PLQ #6Done on:   Tuesday, March 2nd

Question 1 @ 2021-03-02 18:25

Warmup question:

Are the following two definitions of Y valid and equivalent?

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• 1
  Yes.
• 2
  Yes, only if we’re using an eager language.
• 3
  Yes, only if we’re using an lazy language.
• 4
  They’re equivalent, but wrong.
• 5
  They’re equivalent, but wrong: both will loop infinitely.

Question 2 @ 2021-03-02 18:30

Bob finished implementing the Y combinator in a language with Racket-like syntax.

Bob now wants to move part of the Y combinator into a helper function because he is a good Fundies 1 student who uses helper functions.

Will this newY combinator work in the same way as the first?

(Choose the best answer.)

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• 1
  Yes. We just moved the (lambda (n) ((x x) n)) to a new function and otherwise keept the same functionality.
• 2
  Yes. In newY, (x x) does not get evaluated before passed into protect as an input, so the behavior is the same.
• 3
  Yes. In newY, (x x) is evaluated before passed into protect as an input so the behavior is the same.
• 4
  No. In newY, (x x) is evaluated before passed into protect as an input, and so we will be stuck in an infinite loop.
• 5
  It depends. newY will work the same way if the language is eager.
• 6
  It depends. newY will work the same way if the language is lazy.

Question 3 @ 2021-03-02 18:35

What will the following code produce when run?

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• a
  100 ; [10 * (10+1-1)]
• b
  10! ; [the factorial of 10]
• c
  11! ; [since it’s 111098 … 32]
• d
  10! * 10 ; [since it’s 101098 … 32]
• e
  10¹⁰ ; [10^10]
• f
  No answer: it will get stuck in an infinite loop.
• g
  It will run out of memory.
• h
  It will fail with an error.

Question 4 @ 2021-03-02 18:39

Which of these is NOT a combinator?

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• 1
  (lambda (x) (x x))
• 2
  (lambda (x) (lambda (y) (x x)))
• 3
  (lambda (x) (lambda (y) ((x x) y)))
• 4
  (Y (lambda (x) (lambda (y) ((x x) y))))
• All
  of the above are combinators.
• None
  of the above are combinators.

Question 5 @ 2021-03-02 18:44

What do we get if we run the following code:

(Choose the best answer.)

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• 1

  We get a result of 1.

• 1E

  We get a result of 1 only if the language is eager.

• 1L

  We get a result of 1 only if the language is lazy.

• 2

  We get a result of 2.

• 2E

  We get a result of 2 only if the language is eager.

• 2L

  We get a result of 2 only if the language is lazy.

• 3

  We get an error.

• 3E

  We get an error only if the language is eager.

• 3L

  We get an error only if the language is lazy.