Haskell Curry
Encyclopedia
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 single paper by Moses Schönfinkel
, much of the development was done by Curry. Curry is also known for Curry's paradox
and the Curry–Howard correspondence. There are two programming languages named after him, Haskell
and Curry, as well as the concept of currying
, a technique used for transforming functions in mathematics and computer science.
, to Samuel Silas Curry and Anna Baright Curry, who ran a school for elocution
. He entered Harvard University
in 1916 to study medicine but switched to mathematics before graduating in 1920. After two years of graduate work in electrical engineering at MIT, he returned to Harvard to study physics, earning a MA in 1924. Curry's interest in mathematical logic started during this period when he was introduced to the Principia Mathematica
, the attempt by Alfred North Whitehead
and Bertrand Russell
to ground mathematics in symbolic logic. Remaining at Harvard, Curry pursued a Ph.D. in mathematics. While he was directed by George Birkhoff to work on differential equations, his interests continued to shift to logic. In 1927, while an instructor at Princeton University, he discovered the work of Moses Schönfinkel
in combinatory logic. Schönfinkel's work had anticipated much of Curry's own research, and as a consequence, he moved to Göttingen where he could work with Heinrich Behmann
and Paul Bernays
, who were familiar with Schönfinkel's work. Curry was supervised by David Hilbert
and worked closely with Bernays, receiving a Ph.D. in 1930 with a dissertation on combinatory logic.
In 1928, before leaving for Göttingen, Curry married Mary Virginia Wheatley. The couple lived in Germany while Curry completed his dissertation, then, in 1929, moved to State College, Pennsylvania where Curry accepted a position at Penn State College. They had two children, Anne Wright Curry (July 27, 1930) and Robert Wheatley Curry (July 6, 1934). Curry remained at Penn State for the next 37 years. He spent one year at University of Chicago
in 1931–32 under a National Research Fellowship
and one year in 1938–39 at the Institute for Advanced Study
in Princeton. In 1942 he took a leave of absence to do applied mathematics for the US government during World War II
. Immediately after the war he worked on the ENIAC
project, in 1945 and 1946. Under a Fulbright fellowship
, he collaborated with Robert Feys
in Louvain
, Belgium
. After retiring from Penn State in 1966, Curry accepted a position at the University of Amsterdam. In 1970, after finishing the second volume of his treatise on the combinatory logic, Curry retired from the University of Amsterdam and returned to State College, Pennsylvania.
Haskell Curry died on September 1, 1982 in State College, Pennsylvania.
could provide a foundation for mathematics. Towards the end of 1933, he learned of the Kleene–Rosser paradox from correspondence with John Rosser. The paradox, developed by Rosser and Stephen Kleene had proved the inconsistency of a number of related formal systems including the lambda calculus and Curry's own system. However, unlike Church, Kleene, and Rosser, Curry did not give up on the foundational approach, saying that he did not want to "run away from paradoxes."
By working in the area of Combinatory Logic for his entire career, Curry essentially became the founder and biggest name in the field. Combinatory logic is the foundation for one style of functional programming language. The power and scope of combinatory logic is quite similar to that of the lambda calculus
of Alonzo Church
, and the latter formalism has tended to predominate in recent decades.
He taught at Harvard, Princeton
, and from 1929 to 1966, at the Pennsylvania State University
. In 1942, he published Curry's paradox
. In 1966 he became professor of mathematics at the Universiteit van Amsterdam
.
Curry also wrote and taught mathematical logic
more generally; his teaching in this area culminated in his 1963 Foundations of Mathematical Logic. His preferred philosophy of mathematics was formalism (cf. his 1951 book), following his mentor Hilbert, but his writings betray substantial philosophical curiosity and a very open mind about intuitionistic logic
.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and logician. Curry is best known for his work in combinatory logic
Combinatory logic
Combinatory logic is a notation introduced by Moses Schönfinkel and Haskell Curry to eliminate the need for variables in mathematical logic. It has more recently been used in computer science as a theoretical model of computation and also as a basis for the design of functional programming...
; while the initial concept of combinatory logic was based on a single paper by Moses Schönfinkel
Moses Schönfinkel
Moses Ilyich Schönfinkel, also known as Moisei Isai'evich Sheinfinkel , was a Russian logician and mathematician, known for the invention of combinatory logic.- Life :Schönfinkel attended the Novorossiysk University of Odessa, studying mathematics under Samuil Osipovich...
, much of the development was done by Curry. Curry is also known for Curry's paradox
Curry's paradox
Curry's paradox is a paradox that occurs in naive set theory or naive logics, and allows the derivation of an arbitrary sentence from a self-referring sentence and some apparently innocuous logical deduction rules...
and the Curry–Howard correspondence. There are two programming languages named after him, Haskell
Haskell (programming language)
Haskell is a standardized, general-purpose purely functional programming language, with non-strict semantics and strong static typing. It is named after logician Haskell Curry. In Haskell, "a function is a first-class citizen" of the programming language. As a functional programming language, the...
and Curry, as well as the concept of currying
Currying
In mathematics and computer science, currying is the technique of transforming a function that takes multiple arguments in such a way that it can be called as a chain of functions each with a single argument...
, a technique used for transforming functions in mathematics and computer science.
Life
Curry was born on September 12, 1900, in Millis, MassachusettsMillis, Massachusetts
Millis is a town in Norfolk County in the U.S. state of Massachusetts. It is a small town with a population of 7,891 according to the 2010 census. The town is approximately southwest of downtown Boston and is bordered by Norfolk, Sherborn, Holliston, Medfield, and Medway...
, to Samuel Silas Curry and Anna Baright Curry, who ran a school for elocution
Elocution
Elocution is the study of formal speaking in pronunciation, grammar, style, and tone.-History:In Western classical rhetoric, elocution was one of the five core disciplines of pronunciation, which was the art of delivering speeches. Orators were trained not only on proper diction, but on the proper...
. He entered Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
in 1916 to study medicine but switched to mathematics before graduating in 1920. After two years of graduate work in electrical engineering at MIT, he returned to Harvard to study physics, earning a MA in 1924. Curry's interest in mathematical logic started during this period when he was introduced to the Principia Mathematica
Principia Mathematica
The Principia Mathematica is a three-volume work on the foundations of mathematics, written by Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913...
, the attempt by Alfred North Whitehead
Alfred North Whitehead
Alfred North Whitehead, OM FRS was an English mathematician who became a philosopher. He wrote on algebra, logic, foundations of mathematics, philosophy of science, physics, metaphysics, and education...
and Bertrand Russell
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these things...
to ground mathematics in symbolic logic. Remaining at Harvard, Curry pursued a Ph.D. in mathematics. While he was directed by George Birkhoff to work on differential equations, his interests continued to shift to logic. In 1927, while an instructor at Princeton University, he discovered the work of Moses Schönfinkel
Moses Schönfinkel
Moses Ilyich Schönfinkel, also known as Moisei Isai'evich Sheinfinkel , was a Russian logician and mathematician, known for the invention of combinatory logic.- Life :Schönfinkel attended the Novorossiysk University of Odessa, studying mathematics under Samuil Osipovich...
in combinatory logic. Schönfinkel's work had anticipated much of Curry's own research, and as a consequence, he moved to Göttingen where he could work with Heinrich Behmann
Heinrich Behmann
Heinrich Behmann was a German mathematician. He performed research in the field of set theory and predicate logic....
and Paul Bernays
Paul Bernays
Paul Isaac Bernays was a Swiss mathematician, who made significant contributions to mathematical logic, axiomatic set theory, and the philosophy of mathematics. He was an assistant to, and close collaborator of, David Hilbert.-Biography:Bernays spent his childhood in Berlin. Bernays attended the...
, who were familiar with Schönfinkel's work. Curry was supervised by David Hilbert
David Hilbert
David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...
and worked closely with Bernays, receiving a Ph.D. in 1930 with a dissertation on combinatory logic.
In 1928, before leaving for Göttingen, Curry married Mary Virginia Wheatley. The couple lived in Germany while Curry completed his dissertation, then, in 1929, moved to State College, Pennsylvania where Curry accepted a position at Penn State College. They had two children, Anne Wright Curry (July 27, 1930) and Robert Wheatley Curry (July 6, 1934). Curry remained at Penn State for the next 37 years. He spent one year at University of Chicago
University of Chicago
The University of Chicago is a private research university in Chicago, Illinois, USA. It was founded by the American Baptist Education Society with a donation from oil magnate and philanthropist John D. Rockefeller and incorporated in 1890...
in 1931–32 under a National Research Fellowship
United States National Research Council
The National Research Council of the USA is the working arm of the United States National Academies, carrying out most of the studies done in their names.The National Academies include:* National Academy of Sciences...
and one year in 1938–39 at the Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
in Princeton. In 1942 he took a leave of absence to do applied mathematics for the US government during World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
. Immediately after the war he worked on the ENIAC
ENIAC
ENIAC was the first general-purpose electronic computer. It was a Turing-complete digital computer capable of being reprogrammed to solve a full range of computing problems....
project, in 1945 and 1946. Under a Fulbright fellowship
Fulbright Program
The Fulbright Program, including the Fulbright-Hays Program, is a program of competitive, merit-based grants for international educational exchange for students, scholars, teachers, professionals, scientists and artists, founded by United States Senator J. William Fulbright in 1946. Under the...
, he collaborated with Robert Feys
Robert Feys
Robert Feys was a Belgian logician and philosopher, who worked at the University of Leuven .In 1958 Feys and Haskell B. Curry devised the type inference algorithm for the simply typed lambda calculus ....
in Louvain
Leuven
Leuven is the capital of the province of Flemish Brabant in the Flemish Region, Belgium...
, Belgium
Belgium
Belgium , officially the Kingdom of Belgium, is a federal state in Western Europe. It is a founding member of the European Union and hosts the EU's headquarters, and those of several other major international organisations such as NATO.Belgium is also a member of, or affiliated to, many...
. After retiring from Penn State in 1966, Curry accepted a position at the University of Amsterdam. In 1970, after finishing the second volume of his treatise on the combinatory logic, Curry retired from the University of Amsterdam and returned to State College, Pennsylvania.
Haskell Curry died on September 1, 1982 in State College, Pennsylvania.
Work
The focus of Curry's work were attempts to show that combinatory logicCombinatory logic
Combinatory logic is a notation introduced by Moses Schönfinkel and Haskell Curry to eliminate the need for variables in mathematical logic. It has more recently been used in computer science as a theoretical model of computation and also as a basis for the design of functional programming...
could provide a foundation for mathematics. Towards the end of 1933, he learned of the Kleene–Rosser paradox from correspondence with John Rosser. The paradox, developed by Rosser and Stephen Kleene had proved the inconsistency of a number of related formal systems including the lambda calculus and Curry's own system. However, unlike Church, Kleene, and Rosser, Curry did not give up on the foundational approach, saying that he did not want to "run away from paradoxes."
By working in the area of Combinatory Logic for his entire career, Curry essentially became the founder and biggest name in the field. Combinatory logic is the foundation for one style of functional programming language. The power and scope of combinatory logic is quite similar to that of the lambda calculus
Lambda calculus
In mathematical logic and computer science, lambda calculus, also written as λ-calculus, is a formal system for function definition, function application and recursion. The portion of lambda calculus relevant to computation is now called the untyped lambda calculus...
of Alonzo Church
Alonzo Church
Alonzo Church was an American mathematician and logician who made major contributions to mathematical logic and the foundations of theoretical computer science. He is best known for the lambda calculus, Church–Turing thesis, Frege–Church ontology, and the Church–Rosser theorem.-Life:Alonzo Church...
, and the latter formalism has tended to predominate in recent decades.
He taught at Harvard, Princeton
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
, and from 1929 to 1966, at the Pennsylvania State University
Pennsylvania State University
The Pennsylvania State University, commonly referred to as Penn State or PSU, is a public research university with campuses and facilities throughout the state of Pennsylvania, United States. Founded in 1855, the university has a threefold mission of teaching, research, and public service...
. In 1942, he published Curry's paradox
Curry's paradox
Curry's paradox is a paradox that occurs in naive set theory or naive logics, and allows the derivation of an arbitrary sentence from a self-referring sentence and some apparently innocuous logical deduction rules...
. In 1966 he became professor of mathematics at the Universiteit van Amsterdam
Universiteit van Amsterdam
The University of Amsterdam or the UvA is a public research university located in Amsterdam, the Netherlands. Founded in 1632 as the Athenaeum Illustre by the scholars Gerardus Vossius and Caspar Barlaeus, it is the third-oldest university in the Netherlands...
.
Curry also wrote and taught mathematical logic
Mathematical logic
Mathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...
more generally; his teaching in this area culminated in his 1963 Foundations of Mathematical Logic. His preferred philosophy of mathematics was formalism (cf. his 1951 book), following his mentor Hilbert, but his writings betray substantial philosophical curiosity and a very open mind about intuitionistic logic
Intuitionistic logic
Intuitionistic logic, or constructive logic, is a symbolic logic system differing from classical logic in its definition of the meaning of a statement being true. In classical logic, all well-formed statements are assumed to be either true or false, even if we do not have a proof of either...
.
Major publications
- 1930 Grundlagen der kombinatorischen Logik. American Journal of Mathematics
- 1951. Outlines of a formalist philosophy of mathematics. North Holland.
- 1958 (with Robert FeysRobert FeysRobert Feys was a Belgian logician and philosopher, who worked at the University of Leuven .In 1958 Feys and Haskell B. Curry devised the type inference algorithm for the simply typed lambda calculus ....
). Combinatory Logic I. North Holland. - 1972 (with J. R. Hindley, J. P. Seldin). Combinatory Logic II. North-Holland, 1972.
- 1979 (1963). Foundations of Mathematical Logic. Dover.
See also
- CurryingCurryingIn mathematics and computer science, currying is the technique of transforming a function that takes multiple arguments in such a way that it can be called as a chain of functions each with a single argument...
in combinatory logic - Curry's paradoxCurry's paradoxCurry's paradox is a paradox that occurs in naive set theory or naive logics, and allows the derivation of an arbitrary sentence from a self-referring sentence and some apparently innocuous logical deduction rules...
- Functional programmingFunctional programmingIn computer science, functional programming is a programming paradigm that treats computation as the evaluation of mathematical functions and avoids state and mutable data. It emphasizes the application of functions, in contrast to the imperative programming style, which emphasizes changes in state...
- The Lambda calculusLambda calculusIn mathematical logic and computer science, lambda calculus, also written as λ-calculus, is a formal system for function definition, function application and recursion. The portion of lambda calculus relevant to computation is now called the untyped lambda calculus...
- Curry–Howard correspondence
Further reading
- Seldin, J.P., and Hindley, J.R., eds., 1980. To H.B. Curry: Essays on combinatory logic, lambda calculus, and formalism. Academic Press. Includes biographical essay.
External links
- Curry archives provides images of several hundred manuscript pages from 1920 to 1931.
- CLg. bibliography 587 pp