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Natural Numbers:
0 : s.z.z
1 : s.z.s(z)
2 : s.z.s(s(z))
3 : s.z.s(s(s(z)))
etc.
Successor ("add one") function:
S : a.b.c.b(a b c)
Multiply function:
M: a.b.c.a(b c)
Answer the following questions:
#1. Write and show the full evaluation of the following -applications:
- S 0
- S 1
#2. Prove (or argue as fully as you can) that S works for all natural numbers.
#3. Write and show the full evaluation of the following -application:
(M 2 3)
#4. Prove (or argue as fully as you can) that M works for all pairs of natural numbers.
#5. BONUS philosophical question: do you think there is a -application that describes the entire universe in every aspect? Why or why not?
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