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Richard Statman | |
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| Born | September 6, 1946 (age 78) |
| Alma mater | Stanford University |
| Scientific career | |
| Fields | computer science |
| Institutions | Carnegie Mellon |
| Doctoral advisor | Georg Kreisel |
Richard Statman (born September 6, 1946) is an American computer scientist whose principal research interest is the theory of computation, especially symbolic computation. His research involves lambda calculus, type theory, and combinatory algebra.
In 1974, Statman received his Ph.D. from Stanford University for his Ph.D. dissertation, supervised by Georg Kreisel, entitled Structural Complexity of Proofs [1] . His achievements include the proof that the type inhabitation problem in simply typed lambda calculus is PSPACE-complete [2] , lower bounds on simply typed lambda calculus [3] , logical relations [4] , and intersecton types [5] . He was a co-author of the book Lambda Calculus with Types [6] .
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Stephen Arthur Cook is an American-Canadian computer scientist and mathematician who has made significant contributions to the fields of complexity theory and proof complexity. He is a university professor emeritus at the University of Toronto, Department of Computer Science and Department of Mathematics.
In mathematics and theoretical computer science, a type theory is the formal presentation of a specific type system. Type theory is the academic study of type systems.
In programming language theory and proof theory, the Curry–Howard correspondence is the direct relationship between computer programs and mathematical proofs. It is also known as the Curry–Howard isomorphism or equivalence, or the proofs-as-programs and propositions- or formulae-as-types interpretation.
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.
In programming language theory, semantics is the rigorous mathematical study of the meaning of programming languages. Semantics assigns computational meaning to valid strings in a programming language syntax. It is closely related to, and often crosses over with, the semantics of mathematical proofs.
Linear logic is a substructural logic proposed by French logician Jean-Yves Girard as a refinement of classical and intuitionistic logic, joining the dualities of the former with many of the constructive properties of the latter. Although the logic has also been studied for its own sake, more broadly, ideas from linear logic have been influential in fields such as programming languages, game semantics, and quantum physics, as well as linguistics, particularly because of its emphasis on resource-boundedness, duality, and interaction.
Samson Abramsky is a British computer scientist who is a Professor of Computer Science at University College London. He was previously the Christopher Strachey Professor of Computing at Wolfson College, Oxford, from 2000 to 2021.
In logic, a logical framework provides a means to define a logic as a signature in a higher-order type theory in such a way that provability of a formula in the original logic reduces to a type inhabitation problem in the framework type theory. This approach has been used successfully for (interactive) automated theorem proving. The first logical framework was Automath; however, the name of the idea comes from the more widely known Edinburgh Logical Framework, LF. Several more recent proof tools like Isabelle are based on this idea. Unlike a direct embedding, the logical framework approach allows many logics to be embedded in the same type system.
Logic in computer science covers the overlap between the field of logic and that of computer science. The topic can essentially be divided into three main areas:
The simply typed lambda calculus, a form of type theory, is a typed interpretation of the lambda calculus with only one type constructor that builds function types. It is the canonical and simplest example of a typed lambda calculus. The simply typed lambda calculus was originally introduced by Alonzo Church in 1940 as an attempt to avoid paradoxical use of the untyped lambda calculus.
In computational complexity theory, a nonelementary problem is a problem that is not a member of the class ELEMENTARY. As a class it is sometimes denoted as NONELEMENTARY.
Gordon David Plotkin is a theoretical computer scientist in the School of Informatics at the University of Edinburgh. Plotkin is probably best known for his introduction of structural operational semantics (SOS) and his work on denotational semantics. In particular, his notes on A Structural Approach to Operational Semantics were very influential. He has contributed to many other areas of computer science.
In computer science, Programming Computable Functions (PCF) is a typed functional language introduced by Gordon Plotkin in 1977, based on previous unpublished material by Dana Scott. It can be considered to be an extended version of the typed lambda calculus or a simplified version of modern typed functional languages such as ML or Haskell.
Harry George Mairson is a theoretical computer scientist and professor of computer science in the Volen National Center for Complex Systems at Brandeis University in Waltham, Massachusetts. His research is in the fields of logic in computer science, lambda calculus and functional programming, type theory and constructive mathematics, computational complexity theory, and algorithmics.
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.
In mathematical logic and computer science, homotopy type theory (HoTT) refers to various lines of development of intuitionistic type theory, based on the interpretation of types as objects to which the intuition of (abstract) homotopy theory applies.
Arnon Avron is an Israeli mathematician and Professor at the School of Computer Science at Tel Aviv University. His research focuses on applications of mathematical logic to computer science and artificial intelligence.
Helmut Schwichtenberg is a German mathematical logician.
Dale Miller is an American computer scientist and author. He is a Director of Research at Inria Saclay and one of the designers of the λProlog programming language and the Abella interactive theorem prover.
Giuseppe Longo is an Italian mathematician, epistemologist, theoretical biologist, author, and academic. He is the Research Director Emeritus at Centre national de la recherche scientifique at the Cavaillès interdisciplinary center of École Normale Supérieure (ENS) in Paris.
