 as of 2015). It was on this historical occasion, on 19 January 1892 that Cyr pressed the pre-mentioned 273.75 lb. dumbbell. Many years later Doc Aumont, son-in-law of Louis, loaned Cyr's famous dumbbell to the Weider's Your Physique office in Montreal for a month, during which time over 500 people tried and failed to lift the weight.


title: Louis Cyr

text: During his first London show, many other feats followed, all exceeding contemporary records, culminating in the famous Backlift. Placing a number of men upon a heavy platform resting across two trestles, Louis ducked beneath the platform, placed his back below the center, and raised both the contraption and the passengers clear off the trestles. Weight on this occasion was estimated at 3,635 lb. Traveling extensively throughout the UK he also visited Scotland, raising and carrying for a distance one of the famed Dinnie Stones. Cyr was very popular in Britain, being feted by celebrities and Royalty alike, including the Prince of Wales and Queen Victoria.


title: Louis Cyr

text: After returning to the U.S.A. on 27 May, Cyr did his best back lift in Boston, with over 4,000 lb estimated, consisting of 18 'bulky' men.


title: Louis Cyr

text: During his most active period, circa 1896, on March 31 he did a clean and jerk (the clean is a misnomer) of 347 lb, then a World record, without science or skill, little if any dipping.


title: Louis Cyr

text: Reputable witness Oscar Mathes said the lift was closer to a straight-legged press. Cyr did a one-handed deadlift with a dumbbell weighing , made harder by the fact that the bar was 1.5 inches thick. On 7 and 8 May 1896, he performed a crucifix with in his right hand, and in his left. Some authors often credit him with holding out with one arm.- . He also dumbbell pressed 162 lb for 36 reps, did a one finger lift, first with 552 lb and the next day made it . Lifted via one hand, style not specified, but most suspect using hand and thigh method, . plus again, using hand and thigh, .


title: Louis Cyr

text: For years Louis pictured himself as a modern Biblical Samson with tresses to match. In the folds of his long hair he would tie three fifty-pound weights, one on each side, and one in the center, with the three weights dangling from his scalp, he would also spin around, swirling the weights around his head. By co-incidence on his visit to Britain, the top of the pops was a ditty entitled 'Get Your Hair Cut'...Louis must have taken the hint, as afterwards he always sported short hair.


title: Louis Cyr

text: More power of the arm and shoulder was demonstrated by his stunt of stacking four fifty pound weights one on top of the other on his half flexed arm, balancing them whilst walking across the room.


title: Louis Cyr

text: Cyr learned boxing and wrestling for a match. While in Montréal, Que., 25 March 1901, Louis Cyr wrestled Édouard Beaupré, who was known as a giant man. Cyr's height was measured at and he weighed . Beaupré's height was measured at and he weighed . Cyr won.


title: Louis Cyr

text: By 1904 Cyr's health began to fail due to excessive eating and inactivity. At the time, he weighed . He slimmed down as best he could for his last contest of strength, with Hector De Carrie. Cyr retained his title and retired unvanquished.


title: Louis Cyr

text: Cyr died on November 10, 1912, in Montreal, of chronic nephritis and was interred at St-Jean-De-Matha. Great homage was paid by all of Canada, with immense crowds attending the funeral and floral tributes coming from all over the world.


title: Louis Cyr

text: He was portrayed by Antoine Bertrand in the 2013 biographical film "Louis Cyr, l'homme le plus fort du monde".


title: Sherbrooke

text: Sherbrooke ( ; ) is a city in southern Quebec, Canada. It is at the confluence of the Saint-François and Magog rivers in the heart of the Estrie administrative region. Sherbrooke is also the name of a territory equivalent to a regional county municipality (TE) and census division (CD) of Quebec, coextensive with the city of Sherbrooke. With 172,950 residents at the Canada 2021 Census, It is the sixth largest city in the province and the 30th largest in Canada. The Sherbrooke Census Metropolitan Area had 227,398 inhabitants, making it the fourth largest metropolitan area in Quebec and 19th in Canada.


title: Sherbrooke

text: Sherbrooke is the primary economic, political, cultural and institutional centre of Estrie, and was known as the "Queen of the Eastern Townships" at the beginning of the 20th century.


title: Sherbrooke

text: There are eight institutions educating 40,000 students and employing 11,000 people, 3,700 of whom are professors, teachers and researchers. The direct economic impact of these institutions exceeds 1 billion dollars. The proportion of university students is 10.32 students per 100 inhabitants, giving Sherbrooke the largest concentration of students in Quebec.


title: Sherbrooke

text: The Sherbrooke region is surrounded by mountains, rivers and lakes. There are several ski hills nearby and various tourist attractions in regional flavour. Mont-Bellevue Park, a large park in the city, is used for downhill skiing.


title: Sherbrooke

text: First Nations settled the region 8,000-3,000 years ago. The Abenaki called it "Ktinékétolékouac/Kchi Nikitawtegwak" (The Large Forks), or "Shacewanteku" (where one smokes).


title: Sherbrooke

text: The first settler was the farmer Jean-Baptiste Nolain, in 1779. The area was first surveyed in 1792. Americans from Vermont built mills in the area in 1802. Gilbert Hyatt led a group of loyalists, who settled around 1803. He dammed the Magog River and a gristmill and a sawmill were soon built nearby. The settlement was then known as Hyatt's Mills. The first immigrants from England arrived in 1815.


title: Sherbrooke

text: The British American Land Company was formed in 1832 to acquire and develop almost of Crown land and other lands in the area. It prioritized speculation over immigration.


title: Sherbrooke

text: In 1852 a railway linked Montreal and Portland, Maine via Sherbrooke. By the 1890s there were rail connections to Boston, Halifax, and New York City.


title: Sherbrooke

text: By the turn of the 20th century, Sherbrooke was a thriving industrial city, with manufacturing benefiting from locally-produced hydroelectricity. From the 1950s, some the steel and textile industries declined, giving way to government services and education.


title: Sherbrooke

text: As part of the 2000–2006 municipal reorganization in Quebec, the city grew considerably on 1 January 2002, with the amalgamation of Sherbrooke, Ascot, Bromptonville, Deauville, Fleurimont, Lennoxville, Rock Forest, and Saint-Élie-d'Orford. Part of Stoke was also annexed to the newly expanded Sherbrooke.


title: Sherbrooke

text: In 2012, a local Vitamin production factory suffered an explosion, which killed 2, and injured 19, some severely. A large toxic cloud enveloped part of the city, raising health concerns.


title: Sherbrooke

text: Located at the confluence of the Saint-François (St. Francis) and Magog rivers in the heart of the Eastern Townships and the administrative region. Sherbrooke is also the name of a territory equivalent to a regional county municipality (TE) and census division (CD) of Quebec, coextensive with the city of Sherbrooke. Its geographical code is 43.


title: Sherbrooke

text: Sherbrooke has a humid continental climate (Köppen "Dfb"), with long, cold, and snowy winters, warm summers, and short but crisp springs and autumns. Highs range from in January to in July. In an average year, there are 34 nights at or colder than , and 6.5 nights at or colder than ; 4.1 days will see highs reaching . Annual snowfall is large, averaging at , sometimes falling in May and October. Precipitation is not sparse any time of the year, but is the greatest in summer and fall and at its least from January to April, totalling annually.


title: Sherbrooke

text: The highest temperature ever recorded in Sherbrooke was on 1 & 2 July 1931. The coldest temperature ever recorded was on 15 January 2004.


title: Sherbrooke

text: In the 2021 Census of Population conducted by Statistics Canada, Sherbrooke had a population of living in of its total private dwellings, a change of from its 2016 population of . With a land area of , it had a population density of in 2021.


title: Sherbrooke

text: 86.4% of Sherbrooke residents spoke French as a first language in 2021, while those whose mother tongue was English accounted for 3.9%. The next most common first languages were Spanish (2%), Arabic (1.3%) and Dari (0.7%)


title: Sherbrooke

text: As of 2021, approximately 88.7% of Sherbrooke residents were white, while 9.6% were visible minorities and 1.7% were aboriginal. The largest visible minority groups in Sherbrooke were Black (3.1%), Latin American (2%), Arab (1.7%), and West Asian (1%).


title: Sherbrooke

text: The Census Metropolitan Area (CMA) comprises the cities of Sherbrooke, Magog and Waterville, the municipalities of Ascot Corner, Compton, Saint-Denis-de-Brompton, Stoke and Val-Joli; the township municipalities of Hatley and Orford; and the village municipality of North Hatley. The population in 2021 was 227,398. The median age was 43.


title: Sherbrooke

text: Approximately 90.5% of the greater Sherbrooke area residents were white, while 7.7% were visible minorities and 1.8% were Aboriginal.


title: Sherbrooke

text: French was mother tongue to 87.3% of residents. The next most common mother tongues were English (4.5%), Spanish (1.6%), Arabic (1.0%) Dari (0.5%), Mandarin (0.2%), Portugese (0.2%) and Serbian (0.2%).


title: Sherbrooke

text: About 55.7% of the population identified as Catholic in 2021 while 32.2% said they had no religious affiliation, 2.9% were Muslim, 0.5% Anglican, 0.5% Eastern Orthodox, 0.4% Jehovah's Witness and 0.4% Baptist. United Church and Pentecostals made up 0.3% of the population each while buddhist made 0.2%.


title: Sherbrooke

text: Sherbrooke, which is the economic centre of Estrie, is a significant cultural, industrial, and academic hub in the province. The city is directly served by two railways: the St. Lawrence and Atlantic Railroad and the Canadian Pacific Railway. Sherbrooke is also served by four highways as well as the regional airport named Sherbrooke Airport but located in the nearby city of Cookshire-Eaton. Sherbrooke Airport no longer offers scheduled passenger services as of March 2010.


title: Sherbrooke

text: According to data from the "Institut de la statistique du Québec", average personal income per capita in the Census Metropolitan Area (CMA) of Sherbrooke amounted to in 2010. Estrie's GDP for the same year was $.


title: Sherbrooke

text: As of 2010, the largest employers in Sherbrooke are Université de Sherbrooke (6,000 employees), Centre hospitalier universitaire de Sherbrooke (5,511), Commission scolaire de la Région-de-Sherbrooke (3,050), Centre de santé et de services sociaux – Institut universitaire de gériatrie de Sherbrooke (2,650), City of Sherbrooke (1,913), Desjardins Group (1,713), Cégep de Sherbrooke (800), Centre Jeunesse de l'Estrie (527), Nordia Inc. (500), Canada Post (497), Kruger Inc. - Publication papers business unit (455), Bishop's University (450) and McDonald's (400). These include enterprises operating in Sherbrooke only and having 400 or more employees.


title: Sherbrooke

text: In the summer season, several festivals, concerts, and events are held in the city, such as the "Fête du Lac des Nations", "Sherblues & Folk", and the "Festival des traditions du monde". Come winter, the city hosts the "Carnaval de Sherbrooke".


title: Sherbrooke

text: Sherbrooke has the fourth largest theatre in Quebec, the Maurice O'Bready University Cultural Centre of Sherbrooke (Salle Maurice-O’bready du centre culturel de l’Université de Sherbrooke). Music, theatre, and dance shows are staged there. The Centennial Theatre of Bishop's University also hosts music and dance concerts from around the world. The Vieux Clocher, owned by the Université de Sherbrooke, has two stages, the primary being used by various music groups and comedians from around the province. The "Théâtre Granada", designated as a historical site by the Canadian government, holds music concerts. It has retained its original architecture since its opening. The "Petit Théâtre de Sherbrooke", located downtown, presents musicals and plays for children.


title: Sherbrooke

text: Since 2007, the "Centre des arts de la scène Jean-Besré" (CASJB), built by the city with the support of the Ministry of Culture and Communications, has assisted in the creation and production of material for the region's artistic community. It serves as the location for training theatre, music, and dance professionals. It contains three rehearsal studios, a production room, a decoration workshop, and a costume workshop, as well as administrative offices for each of its resident companies.


title: Sherbrooke

text: The Sherbrooke Expos of the Ligue de Baseball Majeur du Québec, an amateur baseball league, play their home games at Amedée Roy Stadium.


title: Sherbrooke

text: The city also hosted some games of the 2002 World Junior Baseball Championship, and the 2013 Canada Games.


title: Sherbrooke

text: Historically, several professional teams based in Sherbrooke competed in Minor League Baseball or in independent baseball leagues:


title: Sherbrooke

text: Under the 2000–2006 municipal reorganization in Quebec, Sherbrooke merged with most of the suburban municipalities in the surrounding area: Rock Forest, Saint-Élie-d'Orford, Deauville, Fleurimont, Bromptonville, Ascot, and Lennoxville. This resulted in the creation of six Boroughs of Sherbrooke: Brompton, Fleurimont, Lennoxville, Mont-Bellevue, Rock Forest–Saint-Élie–Deauville, and Jacques-Cartier. Each of the boroughs is subdivided into electoral districts, with the number varying based on population. For example, there are only two districts in Brompton, which only has 6,314 inhabitants, whereas Fleurimont (pop. 40,824) has five. Sherbrooke has 21 districts total, for which the average population is 7,200 inhabitants.


title: Sherbrooke

text: Sherbrooke is split into the federal electoral districts of Sherbrooke, represented by Élisabeth Brière of the Liberal party of Canada and Compton—Stanstead, represented by Marie-Claude Bibeau of the Liberals.


title: Sherbrooke

text: Provincially, Sherbrooke is divided into three electoral districts. Sherbrooke is represented by Christine Labrie of the Québec solidaire (QS), Saint-François is represented by Guy Hardy of the PLQ and Richmond is represented by Karine Vallières of the PLQ.


title: Sherbrooke

text: Sherbrooke does not host any units from the Regular Force with the exception of a recruiting centre, but four Primary Reserve units are stationed in the city:


title: Sherbrooke

text: A Canadian military artifact is preserved at the William Street Armoury, the Sherman tank "Bomb" which helped liberate Europe fighting with the Sherbrooke Fusilier Regiment and is the only Canadian tank to have landed on the Normandy beach on D-Day and fought through to VE Day without being knocked out.


title: Sherbrooke

text: Transdev Limocar provides bus service to Montreal via Granby and Magog. Formerly, Autobus Jordez linked Sherbrooke to Drummondville and Trois-Rivières, and also to Victoriaville and Quebec City, but since the company lost their licence to operate heavy vehicles, they have sold their licence to Autobus La Québécoise, who now provide the service.


title: Sherbrooke

text: Société de transport de Sherbrooke (STS) provides bus service within the city. It operates 17 bus routes, 11 minibus routes, and 5 taxibus routes.


title: Sherbrooke

text: The city is located at the eastern terminus of A-10, and directly on the Autoroute Trans-Québécoise (A-55). A-10 provides a direct freeway connection to Montreal and points west, while A-55 connects directly to Trois-Rivières, Shawinigan, and points north, as well as to Interstate 91 to the south (Vermont). A-410 and A-610 are the southern and northern bypass roads, respectively.


title: Sherbrooke

text: The last passenger train for the city was VIA Rail's Montreal – Saint John, New Brunswick "Atlantic", which ended service in 1994. There have been recent proposals to provide rail service from Montreal to Boston with a stop in Sherbrooke.


title: Sherbrooke

text: Sherbrooke Airport, in Cookshire-Eaton is just east of the city. There are currently no scheduled flights operating out of the airport.


title: Sherbrooke

text: The suburban Sherbrooke University Hospital ("CHUS" or "Centre Hospitalier Universitaire de Sherbooke) has over 5,200 employees, including 550 doctors. It includes a clinical research facility, the Étienne-Lebel Research Centre.


title: Sherbrooke

text: Sherbrooke has eight institutions that make up the Sherbrooke University Pole, which educates some 40,000 students and employs about 11,000 persons. University students comprise 10.32% of the population, the highest concentration in Quebec.


title: Sherbrooke

text: The city is the location of one French-language university, the Université de Sherbrooke, and an English-language university, Bishop's University. Université de Sherbrooke is a comprehensive university with schools of medicine and law and extensive graduate programs. Bishop's University is smaller and predominantly undergraduate. There are three CEGEPs in Sherbrooke, two of them French-language, the Cégep de Sherbrooke and the Séminaire de Sherbrooke, and one English-language, Champlain College Lennoxville. CCSQ and CDE College which currently enrols International Students. In the past over 100 International students have graduated and landed jobs in Sherbrooke City itself, making it an attraction to the Indian student division. There currently over 100 South Asians residing in the City of Sherbrooke which consists of Hindu, Punjabi and Gujrati ethnic background.


title: Sherbrooke

text: There are also public high school boards such as the English Eastern Townships School Board, French Commission scolaire de la Région-de-Sherbrooke and private high schools such as Séminaire de Sherbrooke founded in 1875, Bishop's College School founded in 1836, etc.


title: Matthew Wilder

text: Matthew Wilder ( Weiner; January 24, 1953) is an American musician, singer, songwriter and record producer. In early 1984, his single "Break My Stride" hit No. 2 on the "Cash Box" chart and No. 5 on the "Billboard" Hot 100. He also wrote the music for the Disney animated feature film "Mulan" and provided the singing voice for the character Ling.


title: Matthew Wilder

text: Wilder was one-half of the Greenwich Village folk rock group Matthew & Peter in the 1970s. In 1978, he moved to Los Angeles, and sang for television commercials and as a backing vocalist for Rickie Lee Jones and Bette Midler.


title: Matthew Wilder

text: Wilder's debut album, "I Don't Speak the Language" (1983), reached No. 49 on the "Billboard" 200, fueled by "Break My Stride". Wilder had some continued success with the single "The Kid's American", which reached No. 33 in 1984, but the single failed to match the success of "Break My Stride". Wilder's second album, "Bouncin' Off the Walls" (1984), failed to gain much momentum — even with an innovative music video for the single "Bouncin' Off the Walls" — with only the title track making the charts (No. 52), and was subsequently deemed a commercial failure.


title: Matthew Wilder

text: Despite the downturn in his solo career, Wilder continued his career in the music industry as a songwriter and as a record producer for such acts as No Doubt (the hit album "Tragic Kingdom"), 702, Christina Aguilera, Kelly Clarkson, Miley Cyrus on her "Hannah Montana" song "G.N.O. (Girls Night Out)", The Belle Brigade, King Charles, and Joanna Pacitti. He has also done production work on Australian singer-songwriter Mig Ayesa's self-titled album released in April 2007 and has helped with production on Hayden Panettiere's unreleased album.


title: Matthew Wilder

text: For the Disney film "Mulan", Wilder wrote the songs and co-wrote the score with composer Jerry Goldsmith. Wilder also lent his singing voice to the character of Ling. He won an Annie Award nomination for Music in an Animated Feature Production, and was nominated for an Academy Award for Best Original Musical or Comedy Score (along with David Zippel and Jerry Goldsmith) for his work on that film.


title: Matthew Wilder

text: For theatre, Wilder once again paired with Zippel to provide the music and lyrics for "Princesses", a musical comedy update of Frances Hodgson Burnett's novel "A Little Princess". The production ran at the 5th Avenue Theatre in Seattle in 2003.


title: Type theory

text: In mathematics, logic, and computer science, a type theory is the formal presentation of a specific type system, and in general type theory is the academic study of type systems. Some type theories serve as alternatives to set theory as a foundation of mathematics. Two influential type theories that were proposed as foundations are Alonzo Church's typed λ-calculus and Per Martin-Löf's intuitionistic type theory. Most computerized proof-writing systems use a type theory for their foundation. A common one is Thierry Coquand's Calculus of Inductive Constructions.


title: Type theory

text: Type theory was created to avoid a paradox in a mathematical foundation based on naive set theory and formal logic. Russell's paradox, which was discovered by Bertrand Russell, existed because a set could be defined using "all possible sets", which included itself. Between 1902 and 1908, Bertrand Russell proposed various "theories of type" to fix the problem. By 1908 Russell arrived at a "ramified" theory of types together with an "axiom of reducibility" both of which featured prominently in Whitehead and Russell's "Principia Mathematica" published between 1910 and 1913. This system avoided Russell's paradox by creating a hierarchy of types and then assigning each concrete mathematical entity to a type. Entities of a given type are built exclusively of subtypes of that type, thus preventing an entity from being defined using itself. Russell's theory of types ruled out the possibility of a set being a member of itself.


title: Type theory

text: Types were not always used in logic. There were other techniques to avoid Russell's paradox. Types did gain a hold when used with one particular logic, Alonzo Church's lambda calculus.


title: Type theory

text: The most famous early example is Church's simply typed lambda calculus. Church's theory of types helped the formal system avoid the Kleene–Rosser paradox that afflicted the original untyped lambda calculus. Church demonstrated that it could serve as a foundation of mathematics and it was referred to as a higher-order logic.


title: Type theory

text: The phrase "type theory" now generally refers to a typed system based around lambda calculus. One influential system is Per Martin-Löf's intuitionistic type theory, which was proposed as a foundation for constructive mathematics. Another is Thierry Coquand's calculus of constructions, which is used as the foundation by Coq, Lean, and other "proof assistants" (computerized proof writing programs). Type theories are an area of active research, as demonstrated by homotopy type theory.


title: Type theory

text: There are many type theories, which makes it difficult to produce a comprehensive taxonomy; this article is not an exhaustive categorization. What follows is an introduction for those unfamiliar with type theory, covering some of the major approaches.


title: Type theory

text: In type theory, every term has a type. A term and its type are often written together as ""term" : "type"". A common type to include in a type theory is the Natural numbers, often written as "formula_1" or "nat". Another is Boolean logic values. So, some very simple terms with their types are:


title: Type theory

text: Terms can be built out of other terms using function calls. In type theory, a function call is called "function application". Function application takes a term of a given type and results in a term of another given type. Function application is written ""function" "argument" "argument" ...", instead of the conventional ""function"("argument","argument", ...)". For natural numbers, it is possible to define a function called "add" that takes two natural numbers. Thus, some more terms with their types are:


title: Type theory

text: In the last term, parentheses were added to indicate the order of operations. Technically, most type theories require the parentheses to be present for every operation, but, in practice, they are not written and authors assume readers can use precedence and associativity to know where they are. For similar ease, it is a common notation to write "formula_2" instead of "add formula_3 formula_4". So, the above terms might be rewritten as:


title: Type theory

text: Terms may also contain variables. Variables always have a type. So, assuming "x" and "y" are variables of type "nat", the following are also valid terms:


title: Type theory

text: There are more types than "nat" and "bool". We have already seen the term "add", which is not a "nat", but a function that, when applied to two "nat"s, computes to a "nat". The type of "add" will be covered later. First, we need to describe "computes to".


title: Type theory

text: but they all compute to the term "5 : nat". In type theory, we use the words "reduction" and "reduce" to refer to computation. So, we say "0 + 5 : nat" reduces to "5 : nat". It can be written "0 + 5 : nat formula_5 5 : nat". The computation is mechanical, accomplished by rewriting the term's syntax.


title: Type theory

text: Terms that contain variables can be reduced too. So the term "x + (1 + 4) : nat" reduces to "x + 5 : nat". (We can reduce any sub-term within a term, thanks to the Church-Rosser theorem.)


title: Type theory

text: A term without any variables that cannot be reduced further is a "canonical term". All the terms above reduce to "5 : nat", which is a canonical term. The canonical terms of the natural numbers are:


title: Type theory

text: Obviously, terms that compute to the same term are equal. So, assuming "x : nat", the terms "x + (1 + 4) : nat" and "x + (4 + 1) : nat" are equal because they both reduce to "x + 5 : nat". When two terms are equal, they can be substituted for each other. Equality is a complex topic in type theory and there are many kinds of equality. This kind of equality, where two terms compute to the same term, is called "judgemental equality".


title: Type theory

text: A lambda term looks like "(λ "variablename" : "type1" . "term")" and has type ""type1" formula_6 "type2"". The type ""type1" formula_6 "type2"" indicates that the lambda term is a function that takes a parameter of type ""type1"" and computes to a term of type ""type2"". The term inside the lambda term must be a value of ""type2"", assuming the variable has type ""type1"".


title: Type theory

text: The variable name is "x" and the variable has type "nat". The term "(add x x)" has type "nat", assuming "x : nat". Thus, the lambda term has type "nat formula_6 nat", which means if it is given a "nat" as an argument, it will compute to a "nat". Reduction (a.k.a. computation) is defined for lambda terms. When the function is applied (a.k.a. called), the argument is substituted for the parameter.


title: Type theory

text: Earlier, we saw that function application is written by putting the parameter after the function term. So, if we want to call the above function with the parameter "5" of type "nat", we write:


title: Type theory

text: The lambda term was type "nat formula_6 nat", which meant that given a "nat" as an argument, it will produce a term of type "nat". Since we have given it the argument "5", the above term has type "nat". Reduction works by substituting the argument "5" for the parameter "x" in the term "(add x x)", so the term computes to:


title: Type theory

text: A lambda term is often called an "anonymous function" because it has no name. Often, to make things easier to read, a name is given to a lambda term. This is merely a notation and has no mathematical meaning. Some authors call it "notational equality". A name might be given to the function above using the notation:


title: Type theory

text: Dependent typing is when the type returned by a function depends on the value of its argument. For example, when a type theory has a rule that defines the type "bool", it also defines the function "if". The function "if" takes 3 arguments and "if true b c" computes to "b" and "if false b c" computes to "c". But what is the type of "if a b c"?


title: Type theory

text: If "b" and "c" have the same type, it is obvious: "if a b c" has the same type as "b" and "c". Thus, assuming "a : bool",


title: Type theory

text: But if "b" and "c" have different types, then the type of "if a b c" depends on the value of "a". We use the symbol "Π" to indicate a function that takes an argument and returns a type. Assuming we have some types "B" and C" and "a : bool", "b : B" and "c : C", then


title: Type theory

text: That is, the type of the "if" term is either the type of the second or third argument, depending on the value of the first argument. In actuality, "if a B C" isn't defined using "if", but that gets into details too complicated for this introduction.


title: Type theory

text: Because the type can contain computation, dependent typing is amazingly powerful. When mathematicians say "there exists a number formula_3 such that formula_3 is prime" or "there exists a number formula_3 such that property formula_17 holds", it can be expressed as a dependent type. That is, the property is proven for the specific "formula_3" and that is visible in the type of the result.


title: Type theory

text: There are many details to dependent typing. They are too long and complicated for this introduction. See the article on dependent typing and the lambda cube for more information.


title: Type theory

text: Π-terms return a type. So what is the type of their return value? Well, there must be a type that contains types. A type that contains other types is called a "universe". It is often written with the symbol formula_19. Sometimes there is a hierarchy of universes, with "formula_20 : formula_21", "formula_21 : formula_23", etc..


title: Type theory

text: Type theories are defined by their rules of inference. There are rules for a "functional core", described above, and rules that create types and terms. Below is a non-exhaustive list of common types and their associated terms.


title: Type theory

text: The list ends with "inductive types", which is a powerful technique that is able to construct all the other ones in the list. The mathematical foundations used by the proof assistants "Coq" and "Lean" are based on the "Calculus for Inductive Constructions" which is the "Calculus of Constructions" (its "functional core") with inductive types.


title: Type theory

text: It is used to show that something is uncomputable. If for a type "A", you can create a function of type "A formula_26", you know that "A" has no terms. An example for the type "A" might be "there exists a number formula_3 such that both formula_3 is even and formula_3 is odd". (See "Product Type" below for how the example "A" is constructed.) When a type has no terms, we say it is "uninhabited".


title: Type theory

text: The unit type has exactly 1 canonical term. The type is written "formula_30" or "formula_31" and the single canonical term is written "*".


title: Type theory

text: The unit type is used to show that something exists or is computable. If for a type "A", you can create a function of type "formula_32 A", you know that "A" has one or more terms. When a type has at least 1 term, we say it is "inhabited".


title: Type theory

text: The Boolean type has exactly 2 canonical terms. The type is usually written "bool" or "formula_33" or "formula_34". The canonical terms are usually "true" and "false".


title: Type theory

text: The product type has terms that are ordered pairs. For types "A" and "B", the product type is written "A formula_37 B". Canonical terms are created by the constructor function "pair". The terms are "pair a b", where "a" is a term of type "A" and "b" is a term of type "B". The product type is defined with eliminator functions "first" and "second" such that:


title: Type theory

text: Besides ordered pairs, this type is used for the logical operator "and", because it holds an "A" and a "B". It is also used for intersection, because it holds one of both types.


title: Type theory

text: If a type theory has dependent typing, it has dependent pairs. In a dependent pair, the second type depends on the value of the first term. Thus, the type is written "formula_40 a:A . B(a)" where "B" has type "A formula_6 U". It is useful when showing existence of an "a" with property "B(a)".


title: Type theory

text: The sum type is a "tagged union". That is, for types "A" and "B", the type "A + B" holds either a term of type "A" or a term of type "B" and it knows which one it holds. The type comes with the constructors "injectionLeft" and "injectionRight". The call "injectionLeft a" takes "a : A" and returns a canonical term of type "A + B". Similarly, injectionRight b" takes "b : B" and returns a canonical term of type "A + B". The type is defined with an eliminator function "match" such that for a type "C" and functions "f : A formula_6 C" and "g : B formula_6 C":


title: Type theory

text: The natural numbers are usually implemented in the style of Peano Arithmetic. There is a canonical term, "0 : nat" for zero. Canonical values larger than zero use the constructor function "S : nat formula_6 nat". Thus, "S 0" is one. "S (S 0)" is two. "S (S (S 0)))" is three. Etc. The decimal numbers are just notationally equal to those terms.


title: Type theory

text: The natural numbers are defined with an eliminator function "R" that uses recursion to define a function for all nats. It takes a function "P : nat formula_6 U" which is the type of the function to define. It also takes a term "PZ : P 0" which is the value at zero and a function "PS : P n formula_6 P (S n)" which says how to transform the value at "n" into the value at "n + 1". Thus, its computation rules are:


title: Type theory

text: The identity type is the third concept of equality in type theory. The first is "notational equality", which is for definitions like "2 : nat ::= (S (S 0))" that have no mathematical meaning but are useful to readers. The second is "judgemental equality", which is when two terms compute to the same term, like "x + (1 + 4)" and "x + (4 + 1)", which both compute to "x + 5". But type theory needs another form of equality, known as the "identity type" or "propositional equality".


title: Type theory

text: The reason it needs the identity type is because some equal terms do not compute to the same term. Assuming "x : nat", the terms "x + 1" and "1 + x" do not compute to the same term. Recall that "+" is a notation for the function "add", which is a notation for the function "R". We cannot compute on "R" until the value for "x" is specified and, until it is specified, two different calls to "R" will not compute to the same term.


title: Type theory

text: An identity type requires two terms "a" and "b" of the same type and is written "a = b". So, for "x + 1" and "1 + x", the type would be "x+1 = 1+x". Canonical terms are created with the constructor "reflexivity". The call "reflexivity a" takes a term "a" and returns a canonical term of the type "a = a".


title: Type theory

text: Computation with the identity type is done with the eliminator function "J". The function "J" lets a term dependent on "a", "b", and a term of type "a = b" to be rewritten so that "b" is replaced by "a". While "J" is one directional, only able to substitute "b" with "a", it can be proven that the identity type is reflexive, symmetric and transitive.


title: Type theory

text: If the canonical terms are always "a=a" and "x+1" does not compute to the same term as "1+x", how do we create a term of "x+1 = 1+x"? We use the "R" function. (See "Natural Numbers" above.) The "R" function's argument "P" is defined to be "(λ x:nat . x+1 = 1+x)". The other arguments act like the parts of an induction proof, where "PZ : P 0" becomes the base case "0+1 = 1+0" and "PS : P n formula_6 P (S n)" becomes the inductive case. Essentially, this says that when "x+1 = 1+x" has "x" replaced with a canonical value, the expression will be the same as "reflexivity (x+1)". This application of the function "R" has type "x : nat formula_6 x+1 = 1+x". We can use it and the function "J" to substituted "1+x" for "x+1" in any term. In this way, the identity type is able to capture equalities that are not possible with judgemental equality.


title: Type theory

text: To be clear, it is possible to create the type "0 = 1", but there will not be a way to create terms of that type. Without a term of type "0 = 1", it will not be possible to use the function "J" to substitute "0" for "1" in another term.


title: Type theory

text: The complexities of equality in type theory make it an active research area, see homotopy type theory.


title: Type theory

text: Inductive types is a way to create a large variety of types. In fact, all the types described above and more can be defined using the rules of inductive types. Once the type's constructors are specified, the eliminator functions and computation is determined by structural recursion.


title: Type theory

text: There are similar, more powerful ways to create types. These include induction-recursion and induction-induction. There is also a way to create similar types using only lambda terms, called Scott encoding.


title: Type theory

text: The traditional foundation for mathematics has been set theory paired with a logic. The most common one cited is Zermelo–Fraenkel set theory, known as "ZF" or, with the Axiom of choice, "ZFC". Type theories differ from this foundation in a number of ways.


title: Type theory

text: Proponents of type theory will also point out its connection to constructive mathematics through the BHK interpretation, its connected to logic by the Curry–Howard isomorphism, and its connections to Category theory.


title: Type theory

text: A type theory is a mathematical logic. It is a collection of rules of inference that result in judgements. Most logics have judgements meaning "The term formula_3 is true." or "The term formula_3 is a well-formed formula.". A type theory has additional judgements that define types and relate terms to types.


title: Type theory

text: A term in logic is recursively defined as a constant symbol, variable, or a function application, where a term is applied to another term. Some constant symbols will be "0" of the natural numbers, "true" of the Booleans, and functions like "S" and "if". Thus some terms are "0", "(S 0)", "(S (S x))", and "if true 0 (S 0)".


title: Type theory

text: The judgements can be made under an assumption. Thus, we might say, "assuming formula_3 is a term of type "bool" and formula_4 is a term of type "nat" , (if x y y) is a term of type "nat"". The mathematical notation for assumptions is a comma-separate list of ""term" : "type"" that precede the turnstile symbol 'formula_73'. Thus, the example statement is formally written:


title: Type theory

text: The list of assumptions is called the "context". It is very common to see the symbol 'formula_77' used to represent some or all of the assumptions. Thus, the formal notation for the 4 different judgements is usually:


title: Type theory

text: The judgements enforce that every term has a type. The type will restrict which rules can be applied to a term.


title: Type theory

text: A type theory's rules say what judgements can be made, based on the existence of other judgements. The rules are expressed using a horizontal line, with the required input judgements above the line and the resulting judgement below the line. The rule for creating a lambda term is:


title: Type theory

text: The judgements required to create the lambda term go above the line. In this case, only one judgement is required. It is that there is some term "b" of some type "B", assuming there is some term "a" of some type "A" and some other assumptions "formula_77". (Note: "formula_77" "a", "A", "b", and "B" are all metavariables in the rule.) The resulting judgement goes below the line. This rule's resulting judgement states that the new lambda term has type "A formula_6 B" under the other assumptions formula_77.


title: Type theory

text: The rules are syntactic and work by rewriting. Thus, the metavariables like "formula_77", "a", "A", etc. may actually consist of complex terms that contain many function applications, not just single symbols.


title: Type theory

text: To generate a particular judgement in type theory, there must be a rule to generate it. Then, there must be rules to generate all of that rule's required inputs. And then rules for all the inputs for those rules. The applied rules form a proof tree. This is usually drawn Gentzen-style, where the target judgement (root) is at the bottom and rules that do not require any inputs (leaves) at the top. (See Natural deduction#Proofs_and_type_theory.) An example of a rule that does not require any inputs is one that states there is a term "0" of type "nat":


title: Type theory

text: Computation takes place by repeated application of rules. Many type theories are strongly normalizing, which means that any order of applying the rules will always end in the same result. However, some are not. In a normalizing type theory, the one-directional computation rules are called "reduction rules" and applying the rules "reduces" the term. If a rule is not one-directional, it is called a "conversion rule".


title: Type theory

text: Some combinations of types are equivalent to other combinations of types. When functions are considered "exponentiation", the combinations of types can be written similar to algebraic identities. Thus, formula_85, formula_86, formula_87, formula_88, formula_89.


title: Type theory

text: Most type theories do not have axioms. This is because a type theory is defined by its rules of inference. (See "Rules" above). This is a source of confusion for people familiar with Set Theory, where a theory is defined by both the rules of inference for a logic (such as first-order logic) and axioms about sets.


title: Type theory

text: Sometimes, a type theory will add a few axioms. An axiom is a judgement that is accepted without a derivation using the rules of inference. They are often added to ensure properties that cannot be added cleanly through the rules.


title: Type theory

text: Axioms can cause problems if they introduce terms without a way to compute on those terms. That is, axioms can interfere with the normalizing property of the type theory.


title: Type theory

text: The Axiom of Choice does not need to be added to type theory, because in most type theories it can be derived from the rules of inference. This is because of the constructive nature of type theory, where proving that a value exists requires a method to compute the value. The Axiom of Choice is less powerful in type theory than most set theories, because type theory's functions must be computable and, being syntax-driven, the number of terms in a type must be countable. (See .)


title: Type theory

text: Girard's paradox shows that type inhabitation is strongly related to the consistency of a type system with Curry–Howard correspondence. To be sound, such a system must have uninhabited types.


title: Type theory

text: The opposition of terms and types can also be views as one of "implementation" and "specification". By program synthesis (the computational counterpart of) type inhabitation (see below) can be used to construct (all or parts of) programs from specification given in form of type information.


title: Type theory

text: Many programs that work with type theory (e.g., interactive theorem provers) also do type inferencing. It lets them select the rules that the user intends, with fewer actions by the user.


title: Type theory

text: Homotopy type theory differs from intuitionistic type theory mostly by its handling of the equality type. In 2016 cubical type theory was proposed, which is a homotopy type theory with normalization.


title: Type theory

text: Type theory has connections to other areas of mathematics. Proponents of type theory as a foundation often mention these connections as justification for its use.


title: Type theory

text: When used as a foundation, certain types are interpreted as propositions (statements that can be proven) and a term of the type is a proof of that proposition. Thus, the type "Π x:nat . x+1=1+x" represents that, for any "x" of type "nat", "x+1" and "1+x" are equal. And a term of that type represents its proof.


title: Type theory

text: The Curry–Howard correspondence is the observed similarity between logics and programming languages. The implication in logic, "A formula_6 B" resembles a function from type "A" to type "B". For a variety of logics, the rules are a similar to expression in a programming language's types. The similarity goes farther, as applications of the rules resemble programs in the programming languages. Thus, the correspondence is often summarized as "proofs as programs".


title: Type theory

text: When some types are interpreted as propositions, there is a set of common types that can be used to connect them to make a logic out of types. However, that logic is not classical logic but intuitionistic logic. That is, it does not have the law of excluded middle nor double negation.


title: Type theory

text: There is a natural relation of types to logical propositions. If "A" is a type representing a proposition, being able to create a function of type "formula_97 A" indicates that A has a proof and being able to create the function "A formula_26" indicates that A does not have a proof. That is, inhabitable types are proven and uninhabitable types are disproven.


title: Type theory

text: "WARNING: This interpretation can lead to a lot of confusion. A type theory may have "terms" "true" and "false" of type "bool", which act like a Boolean logic, and at the same time have "types" formula_30 and formula_24 to represent "true" (provable) and "false" (disproven), as part of a intuitionistic logic for proposition."


title: Type theory

text: But under this interpretation, there is no law of excluded middle. That is, there is no term of type Π A . A + (A formula_26).


title: Type theory

text: Likewise, there is no double negation. There is no term of type Π A . ((A formula_26) formula_26) formula_104 A. (Note: Intuitionistic logic does allow formula_105 and there is a term of type (((A formula_26) formula_26) formula_26) formula_104 (A formula_26).)


title: Type theory

text: Thus, the logic-of-types is an intuitionistic logic. Type theory is often cited as an implementation of the Brouwer–Heyting–Kolmogorov interpretation.


title: Type theory

text: It is possible to include the law of excluded middle and double negation into a type theory, by rule or assumption. However, terms may not compute down to canonical terms and it will interfere with the ability to determine if two terms are judgementally equal to each other.


title: Type theory

text: Per Martin-Löf proposed his intuitionistic type theory as a foundation for constructive mathematics. Constructive mathematics requires when proving "There exists an formula_3 with property P(formula_3)", there must be a particular formula_3 and a proof that it has property "P". In type theory, existence is accomplished using the dependent product type and, its proof, requires a term of that type. For the term formula_64, "first formula_64" will produce the formula_3 and "second formula_64" will produce the proof of P(formula_3).


title: Type theory

text: An example of a non-constructive proof is a "proof by contradiction". The first step is assuming that formula_3 does not exist and refuting it by contradiction. The conclusion from that step is "it is not the case that formula_3 does not exist". The last step is, by double negation, concluding that formula_3 exists. To be clear, constructive mathematics still allows "refute by contradiction". It can prove that "it is not the case that formula_3 does not exist". But constructive mathematics does not allow the last step of removing the double negation to conclude that formula_3 exists.


title: Type theory

text: Constructive mathematics has often used intutionistic logic, as evidenced by the Brouwer–Heyting–Kolmogorov interpretation.


title: Type theory

text: Most of the type theories proposed as foundations are constructive. This includes most of the ones used by proof assistants.


title: Type theory

text: It is possible to add non-constructive features to a type theory, by rule or assumption. These include operators on continuations such as call with current continuation. However, these operators tend to break desirable properties such as canonicity and parametricity.


title: Type theory

text: Although the initial motivation for category theory was far removed from foundationalism, the two fields turned out to have deep connections. As John Lane Bell writes: "In fact categories can "themselves" be viewed as type theories of a certain kind; this fact alone indicates that type theory is much more closely related to category theory than it is to set theory." In brief, a category can be viewed as a type theory by regarding its objects as types (or sorts), i.e. "Roughly speaking, a category may be thought of as a type theory shorn of its syntax." A number of significant results follow in this way:


title: Type theory

text: The interplay, known as categorical logic, has been a subject of active research since then; see the monograph of Jacobs (1999) for instance.


title: Type theory

text: Homotopy type theory attempts to combine type theory and category theory. It focuses on equalities, especially equalities between types.


title: Type theory

text: The first computer proof assistant, called Automath, used type theory to encode mathematics on a computer. Martin-Löf specifically developed intuitionistic type theory to encode "all" mathematics to serve as a new foundation for mathematics. There is ongoing research into mathematical foundations using homotopy type theory.


title: Type theory

text: Mathematicians working in category theory already had difficulty working with the widely accepted foundation of Zermelo–Fraenkel set theory. This led to proposals such as Lawvere's Elementary Theory of the Category of Sets (ETCS). Homotopy type theory continues in this line using type theory. Researchers are exploring connections between dependent types (especially the identity type) and algebraic topology (specifically homotopy).


title: Type theory

text: Much of the current research into type theory is driven by proof checkers, interactive proof assistants, and automated theorem provers. Most of these systems use a type theory as the mathematical foundation for encoding proofs, which is not surprising, given the close connection between type theory and programming languages:


title: Type theory

text: Many type theories are supported by LEGO and Isabelle. Isabelle also supports foundations besides type theories, such as ZFC. Mizar is an example of a proof system that only supports set theory.


title: Type theory

text: Any static program analysis, such as the type checking algorithms in the semantic analysis phase of compiler, has a connection to type theory. A prime example is Agda, a programming language which uses UTT (Luo's Unified Theory of dependent Types) for its type system.


title: Type theory

text: The programming language ML was developed for manipulating type theories (see LCF) and its own type system was heavily influenced by them.


title: Type theory

text: Type theory is also widely used in formal theories of semantics of natural languages, especially Montague grammar and its descendants. In particular, categorial grammars and pregroup grammars extensively use type constructors to define the types ("noun", "verb", etc.) of words.


title: Type theory

text: The most common construction takes the basic types formula_93 and formula_64 for individuals and truth-values, respectively, and defines the set of types recursively as follows:


title: Type theory

text: A complex type formula_128 is the type of functions from entities of type formula_126 to entities of type formula_127. Thus one has types like formula_132 which are interpreted as elements of the set of functions from entities to truth-values, i.e. indicator functions of sets of entities. An expression of type formula_133 is a function from sets of entities to truth-values, i.e. a (indicator function of a) set of sets. This latter type is standardly taken to be the type of natural language quantifiers, like " everybody" or " nobody" (Montague 1973, Barwise and Cooper 1981).


title: Type theory

text: Gregory Bateson introduced a theory of logical types into the social sciences; his notions of double bind and logical levels are based on Russell's theory of types.


title: The Great Jahy Will Not Be Defeated!

text: by Square Enix. An anime television series adaptation by Silver Link aired from August to December 2021 on ABC and TV Asahi's ANiMAZiNG!!! programming block.


title: The Great Jahy Will Not Be Defeated!

text: Jahy, the feared and respected number-two ruler of the Dark Realm, suddenly finds herself powerless and shrunken in the human world after a magical girl destroys a powerful mana crystal, which also destroys her home realm. The manga follows Jahy and her daily life as she learns to live in her new surroundings while she works to restore her original form, the mana crystal, and the Dark Realm.


title: The Great Jahy Will Not Be Defeated!

text: Originally starting as a one-shot in March 2017, Square Enix has serialized "The Great Jahy Will Not Be Defeated!" in its monthly "shōnen" magazine, "Gangan Joker", since August of the same year. As of October 21, 2022, nine "tankōbon" volumes have been published, starting with the first volume released on February 22, 2018. In North America, the manga is published by the Manga & Books division of Square Enix. The first volume was originally scheduled to release in September 2020, but had to be delayed due to the COVID-19 pandemic. The release date was changed to July 27, 2021.


title: The Great Jahy Will Not Be Defeated!

text: An anime television series adaptation was announced on April 16, 2021. The two-cour series was animated by Silver Link and directed by Mirai Minato, with Michiko Yokote overseeing series scripts, Saori Nakashiki designing characters and serving as chief animation director, and Kōji Fujimoto and Osamu Sasaki composing the music. It aired from August 1 to December 19, 2021 on ABC and TV Asahi's programming block. The first opening theme is "Fightin★Pose", performed by Yui Ogura, while the ending theme is , performed by NEGI☆U, a unit formed of Hololive Production-affiliated VTubers Minato Aqua, Oozora Subaru, and Momosuzu Nene. The second opening theme is , performed by Sumire Uesaka, while the ending theme is , performed by Miho Okasaki. Crunchyroll licensed the series outside of Asia. Plus Media Networks Asia licensed the series in Southeast Asia and released it on Aniplus Asia.


title: The Great Jahy Will Not Be Defeated!

text: On July 19, 2022, Crunchyroll announced that the series would receive an English dub, which premiered the following day.


title: Planet 51

text: Planet 51 is a 2009 computer-animated science fiction comedy film directed by Jorge Blanco and co-directed by Javier Abad and Marcos Martínez, from a script by Joe Stillman, based on an original idea by Javier Abad, Jorge Blanco, Marcos Martínez and Ignacio Pérez Dolset. Starring Dwayne Johnson, Jessica Biel, Justin Long, Gary Oldman, Seann William Scott and John Cleese, the film follows an astronaut who lands on an alien planet, as one of the aliens helps him return to his ship while evading the military.


title: Planet 51

text: An international co-production by Spain, United Kingdom, United States, and Canada, with the studios Ilion Animation Studios based in Madrid, and HandMade Films in London, the film was originally acquired for North American distribution by New Line Cinema, but then sold to Sony Pictures before completion. Originally titled "Planet One", and later named as an allusion to Area 51, the film was completed on a $70 million budget, which, as of 2010, was the most expensive film produced in Spain.


title: Planet 51

text: "Planet 51" was released on 20 November 2009 in the United States and Canada by Sony Pictures Releasing's TriStar Pictures and Remstar Media Partners respectively, on 27 November in Spain by DeAPlaneta Distribución, and 4 December in the United Kingdom by HandMade Films International. The film grossed $105.6 million in the worldwide box office. It received generally negative reviews from critics, but earned the Goya Award for Best Animated Film in Spain.


title: Planet 51

text: On Planet 51, green extraterrestrials live peacefully in a society reminiscent of the United States during the 1950s, although the planet's and their nature provide notable differences from Earth and, notably, ignorance about astronomy leads to believing that the whole Universe extends for almost 500 miles.


title: Planet 51

text: One day, a mysterious spacecraft lands in the city of Glipforg. NASA astronaut Charles "Chuck" Baker emerges from it and is shocked to find the planet inhabited. Panicked, Chuck escapes to the town's planetarium, where he meets teenage alien Lem, who works there part-time. Chuck convinces Lem to help return him to his spacecraft before command module "Odyssey" in Planet 51's orbit departs for Earth in three days and leaves him stranded. Planet 51's army, led by the paranoid General Grawl, arrives to inspect and deduces that the astronaut is an alien invader bent on turning the planet's population into zombies, similar to how invaders are depicted in media, and a manhunt ensues.


title: Planet 51

text: Lem enlists the help of his best friend Skiff, an eccentric science fiction aficionado with conspiracy theories about the so-called "Base 9" (Planet 51's equivalent of Area 51), to hide Chuck away from the army. During his efforts to conceal Chuck, Lem inadvertently upsets his neighbor and crush Neera, who believes the alien is friendly, and is also fired from his job when his boss discovers Chuck. In Lem's room, Chuck reunites with a dog-like NASA probe called Rover, which freed itself from the army's base after tracking Chuck with a GPS and headed for the city and which befriends a small, domesticated Xenomorph. After the army searches Lem's home for traces of the alien, Lem and Skiff move Chuck to a comic book store Skiff works at, where the news station manages to capture Chuck acting out references to Earth's pop culture, which is misinterpreted as alien threats. After escaping the store from the invading army, Grawl has Chuck's spacecraft moved to a secret location. Chuck is later captured by Grawl's forces during a festive movie premiere in town, and is slated to have his brain removed by alien scientist Professor Kipple. When Lem defends Chuck, Kipple deems him a zombie minion. Resigned to his fate, Chuck pretends to release Lem from his "mind control" and is taken away with Rover to Base 9.


title: Planet 51

text: Lem gets his job back, but is determined to rescue Chuck. Joined by Skiff, Neera, her younger brother Eckle, and Rover, Lem tracks down Base 9's location in the desert to a gas station where Skiff inadvertently opens a gate to the underground base. They free Chuck from Kipple and find his spacecraft, but they are cornered by Grawl and his forces. Bent on eliminating the human, Grawl reveals he has the base rigged to explode. Lem attempts to reason with The General to not shoot Chuck but inadvertently activates the countdown. Enraged, Grawl attempts to shoot Lem, but Eckle tosses a hook to him and ignites an explosive, causing him to be trapped under debris. Chuck rescues him before launching his spacecraft into Planet 51's orbit, escaping Base 9's destruction. After admiring Planet 51's view from space, Lem successfully asks Neera out on a date, while Grawl expresses his gratitude to Chuck for saving him. Chuck returns his friends home and allows Rover to stay behind with Skiff, who has bonded with the probe, and bids Lem and the rest of the town farewell before launching back into space, but the last seconds of the film reveal that the little Xenomorph pet befriended by Rover is on board.


title: Planet 51

text: In a mid-credits scene, Kipple climbs out of the underground base, but is taken back to his own lab for brain surgery by two of his own patients, whom he wrongly deemed to be mind controlled by Chuck earlier in the movie. Meanwhile, Chuck is stuck being licked by the alien pet as he comments that 'this is going to be a long trip'.


title: Planet 51

text: "Planet 51" is based on the original idea by Jorge Blanco, Marcos Martínez, Ignacio Pérez Dolset and Javier Abad. The film finished production by June 2009.


title: Planet 51

text: The name change from "Planet One" to "Planet 51" was a result of the demands made from another entity branded "Planet One" which produces children and teen TV programmes. They made contact with the film's producers early on to resolve the trademark and brand confusion issues. The Spanish film company behind it, Ilion Animation Studios, made an offer to the existing entity for all ownership rights to their "Planet One" trademarks and related website URLs. Planet One chose not to take that offer and to protect their brand and trademarks that had been active for many years. As a result, the film's producers chose to rename the film "Planet 51": a reference to the top-secret military base, Area 51, where conspiracy theorists claim that data and specimens from a space alien that landed on Earth in 1947 are stored.


title: Planet 51

text: The character of Lem was named by screenwriter Joe Stillman after Polish science-fiction writer Stanisław Lem. Since the film was intended to be a parody of American pulp science fiction shot in Eastern Europe, Stillman thought it would be hilarious to have the name hint about a writer whose works have nothing to do with "little green men" stereotypes.


title: Planet 51

text: In November 2007, New Line Cinema had picked up the United States distribution rights; the studio itself was to release the film in the summer of 2009. However, TriStar Pictures became the film's home after New Line Cinema sold the rights to them through Sony Pictures Worldwide Acquisitions Group. According to the "Variety" magazine, New Line Cinema's owner, Warner, "decided to let the pic go after the producers insisted on a November release, when Warner is releasing its sixth Harry Potter pic." The new distributor moved the U.S. release date from the summer of 2009 to November of that year.


title: Planet 51

text: The movie was then released a week later in Spain, on 27 November 2009, where it was distributed by DeAPlaneta.


title: Planet 51

text: The film was released by Sony Pictures Home Entertainment on Blu-ray and DVD on 9 March 2010; it would also see various other rereleases alongside other animated and/or family films by Sony Pictures afterwards, including as part of a triple pack with "Surf's Up" and "The Pirates!: Band of Misfits".


title: Planet 51

text: The film was released in 3,035 cinemas, grossing $3.2 million on its opening day and $12.6 million over the weekend, resulting in the number four position at the box office behind "2012", "The Blind Side" and "" respectively. During its theatrical run, it made over $42 million, with a total of $105 million worldwide.


title: Planet 51

text: Rotten Tomatoes reported that 23% of critics gave "Planet 51" positive reviews based on 110 reviews with an average score of 4.2/10. The site's consensus reads: ""Planet 51" squanders an interesting premise with an overly familiar storyline, stock characters, and humor that alternates between curious and potentially offensive." Another review aggregator, Metacritic, gave it a metascore of 39, indicating "generally unfavorable reviews" , based on 21 reviews.


title: Planet 51

text: Adam Markovitz of "Entertainment Weekly" graded the film a B, as it "delivers a few pleasant surprises, including a smart story". Roger Ebert of the "Chicago Sun-Times" gave 2 stars out of 4 and positively wrote of the film being "perfectly pleasant as kiddie entertainment, although wall-to-wall with pop references to the American 1950s." Furthermore, some critics such as Markovitz of "EW", Steven Rea of "The Philadelphia Inquirer", and Brian Miller of "The Village Voice" acknowledged "Planet 51" as "an "E.T." in reverse" (a role reversal where the human is the "alien").


title: Planet 51

text: The soundtrack album for the film was released by Decca Label Group on 10 November 2009 (digital) and 17 November 2009 (CD).


title: Planet 51

text: A video-game based on the film was announced in November 2009. The game was published by Sega and was released on Nintendo DS, PlayStation 3, Wii and Xbox 360 on 17 November 2009. The console versions was developed by Pyro Studios and the Nintendo DS version was developed by Firebrand Games. Zed Group, a long-time customer of Trinigy's, worked on the online version of the game with the Vision Engine. There are also "Planet 51" games for iPhone, mobile devices and Facebook, developed by Zed Worldwide.


title: Nan Britton

text: Nanna Popham Britton (November 9, 1896 – March 21, 1991) was an American secretary who was a mistress of Warren G. Harding, the 29th President of the United States. In 1927, she revealed that her daughter, Elizabeth, had been fathered by Harding while he was serving in the United States Senate, one year before he was elected to the presidency. Her claim was open to question during her life, but was confirmed by DNA testing in 2015.


title: Nan Britton

text: Nan's father, Samuel H. Britton, spoke to Harding about his daughter's infatuation, and Harding met with her, telling her that some day she would find the man of her dreams. Harding was already married and involved in a passionate affair with Carrie Fulton Phillips, wife of James Phillips, co-owner of a local department store. After she graduated from high school in 1914, Britton moved to New York City, to begin a career as a secretary. However, she claimed she also began an intimate relationship with Harding.


title: Nan Britton

text: Following Harding's death, Britton wrote what is considered to be the first kiss-and-tell book. In "The President's Daughter", published in 1927, she told of her life as Harding's mistress throughout his presidency and named him as the father of her daughter, Elizabeth Ann (1919–2005). One famous passage told of their having sex in a coat closet in the executive office of the White House.


title: Nan Britton

text: According to Britton, Harding had promised to support their daughter, but after his sudden death in 1923, his wife, Florence, refused to honor the obligation. Britton insisted that she wrote her book to earn money to support her daughter and to champion the rights of illegitimate children. She brought a lawsuit ("Britton v. Klunk"), but she was unable to provide any concrete evidence and was shaken by the vicious personal attacks made by Congressman Grant Mouser during the cross examination, which cost her the case.


title: Nan Britton

text: Britton's portrayal of Harding and his colloquialisms paints a picture of a crude womanizer. In his 1931 book "Only Yesterday: An Informal History of the 1920s", Frederick Lewis Allen wrote that on the testimony of Britton's book, Harding's private life was "one of cheap sex episodes" and that "one sees with deadly clarity the essential ordinariness of the man, the commonness of his 'Gee dearie' and 'Say, you darling'." Britton's book was among those irreverently reviewed by Dorothy Parker for "The New Yorker" magazine as part of her famous "Constant Reader" column, under the title "An American DuBarry".


title: Nan Britton

text: In 1964, the discovery of more than 250 love letters that Harding had written to Carrie Fulton Phillips between 1909 and 1920 gave further support to Britton's own claims. Journalist R. W. Apple Jr. found Britton, who had long lived in seclusion, but was refused an interview. At the time, she was living in the Chicago area. Even at this time, over a generation later, her daughter and grandchildren would "occasionally be hounded by hateful skeptics" with threats and other unwanted attention that seemed to intensify during presidential elections.


title: Nan Britton

text: In the 1980s, Britton and her extended family moved to Oregon, where her three grandchildren were living as of 2015.


title: Nan Britton

text: Britton died in 1991 in Sandy, Oregon, where she had lived during the last years of her life. She insisted until her death that Harding was her daughter's father. Twenty-four years after her death, in 2015, Ancestry.com confirmed through DNA testing of descendants of Harding's brother and Britton's grandchildren that Elizabeth was indeed Harding's daughter.


title: Pacific Coast League

text: The Pacific Coast League (PCL) is a Minor League Baseball league that operates in the Western United States. Along with the International League, it is one of two leagues playing at the Triple-A level, which is one grade below Major League Baseball (MLB).


title: Pacific Coast League

text: The PCL was one of the premier regional baseball leagues in the first half of the 20th century. Although it was never recognized as a true major league, to which it aspired, its quality of play was considered very high. A number of top stars of the era, including Joe DiMaggio and Ted Williams, were products of the league. In 1958, with the arrival of major league teams on the west coast and the availability of televised major league games, the PCL's modern era began with each team signing Player Development Contracts to become farm teams of major league clubs. Following MLB's reorganization of the minor leagues in 2021, it operated as the Triple-A West for one season before switching back to its previous moniker in 2022.


title: Pacific Coast League

text: A league champion is determined at the end of each season. The San Francisco Seals won 14 Pacific Coast League titles, the most in the league's history, followed by the Los Angeles Angels (12) and the Albuquerque Dukes and Portland Beavers (8).


title: Pacific Coast League

text: The Pacific Coast League was formed on December 29, 1902, when officials from the California State League (1899–1902) met in San Francisco for the purpose of expanding the league beyond California. Six franchises were granted. These were the Los Angeles Angels, Oakland Oaks, Portland Beavers, Sacramento Senators, San Francisco Seals, and Seattle Indians. A dispute over territories owned by the Pacific Northwest League, in which the PCL had placed franchises, and the PCL's allowing blacklisted players to compete led to the National Association of Professional Baseball Leagues (NAPBL) labeling the PCL as an outlaw league.


title: Pacific Coast League

text: The mild climate of the West Coast, especially California, allowed the league to play longer seasons, sometimes starting in late February and ending as late as the beginning of December. During the 1905 season the San Francisco Seals set the all-time PCL record by playing 230 games. Teams regularly played between 170 and 200 games in a season until the late 1950s. This allowed players, who were often career minor leaguers, to hone their skills, earn an extra month or two of pay, and reduce the need to find off-season work. These longer seasons gave owners the opportunity to generate more revenue. Another outcome was that a number of the all-time minor league records for season statistical totals are held by players from the PCL.


title: Pacific Coast League

text: The inaugural 1903 season, which consisted of over 200 scheduled games for each team, began on March 26. The Los Angeles Angels finished the season in first place with a 133–78 (.630) record, making them the first league champions.


title: Pacific Coast League

text: In 1904, NAPBL president Patrick T. Powers brokered terms with the PCL, clearing it of its outlaw status and designating it as a Class A league. In 1909, the league classification was raised to Double-A. In 1919, with the earlier addition of the Salt Lake Bees and Vernon Tigers, league membership reached eight teams for the first time. While the league had experienced little commercial success up to this point, the 1920s were a turning point which saw increased attendance and teams fielding star players.


title: Pacific Coast League

text: The Great Depression of the 1930s resulted in a lower quality of play due to the league's salary reduction. Still, a number of top stars, including Joe DiMaggio, Ted Williams, Bobby Doerr, and Ox Eckhardt, competed on PCL teams that decade. Also helping attendance was the introduction of night games. At Sacramento's Moreing Field, the Sacramento Solons and the Oakland Oaks played the first night baseball game, five years before any major league night game, on June 10, 1930. The Hollywood Stars and San Diego Padres were added to the league in the 1930s as well.


title: Pacific Coast League

text: During the first half of the 20th century, the Pacific Coast League developed into one of the premier regional baseball leagues. The cities enfranchised by the other two high-minor leagues, the International League and the American Association, were generally coordinated geographically with the major leagues, but such was not the case with the PCL. With no major league baseball team existing west of St. Louis, the PCL was unrivaled for American west coast baseball. Although it was never recognized as a true major league, its quality of play was considered very high. Drawing from a strong pool of talent in the area, the PCL produced many outstanding players, including such future major-league Hall of Famers as Joe DiMaggio, Ted Williams, Tony Lazzeri, Paul Waner, Earl Averill, Bobby Doerr, Joe Gordon, and Ernie Lombardi. Amid success experienced after World War II, league President Pants Rowland began to envision the PCL as a third major league. During 1945 the league voted to become a major league. However, the American League and National League were uninterested in allowing it to join their ranks.


title: Pacific Coast League

text: While many PCL players went on to play in the major leagues, teams in the league were often successful enough that they could offer competitive salaries to avoid being outbid for their players' services. Some players made a career out of the minor leagues. One of the better known was Frank Shellenback, whose major league pitching career was brief, but who compiled a record PCL total of 295 wins against 178 losses. (It should be mentioned, however, that Shellenback's long career in the PCL was largely due to his use of the spitball, banned in the major leagues in 1920, not the competitive salaries offered by PCL clubs.) Many former major league players came to the PCL to finish their careers after their time in the majors had ended.


title: Pacific Coast League

text: In 1952, the PCL became the only minor league in history to be given the "Open" classification, a grade above the Triple-A level. This limited the rights of major league clubs to draft players from the PCL, and was considered an act toward the circuit becoming a third major league.


title: Pacific Coast League

text: The shift to the Open classification came just as minor league teams from coast to coast suffered a sharp drop in attendance, primarily due to the availability of major league games on television. The hammer blow to the PCL's major league dreams came in 1958 with the arrival of the first MLB teams on the west coast (the Los Angeles Dodgers and San Francisco Giants). As a result, three of the PCL's flagship teams (the Los Angeles Angels, Hollywood Stars, and San Francisco Seals) were immediately forced to relocate to smaller markets. The Oakland Oaks had moved to Canada two years before the Giants arrived. The San Diego Padres and Seattle Rainiers suffered the same fate when they were displaced by major league teams in 1969. Additionally, the PCL lost customers to the major league teams which then occupied the same territory. The league never recovered from these blows. The Pacific Coast League reverted to Triple-A classification in 1958, where it remained, and soon diminished in the public eye to nothing more than another minor league.


title: Pacific Coast League

text: The PCL began to spread out across the nation, and internationally, in the 1950s. Previously, Salt Lake City had been the easternmost city in the league. In 1956, the Oakland Oaks relocated to Canada where they became the Vancouver Mounties, the circuit's first international team. Two years later, the Los Angeles Angels moved to become the Spokane Indians and the San Francisco Seals became the Phoenix Giants.


title: Pacific Coast League

text: The league continued to expand throughout the country in the 1960s. Clubs representing new cities during the decade included the Dallas Rangers, Denver Bears, Hawaii Islanders, Indianapolis Indians, Oklahoma City 89ers, Tacoma/Phoenix Giants, and Tucson Toros. From 1964 to 1968 the PCL swelled to twelve teams. The Albuquerque Dukes were one of several teams to begin play in the 1970s. Several new teams arrived in the 1980s, such as the Calgary Cannons, Colorado Springs Sky Sox, Edmonton Trappers, and Las Vegas Stars, but the league began to stabilize as franchise relocations became less frequent.


title: Pacific Coast League

text: In 1998, the Pacific Coast League took on five teams from the disbanding American Association, which had operated in the Midwest, and a sixth franchise was added to the league as an expansion team, thus providing the scheduling convenience of an even number of teams. The addition of the Iowa Cubs, Nashville Sounds, Oklahoma RedHawks, Omaha Royals, New Orleans Zephyrs, and the expansion Memphis Redbirds grew the league to an all-time-high 16 clubs. Despite its name, the league now extended well beyond the Pacific coast, stretching from Western Washington to Middle Tennessee. Half of its teams were located east of the Rocky Mountains.


title: Pacific Coast League

text: The league's presence in Canada diminished and ended in the early 2000s, as the Calgary Cannons moved to Albuquerque, New Mexico, to become the Albuquerque Isotopes in 2003, and the Edmonton Trappers, the circuit's final Canadian team moved to Round Rock in 2005. Of the cities represented in the PCL in its heyday, only Salt Lake City and Sacramento remain, and even these were represented by franchises different from those that originally called these cities home. In 2005, the Pacific Coast League became the first minor league ever to achieve a season attendance of over 7 million. In 2007, league attendance reached an all-time high of 7,420,095.


title: Pacific Coast League

text: In 2019, the team previously known as the Colorado Springs Sky Sox relocated to San Antonio, Texas and continued play in the PCL as the San Antonio Missions, assuming the identity of a team which had previously competed in the Double-A Texas League. This move was accompanied by realignment in the American Conference. Nashville and Memphis moved to the Northern Division, and Oklahoma City and San Antonio moved to the Southern Division. In a further move, the New Orleans Baby Cakes relocated to Wichita, Kansas where they became known as the Wichita Wind Surge.


title: Pacific Coast League

text: The start of the 2020 season was postponed due to the COVID-19 pandemic before ultimately being cancelled on June 30. As part of Major League Baseball's 2021 reorganization of the minor leagues, the Pacific Coast League was reduced to 10 teams and temporarily renamed the "Triple-A West" for the 2021 season. Following MLB's acquisition of the rights to the names of the historical minor leagues, the Triple-A West was renamed the Pacific Coast League effective with the 2022 season.


title: Pacific Coast League

text: The league is divided into two divisions, East and West, of five teams each. As of the 2022 season, all teams play a 150-game schedule, beginning in early April and concluding in late September.


title: Pacific Coast League

text: At the conclusion of the season, the two division champions meet in a single game to determine a league champion. The PCL champion then meets the International League's champion in the Triple-A National Championship Game, a single game to determine an overall champion of Triple-A baseball, which has been held annually since 2006, excluding 2020 and 2021. Previously, the PCL champion also competed in the Triple-A World Series (1983, 1998–2000), Junior World Series (1919), and other sporadic postseason competitions throughout the league's history.


title: Pacific Coast League

text: Other interleague play occurred during the Triple-A All-Star Game. Traditionally, the game took place on the day after the mid-summer Major League Baseball All-Star Game. The game was meant to mark a symbolic halfway-point in the season (though not the mathematical halfway-point which, for most seasons, is usually one month prior). During the All-Star break, no regular-season games were scheduled for two days before the All-Star Game itself.


title: Pacific Coast League

text: The Pacific Coast League plays by the same rules listed in the "Official Baseball Rules" published by Major League Baseball. One exception was the use of the designated hitter (DH). Whereas the application of the DH rule in Major League Baseball is determined by the identity of the home team, with the rules of the home team's league applying to both teams, PCL pitchers hit when both clubs were National League affiliates and they agreed to have their pitchers hit. Two National League affiliated clubs may agree to use the DH instead. The reason for this is that as players move up and get closer to reaching the majors, teams prefer to have the rules follow (as closely as possible) those of the major leagues. The DH is always used when one or both teams are American League affiliates. Since the universal DH in 2022, this no longer is an issue.


title: Pacific Coast League

text: Other differences lay in the use of professional baseball's pace-of-play initiatives which began to be implemented in 2015. A 15-second pitch clock is used when no runners were on base; 20 seconds are allowed with runners present. Teams are limited to five mound visits during a nine-inning game. Pitchers are required to face a minimum of three consecutive batters until the side is retired or the pitcher is injured and unable to continue playing.


title: Pacific Coast League

text: The 1905 Tacoma Tigers were moved back to Sacramento in the middle of the 1905 season due to poor play, then were moved again to Fresno the following season.<br>


title: Pacific Coast League

text: One league team was acquired by the PCL following the disbandment of the American Association after the 1997 season.


title: Pacific Coast League

text: Two former league teams played in the PCL from 1964 to 1968. Each one had played in the International League during the 1963 season, and each was transferred to the American Association after the 1968 season.


title: Pacific Coast League

text: Seven former league teams were transferred to other leagues in conjunction with the 2021 reorganization of the minors. Memphis, which was created as an expansion team in 1998, was transferred to the International League along with Iowa, Nashville, and Omaha, which joined the PCL from the American Association in 1998. Wichita, which also traces its roots to the American Association, was moved to the Texas League along with San Antonio. Fresno was transferred to the California League.


title: Pacific Coast League

text: League champions have been determined by different means since the Pacific Coast League's formation in 1903. With few exceptions, most PCL champions through 1927 were simply the regular season pennant winners. However, a few seasons during this time did feature a postseason championship series to crown a champion. It was not until the mid-1930s that the league instituted regular postseason play that was only sporadically cancelled due to financial problems or other factors. As of the 2022 season, the two division champions meet in a single game to determine a league champion.


title: Pacific Coast League

text: The San Francisco Seals won 14 PCL championships, the most among all teams in the league, followed by the Los Angeles Angels (12) and the Albuquerque Dukes and Portland Beavers (8).


title: Pacific Coast League

text: The Most Valuable Player Award, first awarded in 1927, is given to honor the best player in the league. The award is voted on by team managers, general managers, broadcasters, and media representatives from around the league, as are all PCL year-end awards.


title: Pacific Coast League

text: The Pitcher of the Year Award, awarded sporadically from 1957 to 1974 and continuously since 2001, serves to recognize the league's best pitcher. Pitchers were also eligible to win the MVP Award from 1927 to 2000.


title: Pacific Coast League

text: The Top MLB Prospect Award, created in 1952 as the Rookie of the Year Award and issued from 1952 to 1972 and since 1998, is given to the best player with no prior PCL experience.


title: Pacific Coast League

text: The Executive of the Year Award, first awarded in 1974, honored team executives who have achieved success in the area of attendance figures, promotions, and community involvement.


title: Pacific Coast League

text: The Pacific Coast League Hall of Fame was established in 1942 to honor league players, managers, and executives who have made significant contributions to the league's ideals. The Hall of Fame inducted its first class of 12 men in 1943. The Hall became dormant after 1957, but was revived in 2003, the PCL's centennial season. Today, the Hall of Fame Committee seeks to recognize worthy players throughout the league's history who have made contributions to the league. New members are elected before the start of each season.