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Lambda Calculus

Explore the evolution of computing from Gottfried Leibniz to Alan Turing, including Lambda Calculus and decision problem solutions by Alonzo Church. Learn about the Enigma machine and Bletchley Park.

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Lambda Calculus

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  1. Lambda Calculus Introduction

  2. History Gottfried Wilhelm Leibniz (1646 - 1716) "It is unworthy of excellent men to lose hours like slaves in the labour of calculation which could safely be regulated to anyone else if machines were used." Stepped Reckoner Sought a formal language for a machine to determine the truth of mathematical statements.

  3. Entscheidungsproblem The “decision problem” (1928): Find an algorithm which takes as input a description of a formal language and a mathematical statement expressed in that language and outputs true or false depending on the mathematical validity of the statement. David Hilbert William Ackermann

  4. Alonzo Church • Church’s Theorem (1936) • Answered the decision problem in the negative Alonzo Church 1903-1995

  5. Alonzo Church • Defined the Lambda (l) Calculus - a language foundation for computing • Led to family of functional programming languages

  6. Alan Turing • Independently answered the decision problem in the negative • Defined the Turing Machine – a machine foundation for computing • Led to Von Neumann computers and family of imperative programming languages Alan Turing 1912-1954 • Work at Bletchley Park in WW2 • Died by suicide (apple laced with cyanide)

  7. Bletchley Park Turing designed the Bombe machine to decrypt Enigma messages. The Enigma Cryptographic Device

  8. The l Calculus <expression> := <name> | <function> | <application> <function> := l <name> . <expression> <application> := <expression> <expression>

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