Title: Scheme Challenge.

Instructions: Part 1. Do this part individually.

A.  Rephrasing.

 Write a Scheme procedure that takes a list representing an
  English sentence in the active voice and returns a sentence
  meaning the same thing, but in the passive voice.
 For example, the behavior should work as follows:

 (active-to-passive '(MIKE CARVED THE PUMPKIN))
  ->
  (the pumpkin was carved by mike)

 You may assume the following:
 1. The sentence has the form
     [SNP][PTAVV][SSNP]
 2. A simple noun phrase ([SNP]) is either someone's one-word name (e.g., MIKE)
 or a common noun
    with an article (A, AN, or THE) in front of it.

 3. A past-tense active voice verb ([PTAVV]) is one of the verbs
    STUDIED, ATE, TOOK, BOUGHT, WROTE, READ, CARVED, CELEBRATED.
 4. A simple singular noun phrase ([SSNP]) is a simple noun phrase
    that represents a single person, place, thing, or idea.
    For example A BOOK is such a phrase but THE PEOPLE is not.
 5. You may hard-code lists of words or word pairs for making
    the translations or for testing the properties of words.


  You should define a helper procedure called VERB-PAST-PARTICIPLE.
  VERB-PAST-PARTICIPLE should take a word like THREW and
  return THROWN.  Any word that it doesn't specifically know about should be
  returned unchanged.  This will work for regular verbs like
  CELEBRATED, which has its past participle identical to its
  direct past form.  Some of the irregular verbs it should know about
  are to eat (ATE -> EATEN), to take (TOOK -> TAKEN), to write
  (WROTE -> WRITTEN), and optionally, the following:
  to do (DID -> DONE), to throw (THREW -> THROWN) and to ride
  (RODE -> RIDDEN).

B. More Rephrasing

 Extend your answer to A by choosing and implementing one of the
 following options:

 i. Handle plural objects as well as singular objects for the
    second noun phrase.
    Define and make use of a procedure PLURAL?
    PLURAL? would return #f on PUMPKIN but #t on PUMPKINS, etc.
    (Again, you can hard-code a list of plural words in your procedure.)
    The sentence (MIKE CARVED THE PUMPKINS) should then translate to
    (THE PUMPKINS WERE CARVED BY MIKE).

 ii. Handle present-tense verbs as well as past-tense verbs.
    You may assume that the subject noun phrases will be singular
    as in (MIKE EATS COLESLAW); you don't have to handle
    (THE GUESTS EAT COLESLAW).  The former list should translate
    to (coleslaw is eaten by mike).

 iii. Handle sentences in which the future tense is used, as in
    (MIKE WILL EAT COLESLAW).  This should translate to
    (coleslaw will be eaten by mike).

 iv. Handle sentences in which a simple prepositional phrase
    may follow either or both of the two noun phrases.  For example,
    (THE MAN WITH A KNIFE ATE THE OYSTER WITH A PEARL).
    This should translate to
    (THE OYSTER WITH A PEARL WAS EATEN BY THE MAN WITH A KNIFE).
    You may assume that such a prepositional phrase has the form 
    [Pp][SNP]
    Where Pp is a preposition such as OF, WITH, FROM, IN, ABOUT,
    OVER, UNDER, ON, BY, or THROUGH.

 v. Recognize whether a sentence is an active-voice or passive
    voice sentence, and then translate it to the other form.
    Your top level function should then be called CHANGE-VOICE
    rather than ACTIVE-TO-PASSIVE.

C. Extra Rephrasing (optional)
 For 5 points of extra credit, implement all four options above.
 For 10 points of extra credit, implement all five options
  above in such a way that they all can work together in a
  natural way.
  In this option, you should have procedures named PAST?
  and PRESENT? that return #t if their argument is a past or
  present-tense verb, respectively.


 Test examples will be provided later.

 Log into INFACT

 Post your answer as (group-invisible) replies to the message
 from SLT entitled, "Assignment 2, Part 1." (posted on Oct 15).

In this part, turn in your solutions using INFACT, but only one 
solution per team is required for each problem.
One team member should reply to
the instructor's message corresponding to Assignment 2, Part 2, D,
or E.

D. Team warmup with macro programming.
    (Note modification made Oct 14)

    Write a Scheme macro INFIX that takes keywords PLUS and TIMES that
    lets the user write simple arithmetic expressions in
    a kind of parenthesized infix but that evaluate properly in Scheme.
    Examples:
    (INFIX 1 PLUS 2) -> 3
    (INFIX (INFIX 10 TIMES 1/2) PLUS (INFIX 3/4 TIMES 8)) -> 11
    You can assume that the addition and multiplication are always
    performed on two operands at a time.

E. The Scheme Challenge.

Write a collection of Scheme procedures that translate algebra
problems stated in English into collections of Scheme formulas.
(Optional:) Provide a Scheme procedure to solve the problems.

This will be a solver for word problems using algebra.
An example of a word problem, encoded as a list, is the following: 

     (if the area of a circle is pi times the square of the radius

     and the radius is 10 meters

     then what is the area of the circle ?)

In 1964, the Ph.D. thesis of Daniel Bobrow presented a program called
STUDENT which could solve problems posed in this manner.  In this
option, you will use Scheme to reimplement some of the functionality
of STUDENT.