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43 lines
1.4 KiB
43 lines
1.4 KiB
2 years ago
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Exercise 2.85: This section mentioned a method
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for “simplifying” a data object by lowering it in the tower of types as far
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as possible. Design a procedure drop that accomplishes this for the
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tower described in Exercise 2.83. The key is to decide, in some general
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way, whether an object can be lowered. For example, the complex number
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1.5
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0
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i
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can be lowered as far as real, the complex number
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1
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+
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0
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i
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can
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be lowered as far as integer, and the complex number
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2
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+
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3
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i
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cannot
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be lowered at all. Here is a plan for determining whether an object can be
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lowered: Begin by defining a generic operation project that “pushes”
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an object down in the tower. For example, projecting a complex number would
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involve throwing away the imaginary part. Then a number can be dropped if,
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when we project it and raise the result back to the type we
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started with, we end up with something equal to what we started with. Show how
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to implement this idea in detail, by writing a drop procedure that drops
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an object as far as possible. You will need to design the various projection
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operations119 and
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install project as a generic operation in the system. You will also
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need to make use of a generic equality predicate, such as described in
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Exercise 2.79. Finally, use drop to rewrite apply-generic
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from Exercise 2.84 so that it “simplifies” its answers.
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