Home > Alonzo Church

He is best known for the development of the lambda calculusThe lambda calculus is a formal system designed to investigate function definition, function application, and recursion. It was introduced by Alonzo Church and Stephen Cole Kleene in the 1930s; Church used the lambda calculus in 1936 to give a negative an in his famous 1936Events January-February January 15 The first building to be completely covered in glass is completed in Toledo, Ohio, for the Owens-Illinois Glass Company. January 20 Death of George V of the United Kingdom. His son Edward VIII succeedes him as King of th paper showing the existence of an "undecidable problem" within it. This result preempted Alan TuringAlan Mathison Turing ( June 23, 1912 June 7, 1954) was a British mathematician, logician, and cryptographer, and is considered to be one of the fathers of modern computer science. He provided an influential formalisation of the concept of algorithm and co's famous work on the halting problemIn computability theory the halting problem is a decision problem which can be informally stated as follows: : Given a description of an algorithm and its initial input, determine whether the algorithm, when executed on this input, ever halts (completes). which also demonstrated the existence of a problem unsolvable by mechanical means. Supervising Turing's doctoral thesis, they then showed that the lambda calculus and the Turing machineThe Turing machine is an abstract model of computer execution and storage introduced in 1936 by Alan Turing to give a mathematically precise definition of algorithm or 'mechanical procedure'. As such it is still widely used in theoretical computer science used in Turing's halting problem were equivalent in capabilities, and subsequently demonstrated a variety of alternative "mechanical processes for computation" had equivalent computational abilities. This resulted in the Church-Turing thesisIn the computability theory the Church-Turing thesis Church's thesis Church's conjecture or Turing's thesis named after Alonzo Church and Alan Turing, is a hypothesis about the nature of mechanical calculation devices, like computers, and what kind of alg, which is also known as Church's Thesis and Turing's Thesis as there is dispute about who proposed it first.

Church's other doctoral students included Stephen Kleene, J. Barkley RosserIn mathematical logic, the Church-Rosser theorem states that, in the lambda calculus, a term has at most one normal form. More formally, the Church-Rosser property states that the simply typed lambda calculus without -reduction is confluent. Specifically,, Leon Henkin, John George Kemeny, Michael O. Rabin, Dana Scott, Simon Kochen , Raymond Smullyan et al (see Enderton, In memoriam).

Church remained a professor of mathematics at Princeton until 1967, when he moved to California.

Church's lambda calculus influenced the design of the Lisp family of computer languages, as well as functional programming languages in general.