1. Spring, 2011 –– Computational Thinking – Dennis Kafura – CS 2984 Lambda Calculus Introduction

2. Spring, 2011 – Computational Thinking – Dennis Kafura – CS 2984 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. Spring, 2011 – Computational Thinking – Dennis Kafura – CS 2984 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. Spring, 2011 – Computational Thinking – Dennis Kafura – CS 2984 Alonzo Church Church’s Theorem (1936) Answered the decision problem in the negative Alonzo Church 1903-1995

5. Spring, 2011 – Computational Thinking – Dennis Kafura – CS 2984 Alonzo Church Defined the Lambda ( ) Calculus - a language foundation for computing Led to family of functional programming languages

6. Spring, 2011 – Computational Thinking – Dennis Kafura – CS 2984 Alan Turing 1912-1954 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 Work at Bletchley Park in WW2 Died by suicide (apple laced with cyanide)

7. Spring, 2011 – Computational Thinking – Dennis Kafura – CS 2984 Bletchley Park The Enigma Cryptographic Device Turing designed the Bombe machine to decrypt Enigma messages.

8. Spring, 2011 – Computational Thinking – Dennis Kafura – CS 2984 The  Calculus := | | :=. :=