# PL7 - CSE233/CSE300 1 Lambda Calculus

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1 /Users/ldm/courses/Spring05_CSE300/lectures/PL9.sxi 1 CSE233/CSE300 Lambda Calculus

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2 /Users/ldm/courses/Spring05_CSE300/lectures/PL9.sxi 2 Overview Computing with Lambda How to represent Booleans, Naturals Combinators I K S Recursion Y
3 /Users/ldm/courses/Spring05_CSE300/lectures/PL9.sxi 3 Lambda Calculus As a programming language We must be able to express Constants Booleans Naturals Elementary operations Successor Addition Multiplication We must be able to deal with recursion

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4 /Users/ldm/courses/Spring05_CSE300/lectures/PL9.sxi 4 Booleans Hint Think about them as functions What are boolean used for ? Branching
5 /Users/ldm/courses/Spring05_CSE300/lectures/PL9.sxi 5 Naturals What we need A function to represent ZERO A function to get the successor of a natural n A function to get the predecessor of a natural n A function to test for ZERO Church numerals Zero: Е s. z.z λ One: Е s. z.s z λ Two: Е s. z.s (s z) λ Three: Е s. z.s (s (s z)) λ

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## This note was uploaded on 01/11/2012 for the course DKFKDF dfdfd taught by Professor Dsfdsfdsf during the Spring '11 term at APU Japan.

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PL7 - CSE233/CSE300 1 Lambda Calculus

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