Tutorial 18/05
This tutorial is about evaluation of untyped lambda calculus. Participants are supposed to program in lambda calculus and carry out reductions by hand to prove equations about lambda terms.
Homework 3 was changed; metavariables v₁, v₂ etc. were introduced so that the call-by-value reduction rules from the lecture notes apply.
Live exercises
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What are Church Booleans? What are tru, fls, and, or, not?
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Define XOR on Church Booleans.
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What are Church numerals? What is addition on Church numerals?
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Prove
1 + 1 = 2
. What did you prove actually? -
Prove that addition is associative:
(k + m) + n = k + (m + n)
for all Church numerals k, m, n. -
Can you prove that addition is commutative?
Result
Most students were not familiar with lambda calculus and got stuck writing XOR. A minority managed to prove 1 + 1 = 2.
How many tasks can you do after homework 4?