Chapter 1 Exercises

(𝜆𝑎𝑏𝑐.𝑐𝑏𝑎)𝑧𝑧(𝜆𝑤𝑣.𝑤)

(𝜆𝑏𝑐.𝑐𝑏𝑧)(𝑧)(𝜆𝑤𝑣.𝑤)

(𝜆𝑐.𝑐𝑧𝑧)(𝜆𝑤𝑣.𝑤)

(𝜆𝑤𝑣.𝑤)(𝑧𝑧)

𝑧𝑧

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(𝜆𝑥.𝜆𝑦.𝑥𝑦𝑦)(𝜆𝑎.𝑎)𝑏

(𝜆𝑦.(𝜆𝑎.𝑎)yy)(𝑏)

(𝜆𝑎.𝑎)𝑏𝑏

𝑏𝑏

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(𝜆𝑦.𝑦)(𝜆𝑥.𝑥𝑥)(𝜆𝑧.𝑧𝑞)

(𝜆𝑥.𝑥𝑥)(𝜆𝑧.𝑧𝑞)

(𝜆𝑧.𝑧𝑞)(𝜆𝑧.𝑧𝑞)

(𝜆𝑧.𝑧𝑞)(𝑞)

𝑞𝑞

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(𝜆𝑧.𝑧)(𝜆𝑧.𝑧𝑧)(𝜆𝑧.𝑧𝑦)

(𝜆𝑧.𝑧𝑧)(𝜆𝑞.𝑞𝑦)

(𝜆𝑞.𝑞𝑦)(𝜆𝑞.𝑞𝑦)

(𝜆𝑞.𝑞𝑦)(y)

yy

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(𝜆𝑥.𝜆𝑦.𝑥𝑦𝑦)(𝜆𝑦.𝑦)𝑦

(𝜆𝑥.𝜆𝑦.𝑥𝑦𝑦)(𝜆𝑞.𝑞)(𝑦)

(𝜆𝑦.(𝜆𝑞.𝑞)𝑦𝑦)(𝑦)

((𝜆𝑞.𝑞)𝑦)(𝑦)

𝑦𝑦

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(𝜆𝑎.𝑎𝑎)(𝜆𝑏.𝑏𝑎)𝑐

(𝜆𝑎.𝑎𝑎)(𝜆𝑏.𝑏𝑎)𝑐

(𝜆𝑏.𝑏𝑎)(𝜆𝑏.𝑏𝑎)(𝑐)

(𝜆𝑏.𝑏𝑎)(𝑎)(𝑐)

𝑎𝑎𝑐

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(𝜆𝑥𝑦𝑧.𝑥𝑧(𝑦𝑧))(𝜆𝑥.𝑧)(𝜆𝑥.𝑎)

(𝜆𝑥.𝜆𝑦.𝜆𝑧.𝑥𝑧(𝑦𝑧))(𝜆𝑥.𝑐)(𝜆𝑥.𝑎)

(𝜆𝑦.𝜆𝑧.(𝜆𝑥.𝑐)(𝑧)(𝑦𝑧))(𝜆𝑥.𝑎)

(𝜆𝑧.(𝜆𝑥.𝑐)(𝑧)((𝜆𝑥.𝑎)𝑧))

(𝜆𝑧.𝑐(𝜆𝑥.𝑎(𝑧)))

(𝜆𝑧.𝑐𝑎)