CSE340Fall2009HW4Solution

CSE340Fall2009HW4Solution - Arizona State University Fulton...

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Unformatted text preview: Arizona State University Fulton School of Engineering Computer Science and Engineering CSE 340 Fall 2009 Homework 4 Solution 1. scc 3 = 4 ? = n. λ s. λ z. s(nsz) 3 = ? . . ? ( ? ( ? )) 4 = ? . . ? ( ? ( ? ( ? ))) ? 3 = n. λ s. λ z. s ¡ nsz ¢£ ¤? ′ . ′ . ? ′ ? ′ ¡? ′ ′ ¢£¥ = ? . . ? ¦¤λ s ′ . λ z ′ . s ′ s ′ ¡ s ′ z ′ ¢£¥ ?§ = ? . . ? ¦¤ ′ . ? ?¡?′¢£¥ § = ? . . ? ¤? ?¡?¢£¥ = 4 2. define "or" operation in lambda calculus OR = λ b. λ c. b tru c We first note that OR u v = (OR = λ b. λ c. b tru c ) u v = ( λ c. u tru c) v = u tru v ?? : ¡ ??? ??? = tru tru tru = = ? . . ?¢ ? . . ?¢??? = . ? . . ?¢??? = ??? ¡ ??? £ = ??? ??? £ = ? . . ?¢ ? . . ?¢£ = .....
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CSE340Fall2009HW4Solution - Arizona State University Fulton...

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