For this assignment, you will modify and add to functions that are provided for you in hw6.ss. Download this file, rename it YOURNAME-hw6.ss and enter your name in the comment at the top. Be careful to name your functions exactly as defined in the exercises, and be sure to comment each function as to its behavior.

PART 1: Eliza

One of the most famous/infamous programs from Artificial Intelligence was Joseph Weizenbaum's Eliza. Written in 1966, the Eliza program was intended to demonstrate the superficiality of AI programs at the time. Despite its lack of deep understanding, the program became extremely popular and earned a place in AI history.

The Eliza program is intended to simulate an interview with psychotherapist. The user interacts with the therapist by entering a comment or question, to which the therapist responds with a comment or question of its own. Despite the fact that the program utilizes no language understanding, it is able to often to produce realistic responses due to its pattern-matching capabilities.

A very basic implementation of Eliza can be found in hw6.ss. You begin by evaluating the expression (eliza), and then type in sentences as lists (with all lowercase words and no punctuation). For example,

Make the following modifications to the Eliza rules:

1. The Eliza rules currently include a rule that looks for the word "computer", and responds accordingly. However, this rule will not catch the plural "computers". Add a rule to the database that similarly responds to user input containing "computers".
   
   
2. Add a rule to the Eliza rule database that recognizes the phrase "I miss ___" in the user's input. When this phrase is found anywhere in the user input, Eliza should respond with either "Do you miss other things" or else a response of the form "What do you miss about ___".
   
   
3. Add at least three more rules to the Eliza rule database of your own design. Add a comment next to each new rule to identify it.
   
   

PART 2: DNA Translations

Add the following definitions to your YOURNAME-hw6.ss file. Note: you should comment each function with a description of its behavior.

4. Define a function named translate that takes one input, a list representing a codon, and returns the abbreviation for the corresponding amino acid. For example, (translate '(G G A)) should evaluate to G.
   
   
5. Define a function named translate-sequence that takes one input, an arbitrarly long sequence of bases, and returns the corresponding list of amino acid abbreviations. That is, the first symbol in the returned list should be the amino acid corresponding to the first three bases, the second symbol should be the amino acid corresponding to the next three bases, etc. If the length of the sequence is not a multiple of three, any trailing bases should be ignored. For example, (translate-sequence '(G G A U U C A C C C)) should evaluate to (G F T).
   
   
6. When scientists extract mRNA samples from a cell, they invariably obtain partial sequences. Since the start of the sequence may be unknown, it is unclear exactly how the codons will be grouped in an actual translation. For example, in the sequence GGAUUCACCC the codons could be grouped starting at the beginning (yielding codons GGA UUC ACC), at the second base (yielding codons GAU UCA CCC), or at the third base (yielding codons AUU CAC). In addition, it is possible that the sequence has been read backwards, so the actual sequence to be translated should be CCCACUUAGG.

   Define a function named translate-all-possible that takes one input, an arbitrarly long sequence of bases, and returns a list containing all six possible translations of that sequence. Any extra bases at the beginning or end of the sequence should be ignored in the translation. For example, (translate-all-possible '(G G A U U C A C C C)) should evaluate to ((G F T) (N S P) (I H) (P T *) (P L R) (H L)).
   
   

PART 3: Binary Trees

In class, we discussed how structured lists could be used to represent binary trees. For example, the following binary tree is represented by the list to the right:

(define ANIMALS '(dog (bird (horse () ()) (cat () ())) (possum (dog () ()) ())))

Several utility functions (empty-tree?, root, left-subtree, and right-subtree) are provided for you in hw6.ss). Add the following functions for manipulating binary trees.

7. Define a function named height that takes one input, a list representing a binary tree, and returns the height (i.e., maximum root-to-leaf path length) in the tree. For example, given the ANIMALS structure above, (height ANIMALS) should evaluate to 3.
   
   
8. Define a function named num-occur that takes two inputs, a list representing a binary tree and a value, and returns the number of occurrences of the value in that tree. For example, given the ANIMALS structure above, (num-occur ANIMALS 'dog) should evaluate to 2.
   
   
9. Define a function named contains? that takes two inputs, a list representing a binary tree and a value, and returns #t if the list contains the value (otherwise #f). For example, given the ANIMALS structure above, (contains? ANIMALS 'emu) should evaluate to #f while (contains? ANIMALS 'cat) should evaluate to #t.
   
   

PART 4: OOP in Scheme

In class, we discussed how first-class functions and closures could support the equivalent of classes, with private data and methods. The following function models a die object, where the number of sides is specified when creating the die.

For example:

10. Modify the code so that there is an additional "method" named num-rolls, which returns the number of times that die object has been rolled. Note: this will involve using non-functional features of Scheme, which is allowable in this instance since those features are hidden inside the object. In particular, you should add a variable definition inside the Die function, initialized to 0. When the roll "method" is called, you will need to update that field (using set!). Also, you should add a num-rolls "method" to enable the user to access the number of times the die has been rolled. For example: > (define d6 (Die 6)) > (d6 'roll) 3 > (d6 'roll) 4 > (d6 'num-rolls) 2