Stephen Cole Kleene斯蒂芬·科尔·克莱尼（Stephen Cole Kleene，1909年1月5日－1994年1月25日）美国数学家、逻辑学家，出生于美国康涅狄克州的哈特福德。
他的递归论研究有助于奠定理论计算机科学的基础。他的父亲古斯塔夫·克莱因（Gustav Adolph Kleene）是一位经济学教授，母亲艾丽丝·科尔（Alice Lena Cole）是一位诗人。
克莱因曾就读于阿默斯特学院（Amherst），1934年获普林斯顿博士学位，他的导师丘奇（Alonzo Church）是著名的逻辑学家。
丘奇在1936年使用lambda演算来证明了判定问题是没有答案的。二战期间成为美国海军的教员。
他也是博物学家，曾发现蝴蝶的新品种。并且喜欢旅行和登山。
美国数理逻辑学家克林编辑本段回目录
Stephen Cole Kleene，1909～1994
Stephen Cole Kleene美国数理逻辑学家。生于康涅狄格州哈特福德。1930年毕业于阿默斯特学院，1934年获普林斯顿大学博士学位。曾在普林斯顿大学、麦迪逊威斯康星大学、阿默斯特学院任教，1979年退休。先后当选为符号逻辑协会主席、国际科学与哲学史联合会主席、美国全国科学院院士、美国艺术与科学学院院士。
曾应邀在国际数学家大会上作报告，并于1983年获美国数学会斯蒂尔奖，于1990年获美国国家科学奖章。1994年卒于威斯康星的麦迪逊。
克林的主要贡献在递归函数理论和有效的可计算性方面。他建立了递归函数类的基本数学性质，并证明了递归函数的概念与可计算数论函数的直觉概念是一致的；给出了克林范式定理和克林递归定理；20世纪40年代，他发展了算术层和高型算术层；1950年，他和波斯特用相对递归定义了“不可解性的度”，有人称之为克林一波斯特不可解理论；1955年开始，他把算术分层分类推广到了广泛的超算术、归纳和解析关系等；1959年开始，他研究了可由递归定义的泛函，还引入了“可数泛函”，从而推广了可计算性理论，对理论计算机科学有重大影响。
与其学生合著有《直觉主义数学的基础，与递归函数的关系》。
个人简介编辑本段回目录
Stephen Cole Kleene (January 5, 1909, Hartford, Connecticut, USA – January 25, 1994, Madison, Wisconsin) was an American mathematician who helped lay the foundations for theoretical computer science. One of many distinguished students of Alonzo Church, Kleene, along with Alan Turing, Emil Post, and others, is best known as a founder of the branch of mathematical logic known as recursion theory. Kleene's work grounds the study of which functions are computable. A number of mathematical concepts are named after him: Kleene hierarchy, Kleene algebra, the Kleene star (Kleene closure), Kleene's recursion theorem and the Kleene fixpoint theorem. He also invented regular expressions, and was a leading American advocate of mathematical intuitionism.
Kleene pronounced his last name /ˈkleɪniː/ "clay-knee"; /ˈkliːniː
Stephen Cole Kleene/ and /ˈkliːn/ are common mispronunciations. (His son, Ken Kleene, wrote: "As far as I am aware this pronunciation is incorrect in all known languages. I believe that this novel pronunciation was invented by my father.")
Kleene was awarded the BA degree from Amherst College in 1930. He was awarded the Ph.D. in mathematics from Princeton University in 1934. His thesis, entitled A Theory of Positive Integers in Formal Logic, was supervised by Alonzo Church. In the 1930s, he did important work on Church's lambda calculus. In 1935, he joined the mathematics department at the University of Wisconsin-Madison, where he spent nearly all of his career. After two years as an instructor, he was appointed assistant professor in 1937.
While a visiting scholar at the Institute for Advanced Study in Princeton, 1939-40, he laid the foundation for recursion theory, an area that would be his lifelong research interest. In 1941, he returned to Amherst College, where he spent one year as an associate professor of mathematics.
During World War II, Kleene was a lieutenant commander in the United States Navy. He was an instructor of navigation at the U.S. Naval Reserve's Midshipmen's School in New York, and then a project director at the Naval Research Laboratory in Washington, D.C.
In 1946, Kleene returned to Wisconsin, becoming a full professor in 1948 and the Cyrus C. MacDuffee professor of mathematics in 1964. He was chair of the Department of Mathematics and Computer Science, 1962-63, and Dean of the College of Letters and Science from 1969 to 1974. The latter appointment he took on despite the considerable student unrest of the day, stemming from the Vietnam War. He retired from the University of Wisconsin in 1979. The mathematics library at the University of Wisconsin was renamed in his honour.
Stephen Cole Kleene著作Kleene's teaching at Wisconsin resulted in three texts in mathematical logic, Kleene (1952, 1967) and Kleene and Vesley (1965), often cited and still in print. Kleene (1952) wrote alternative proofs to the Gödel's incompleteness theorems that enhanced their canonical status and made them easier to teach and understand. Kleene and Vesley (1965) is the classic American introduction to intuitionist logic and mathematics. Kleene's standing among logicians is suggested by the witticism "Kleeneliness is next to Gödeliness", a pun on "Cleanliness is next to godliness".[citation needed]
Kleene served as president of the Association of Symbolic Logic, 1956-58, and of the International Union of the History and the Philosophy of Science, 1961. In 1990, he was awarded the National Medal of Science.
Kleene and his spouse Nancy Elliott had four children. He had a lifelong devotion to the family farm in Maine. An avid mountain climber and canoeist, he had a strong interest in nature and the environment and was active in many conservation causes.
重要著作一览表编辑本段回目录
1952. Introduction to Metamathematics. North-Holland (originally published by D. Van Nostrand).
1956. "Representation of Events in Nerve Nets and Finite Automata" in Automata Studies. Claude Shannon and John McCarthy, eds.
1965 (with Richard Eugene Vesley). The Foundations of Intuitionistic Mathematics. North-Holland.
1967. Mathematical Logic. John Wiley. Dover reprint, 2001. ISBN 0486425339.
1981. "Origins of Recursive Function Theory" in Annals of the History of Computing 3, No. 1.
Lambda 演算简介编辑本段回目录
许多数学工具都是以集合为基础的，而lambda 演算与众不同，它是以函数演算为基础的．它允许任意高阶的
函数运算，也就是说，一个函数的输人和输出都可以是函数．这个特点使它特别适于用作语义描述的表示方
法，尤其是在指称语义描述中更需要用到它．
Stephen Cole KleeneLambda演算是一个形式系统，它被设计出来用来研究函数定义，函数应用和递归。它是在二十世纪三十年代由Alonzo Church 和 Stephen Cole Kleene发明的。Church在1936年使用lambda演算来证明了判定问题是没有答案的。Lambda演算可以用来清晰的定义什么是一个可计算的函数。两个lambda演算表达式是否相等的问题不能够被一个通用的算法解决，这是第一个问题，它甚至排在停机问题之前。为了证明停机问题是没有答案的，不可判定性能够被证明。Lambda演算对于函数式编程语言（例如lisp）有重大的影响。
λ-演算可以说是最简单、最小的一个形式系统。它是在二十世纪三十年代由Alonzo Church 和 Stephen Cole Kleene发明的。至今，在欧洲得到了广泛的发展。可以说，欧洲的计算机科学是从λ-演算开始的，而现在仍然是欧洲计算机科学的基础，首先它是函数式程序理论的基础，而后，在λ-演算的基础上，发展起来的π-演算、χ-演算，成为近年来的并发程序的理论工具之一，许多经典的并发程序模型就是以π-演算为框架的。
