CSCI 2041 Lab09: Functors and Memoization

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                            LAB 09 QUESTIONS
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- Name: (FILL THIS in)
- NetID: (THE kauf0095 IN kauf0095@umn.edu)

Answer the questions below according to the lab specification. Write
your answers directly in this text file and submit it to complete the
lab.


PROBLEM 1: Memfunc1 Module
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(A)
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  Examine `memfunc1.ml' and answer the following questions.
  1. What is the name of the functor defined in the module?
  2. Like all functors, this one takes a parameter module. What bindings
     must the parameter module have according to its signature?
  3. The module that is created by the functor has several internal
     bindings but only one of them is publicly visible. What is it and
     how is this visibility control enforced?


(B)
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  As in any other place a module is being defined, functors can
  establish nested modules.  The functor in `Memfunc1' creates two
  nested modules within its body.  Describe these two modules providing
  their names and what their purpose appears to be. Describe how
  bindings of the parameter module are used in these nested modules.


(C)
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  Analyze the bindings for `arg_ret_map' and the function `call'.
  Describe how these are used in conjunction the a function carried by
  the parameter module.


PROBLEM 2: fib Program
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(A)
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  Examine the first section of the provided `fib.ml' file. Describe how
  the functor in `memfunc1.ml' is used at the top of `fib.ml'. Include a
  description of how the parameter module to the functor is created.


(B)
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  The main intent of the program in `fib.ml' is to compare the amount of
  time it takes to make repeated calls to the `fib' function versus a
  memoized version of it in `MemoFib.call'.  Analyze the main code for
  the program.
  1. Identify where calls to `fib' and `MemoFib.func' are made.
  2. Identify where the results of these calls are stored.
  3. Describe what function is used to gather timing information on how
     long the repeated function calls take.


(C)
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  Use `ocamlc' to Compile and run the `fib.ml' program together with its
  dependency `memfunc1.ml'. Run the resulting program with and paste in
  the output in the space below.

  Note that the program requires command line argument, an integer. Use
  30 as the parameter.


(D)
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  Describe why the time to run `fib' and `MemoFib.call' are very similar
  in the first timing loop but drastically different in the second
  timing loop. Relate your answer to the internal workings of the
  `Memofunc1.Memoize' functor.


Optional Enrichment Problems
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  1. We have seen that `MemoFib.call 30' will take some time on the
     first call but a subsequent call runs in almost no time.  Does this
     mean that the speed of `MemoFib.call 31' will be shorter as well?
     Why or why not?
  2. The functor established in `Memofunc1' works for functions of 1
     parameter.  How would one go about handling functions of two,
     three, or four arguments? If one is writing functions to be
     compatible with memoization, how could one write the functions of
     multiple arguments so as to avoid the need write more functors?