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␈↓ α∧␈↓␈↓ u1


␈↓ α∧␈↓α␈↓ ¬0TERM PROJECTS FOR CS206

␈↓ α∧␈↓␈↓ αTThe␈α⊂term␈α⊂project␈α⊂is␈α⊂a␈α∂chance␈α⊂to␈α⊂write␈α⊂a␈α⊂substantial␈α∂LISP␈α⊂program␈α⊂and␈α⊂write␈α⊂it␈α⊂up.␈α∂ A
␈↓ α∧␈↓second possibility is to write and prove correct a LISP program of moderate size.

␈↓ α∧␈↓␈↓ αTIt␈α
is␈αpossible␈α
to␈α
get␈αa␈α
B␈αin␈α
the␈α
course␈αwithout␈α
a␈α
term␈αproject␈α
but␈αnot␈α
an␈α
A.␈α A␈α
C␈αproject␈α
will
␈↓ α∧␈↓not␈αhelp␈αget␈αa␈αB.␈α The␈αwriteup␈αis␈αthe␈αprimary␈αproduct␈αthat␈αwill␈αbe␈αgraded,␈αso␈αmake␈αit␈αclear␈αwhat
␈↓ α∧␈↓your program does and why.

␈↓ α∧␈↓␈↓ αTHere are some topics that have been used in the past and may be used again:

␈↓ α∧␈↓1. Improving the LCOM4 compiler.  The LCOM4 compiler may be made to

␈↓ α∧␈↓␈↓ β$1.1. Compile iterative code when possible.

␈↓ α∧␈↓␈↓ β$1.2. Compile good arithmetic code.

␈↓ α∧␈↓␈↓ β$1.3. Compile ␈↓↓label.␈↓

␈↓ α∧␈↓␈↓ β$1.4. Compile program feature code.

␈↓ α∧␈↓␈↓ β$1.5. Meet some other deficiency that you notice.

␈↓ α∧␈↓2. Write a compiler that gives very efficient code for arithmetic expressions.

␈↓ α∧␈↓3.␈α
Play␈α∞a␈α
game,␈α
e.g.␈α∞3-dimensional␈α
tic-tac-toe.␈α
 If␈α∞you␈α
do␈α
this␈α∞one,␈α
remember␈α
to␈α∞hold␈α
individual
␈↓ α∧␈↓test␈αruns␈αto␈αa␈αfew␈αseconds.␈α It␈αis␈αvery␈αeasy␈αto␈αhog␈αthe␈αcomputer␈αby␈αmaking␈αa␈αtree␈αsearch␈αone␈αstep
␈↓ α∧␈↓deeper.

␈↓ α∧␈↓4.␈α∞A␈α∂program␈α∞to␈α∂play␈α∞sequence␈α∂solitaire.␈α∞ The␈α∂game␈α∞starts␈α∂with␈α∞all␈α∂cards␈α∞in␈α∂the␈α∞hand,␈α∂and␈α∞the
␈↓ α∧␈↓object␈α
is␈α
to␈αget␈α
them␈α
into␈αthe␈α
four␈α
final␈αpiles␈α
with␈α
the␈α
aid␈αof␈α
the␈α
four␈αstorage␈α
piles.␈α
 The␈αfirst␈α
final
␈↓ α∧␈↓pile␈αwants␈αthe␈αsequence␈α(A␈α2␈α3␈α4␈α5␈α6␈α7␈α8␈α9␈α10␈αJ␈αQ␈αK),␈αthe␈αsecond␈α(2␈α4␈α6␈α8␈α10␈αQ␈αA␈α3␈α5␈α7␈α9␈αJ␈αK),
␈↓ α∧␈↓the␈αthird␈α(3␈α6␈α
9␈αQ␈α2␈α5␈α
8␈αJ␈αA␈α4␈α
7␈α10␈αK),␈αand␈α
the␈αfourth␈α(4␈α8␈α
Q␈α3␈α7␈αJ␈α
2␈α6␈α10␈αA␈α
5␈α9␈αK).␈α A␈αmove␈α
is
␈↓ α∧␈↓either␈α
playing␈α
a␈αcard␈α
from␈α
the␈αtop␈α
card␈α
from␈αthe␈α
hand␈α
to␈αa␈α
storage␈α
pile,␈αplaying␈α
the␈α
top␈αcard␈α
from
␈↓ α∧␈↓the␈αhand␈αto␈αa␈αfinal␈αpile,␈αor␈α
playing␈αthe␈αtop␈αcard␈αon␈αa␈αstorage␈α
pile␈αto␈αa␈αfinal␈αpile.␈α The␈αtop␈αcard␈α
in
␈↓ α∧␈↓the hand may be examined before deciding what move to make.

␈↓ α∧␈↓5. Make an improved Syntax-directed computation system.

␈↓ α∧␈↓␈↓ β$5.1. Handle associative and/or commutative expressions.

␈↓ α∧␈↓6.␈α∩Write␈α⊃and␈α∩prove␈α⊃correct␈α∩a␈α⊃version␈α∩of␈α⊃␈↓↓samefringe␈↓␈α∩based␈α⊃on␈α∩the␈α⊃function␈α∩␈↓↓residue[x,y]␈↓␈α⊃that
␈↓ α∧␈↓matches␈α
the␈α
successive␈α
atoms␈α
of␈α
␈↓↓x␈↓␈α
and␈α
␈↓↓y␈α∞and␈↓␈α
whose␈α
value␈α
gives␈α
the␈α
left-over␈α
atoms␈α
if␈α∞there␈α
are
␈↓ α∧␈↓any:

␈↓ α∧␈↓␈↓↓residue[x, y] ←
␈↓ α∧␈↓↓␈↓ αT␈↓αif␈↓↓ x ␈↓αeq␈↓↓ y ␈↓αthen␈↓↓ ␈↓T␈↓↓
␈↓ α∧␈↓↓␈↓ αT␈↓αelse␈↓↓ ␈↓αif␈↓↓ ␈↓αa␈↓↓t x ∧ ␈↓αa␈↓↓t y ␈↓αthen␈↓↓ ␈↓F␈↓↓
␈↓ α∧␈↓↓␈↓ αT␈↓αelse␈↓↓ ␈↓αif␈↓↓ ␈↓αa␈↓↓t x ␈↓αthen␈↓↓ {gopher y}[λw.␈↓αif␈↓↓ x ␈↓αeq␈↓↓ ␈↓αa␈↓↓ w ␈↓αthen␈↓↓ ␈↓R␈↓↓ . ␈↓αd␈↓↓ w ␈↓αelse␈↓↓ ␈↓F␈↓↓]
␈↓ α∧␈↓↓␈↓ αT␈↓αelse␈↓↓ ␈↓αif␈↓↓ ␈↓αa␈↓↓t y ␈↓αthen␈↓↓ {gopher x}[λw.␈↓αif␈↓↓ y ␈↓αeq␈↓↓ ␈↓αa␈↓↓ w ␈↓αthen␈↓↓ ␈↓L␈↓↓ . ␈↓αd␈↓↓ w ␈↓αelse␈↓↓ ␈↓F␈↓↓]
␈↓ α∧␈↓␈↓ u2


␈↓ α∧␈↓↓␈↓ αT␈↓αelse␈↓↓ {residue[␈↓αa␈↓↓ x,␈↓αa␈↓↓ y]}[λw.
␈↓ α∧␈↓↓                ␈↓αif␈↓↓ w ␈↓αeq␈↓↓ ␈↓F␈↓↓ ␈↓αthen␈↓↓ ␈↓F␈↓↓
␈↓ α∧␈↓↓                ␈↓αelse␈↓↓ residue[␈↓αif␈↓↓ ␈↓αa␈↓↓ w ␈↓αeq␈↓↓ ␈↓L␈↓↓ ␈↓αthen␈↓↓ ␈↓αd␈↓↓ w . ␈↓αd␈↓↓ x ␈↓αelse␈↓↓ ␈↓αd␈↓↓ x,␈↓αif␈↓↓ ␈↓αa␈↓↓ w ␈↓αeq␈↓↓ ␈↓R␈↓↓ ␈↓αthen␈↓↓ ␈↓αd␈↓↓ w . ␈↓αd␈↓↓ y ␈↓αelse␈↓↓ ␈↓αd␈↓↓ y]]␈↓,

␈↓ α∧␈↓7. Write, define correctness, and prove correct a program for multiplying permutations.