Submission

Published date

Nov. 6, 2017

Due date

Nov. 13, 2017

Method of Submission

OCW-i

Please convert/save your essay as a PDF file and upload it at the respective page of OCW-i

Delayed Submission

Each submission is weighed according to half-value period of 10 days. That means if you submit a perfect answer 30 days after the due date, you will receive \(1/8\) the full points. In other words, you lose \(1 - 1/2^{1/10} \approx 6.7\text {%}\) points each day after the due date has passed. It is very wise to keep the due date.¹

Assignment

Answer either (or both) questions and submit your answer as a PDF document. If you answer both questions the better answer will be chosen for your evaluation.

1. What’s \(\alpha\)-conversion for? What kind of problems we will see if \(\alpha\)-conversion were not applied? Find Min-Caml programs that give incorrect answers in absence of proper \(\alpha\)-conversion.

   Hint: You may want to consider the reason why inline.ml refers to Alpha.g.

2. Are optimization modules interdependent? Yes, but in what way? Find a pair of optimization modules \(A\) and \(B\) such that for a program \(P\), \(B\) is effective when it is applied after \(A\):

   \[^\exists P. B(P) = P \text { but } B(A(P)) \not= A(P)\]

The questions seem simple. If you think that they can be described in a short paragraph please think little bit more. Please at least take time to understand the schematic definitions. The implementation may give insight to those who are more implementation-oriented people. If you think enough you may discover more profound issues being questioned on you.

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