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Lambda Calculus

Lambda Calculus. Introduction. 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.

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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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