Problem Set Two, CS257, Spring 1999


Due 7pm Tue Feb 2			(the short time allowed is to
					honor valiant programmers
turn in via				worldwide struggling before
 ~cslab/bin/cs257-handin ps2.scm	the Jan 1, 2000 deadline)

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	PROBLEM 1		No matter what happens, the U.S. Navy
				is not going to be caught napping.

				-Secretary of the Navy Frank Knox,
				 December 5, 1941                       

Define the predicate DATE-OKAY? which takes three arguments: a year, a
month (as a number), and a day of the month.  It returns true iff the
three arguments correspond to a valid date - including months with
only 30 days, leap years, etc.  Also if any of the arguments are
inappropriate the routine should return #f rather than getting an
error.

Your function should assume that the current Gregorian calendar
extends forward and backward in time forever - don't worry about the
10 missing days of Pope Pious or things like that.

Examples: (date-okay? 1963 9 17) -> #t        (17-Sep-1963 is okay)
	  (date-okay? 1963 2 29) -> #f        because '63 wasn't a leap year
	  (date-okay? 1963 13 2) -> #f        13 isn't a valid month
	  (date-okay? 1963 9 17.5) -> #f      17.5 isn't a valid day

Hint1: your code had better be clear rather than a big mess, because if
it's a big mess it'll ooze small bugs.
						It is vain to do with more
						what can be done with fewer.
							-- William of Occam,
							   14th-century

Hint2: break things up into pieces ... but be sure to choose the right
pieces.

Hint3: liberal use of AND and OR, and avoiding explicit #f or #t,
tends to clarify the logic of this kind of code.

Hint4: You may need to look up the rule for what constitutes a leap
year in the library.  If you don't know how, ask a librarian!

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			      PROBLEM 2

Indent this nicely:

(+ (* (+ (* a u u u) (* b u u) (* c u) d) (+ (* a v v v) (* b v v) (*
c v) d)) (* (+ (* a w w w) (* b w w) (* c w) d) (+ (* a x x x) (* b x
x) (* c x) d)) (* (+ (* a y y y) (* b y y) (* c y) d) (+ (* a z z z)
(* b z z) (* c z) d)))

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			     Extra Credit

Goof around with Scheme, and write a short description of something
unexpected but cool you found by playing, rather than by reading the
documentation.  Be sure to explain why it's cool, and how you bumped
into it.

Eg: (+) evaluates to 0, which is the identity element for addition.