Thorsten Altenkirch

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Thorsten Altenkirch
Alma mater University of Edinburgh
Scientific career
Fields Constructive mathematics
Type theory
Homotopy type theory
Institutions University of Nottingham
Institute for Advanced Study
Doctoral advisor Rod Burstall

Thorsten Altenkirch (German pronunciation: [ˈtɔʁstn̩ ˈʔaltn̩kɪʁç] ) is a German Professor of Computer Science at the University of Nottingham [1] known for his research on logic, type theory, and homotopy type theory. Altenkirch was part of the 2012/2013 special year on univalent foundations at the Institute for Advanced Study. [2] At Nottingham he co-chairs the Functional Programming Laboratory with Graham Hutton.

Germany Federal parliamentary republic in central-western Europe

Germany, officially the Federal Republic of Germany, is a country in Central and Western Europe, lying between the Baltic and North Seas to the north and the Alps, Lake Constance and the High Rhine to the south. It borders Denmark to the north, Poland and the Czech Republic to the east, Austria and Switzerland to the south, France to the southwest, and Luxembourg, Belgium and the Netherlands to the west.

University of Nottingham university in Nottingham, United Kingdom

The University of Nottingham is a public research university in Nottingham, United Kingdom. It was founded as University College Nottingham in 1881, and was granted a royal charter in 1948.

In mathematics, logic, and computer science, a type theory is any of a class of formal systems, some of which can serve as alternatives to set theory as a foundation for all mathematics. In type theory, every "term" has a "type" and operations are restricted to terms of a certain type.

Contents

Education

Altenkirch obtained his PhD from the University of Edinburgh under Rod Burstall. [3]

University of Edinburgh public research university in Edinburgh, Scotland

The University of Edinburgh, founded in 1582, is the sixth oldest university in the English-speaking world and one of Scotland's ancient universities. The university has five main campuses in the city of Edinburgh, with many of the buildings in the historic Old Town belonging to the university. The university played an important role in leading Edinburgh to its reputation as a chief intellectual centre during the Age of Enlightenment, and helped give the city the nickname of the Athens of the North.

Rodney Martineau "Rod" Burstall FRSE is a British computer scientist and one of four founders of the Laboratory for Foundations of Computer Science at the University of Edinburgh.

Contributions

Altenkirch's work includes: Containers, Epigram programming language, and Homotopy Type Theory: Univalent Foundations of Mathematics (The HoTT Book).

In type theory, containers are abstractions which permit various "collection types", such as lists and trees, to be represented in a uniform way. A (unary) container is defined by a type of shapes S and a type family of positions P, indexed by S. The extension of a container is a family of dependent pairs consisting of a shape and a function from positions of that shape to the element type. Containers can be seen as canonical forms for collection types.

Epigram is a functional programming language with dependent types. Epigram also refers to the IDE usually packaged with the language. Epigram's type system is strong enough to express program specifications. The goal is to support a smooth transition from ordinary programming to integrated programs and proofs whose correctness can be checked and certified by the compiler. Epigram exploits the propositions as types principle, and is based on intuitionistic type theory.

Altenkirch has also been a guest on the YouTube channel Computerphile [4]

Related Research Articles

Set theory Branch of mathematics that studies sets

Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. The language of set theory can be used to define nearly all mathematical objects.

Vladimir Voevodsky Russian mathematician

Vladimir Alexandrovich Voevodsky was a Russian-American mathematician. His work in developing a homotopy theory for algebraic varieties and formulating motivic cohomology led to the award of a Fields Medal in 2002. He is also known for the proof of the Milnor conjecture and motivic Bloch-Kato conjectures and for the univalent foundations of mathematics and homotopy type theory.

Institute for Advanced Study postgraduate center in Princeton, New Jersey

The Institute for Advanced Study (IAS), located at 1 Einstein Drive, Princeton, New Jersey, in the United States, is an independent postdoctoral research center for theoretical research and intellectual inquiry. It was founded in 1930 by American educator Abraham Flexner, together with philanthropists Louis Bamberger and Caroline Bamberger Fuld.

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In computer science, a function type is the type of a variable or parameter to which a function has or can be assigned, or an argument or result type of a higher-order function taking or returning a function.

The vertical bar ( | ) is a computer character and glyph with various uses in mathematics, computing, and typography. It has many names, often related to particular meanings: Sheffer stroke, verti-bar, vbar, stick, vertical line, vertical slash,bar, pike, or pipe, and several variants on these names. It is occasionally considered an allograph of broken bar.

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Conor McBride is a lecturer in the department of Computer and Information Sciences at the University of Strathclyde. In 1999 he completed a PhD in 'Dependently Typed Functional Programs and their Proofs' at the University of Edinburgh for his work in type theory. He previously worked at Durham University and briefly at Royal Holloway, University of London before joining the academic staff at the University of Strathclyde.

Homotopy type theory

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References

  1. "Thorsten Altenkirch".
  2. "Program Participants".
  3. Thorsten Altenkirch at the Mathematics Genealogy Project
  4. "Computerphile". YouTube. Retrieved 11 January 2017.