Hendrik Pieter (Henk) Barendregt (born 18 December 1947, Amsterdam) [1] is a Dutch logician, known for his work in lambda calculus and type theory.
Hendrik Pieter (Henk) Barendregt (born 18 December 1947, Amsterdam) [1] is a Dutch logician, known for his work in lambda calculus and type theory.
Barendregt studied mathematical logic at Utrecht University, obtaining his master's degree in 1968 and his PhD in 1971, both cum laude , under Dirk van Dalen and Georg Kreisel. After a postdoctoral position at Stanford University, he taught at Utrecht University.
Since 1986, Barendregt has taught at Radboud University Nijmegen, where he now holds the Chair of Foundations of Mathematics and Computer Science. His research group works on Constructive Interactive Mathematics. He is also Adjunct Professor at Carnegie Mellon University, Pittsburgh, USA. He has been a visiting scholar at Darmstadt, ETH Zürich, Siena, and Kyoto.
Barendregt was elected a member of Academia Europaea in 1992. [2] In 1997 Barendregt was elected member of the Royal Netherlands Academy of Arts and Sciences. [3] On 6 February 2003 Barendregt was awarded the Spinozapremie for 2002, the highest scientific award in the Netherlands. [4] In 2002 he was knighted in the Orde van de Nederlandse Leeuw.
Barendregt received an honorary doctorate from Heriot-Watt University in 2015. [5]
Lambda calculus is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. It is a universal model of computation that can be used to simulate any Turing machine. It was introduced by the mathematician Alonzo Church in the 1930s as part of his research into the foundations of mathematics.
Haskell Brooks Curry was an American mathematician and logician. Curry is best known for his work in combinatory logic. While the initial concept of combinatory logic was based on a paper by Moses Schönfinkel, Curry did much of the development. Curry is also known for Curry's paradox and the Curry–Howard correspondence. There are three programming languages named after him, Haskell, Brook and Curry, as well as the concept of currying, a technique used for transforming functions in mathematics and computer science.
In lambda calculus, the Church–Rosser theorem states that, when applying reduction rules to terms, the ordering in which the reductions are chosen does not make a difference to the eventual result.
A typed lambda calculus is a typed formalism that uses the lambda-symbol to denote anonymous function abstraction. In this context, types are usually objects of a syntactic nature that are assigned to lambda terms; the exact nature of a type depends on the calculus considered. From a certain point of view, typed lambda calculi can be seen as refinements of the untyped lambda calculus, but from another point of view, they can also be considered the more fundamental theory and untyped lambda calculus a special case with only one type.
System F is a typed lambda calculus that introduces, to simply typed lambda calculus, a mechanism of universal quantification over types. System F formalizes parametric polymorphism in programming languages, thus forming a theoretical basis for languages such as Haskell and ML. It was discovered independently by logician Jean-Yves Girard (1972) and computer scientist John C. Reynolds.
In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human-machine collaboration. This involves some sort of interactive proof editor, or other interface, with which a human can guide the search for proofs, the details of which are stored in, and some steps provided by, a computer.
Rewriting Techniques and Applications (RTA) is an annual international academic conference on the topic of rewriting. It covers all aspects of rewriting, including termination, equational reasoning, theorem proving, higher-order rewriting, unification and the lambda calculus. The conference consists of peer-reviewed papers with the proceedings published by Springer in the LNCS series until 2009, and since then in the LIPIcs series published by the Leibniz-Zentrum für Informatik. Several rewriting-related workshops are also affiliated with RTA.
In computer science, termination analysis is program analysis which attempts to determine whether the evaluation of a given program halts for each input. This means to determine whether the input program computes a total function.
Johannes Aldert "Jan" Bergstra is a Dutch computer scientist. His work has focussed on logic and the theoretical foundations of software engineering, especially on formal methods for system design. He is best known as an expert on algebraic methods for the specification of data and computational processes in general.
In the branches of mathematical logic known as proof theory and type theory, a pure type system (PTS), previously known as a generalized type system (GTS), is a form of typed lambda calculus that allows an arbitrary number of sorts and dependencies between any of these. The framework can be seen as a generalisation of Barendregt's lambda cube, in the sense that all corners of the cube can be represented as instances of a PTS with just two sorts. In fact, Barendregt (1991) framed his cube in this setting. Pure type systems may obscure the distinction between types and terms and collapse the type hierarchy, as is the case with the calculus of constructions, but this is not generally the case, e.g. the simply typed lambda calculus allows only terms to depend on terms.
Gérard Pierre Huet is a French computer scientist, linguist and mathematician. He is senior research director at INRIA and mostly known for his major and seminal contributions to type theory, programming language theory and to the theory of computation.
Dirk van Dalen is a Dutch mathematician and historian of science.
In the study of denotational semantics of the lambda calculus, Böhm trees, Lévy-Longo trees, and Berarducci trees are tree-like mathematical objects that capture the "meaning" of a term up to some set of "meaningless" terms.
Jan Willem Klop is a professor of applied logic at Vrije Universiteit in Amsterdam. He holds a Ph.D. in mathematical logic from Utrecht University. Klop is known for his work on the Algebra of Communicating Processes, co-author of TeReSe and his fixed point combinator
In mathematical logic, category theory, and computer science, kappa calculus is a formal system for defining first-order functions.
Jean-Pierre Jouannaud is a French computer scientist, known for his work in the area of term rewriting.
Nachum Dershowitz is an Israeli computer scientist, known e.g. for the Dershowitz–Manna ordering and the multiset path ordering used to prove termination of term rewrite systems.
Wayne Snyder is an associate professor at Boston University known for his work in E-unification theory.
Tobias Nipkow is a German computer scientist.
Mariangiola Dezani-Ciancaglini is an Italian logician and theoretical computer scientist whose research topics include type theory and intersection type disciplines, lambda calculus, and programming language semantics. She is a professor emerita at the University of Turin.
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