A program which performs 'obvious' (non-controversial) simplifying

transformations on algebraic expressions (written in LISP prefix

notation) is described. Cancellation of inverses and consolidation

of sums and products are the basic accomplishments of the program;

however, if the user desires to do so, he may request the program to

perform special tasks, such as collect common factors from the

products in sums or expand products. Polynomials are handled by

routines which take advantage of the special form by polynomials; in

particular, division (not cancellation) is always done in terms of

polynomials. The program (run on the IBM 7090) is slightly faster

than a human; however, the computer does not need to check its work

by repeating the simplification.

Although the program is usable -- no bugs are known to exist -- it

is by no means a finished project. A rewriting of the simplify

system is anticipated; this will eliminate much of the existing

redundancy and other inefficiency, as well as implement an

identity-recognizing scheme.

This memo gives empirical justification for the assumption that the

number of bisections of an NxN (N even) checkerboard is

approximately given by the binomial coefficient (A, A/2) where 2A is

the length of the average bisecting cut.

Experience with writing large LISP progrrams and helping students

learning LISP suggests that spectacular improvements can be made in

this area. These improvements are partly an elimination of sloppy

coding in LISP 1.5, but mostly an elaboration of DEFINE, the push

down list backtrace, and the current tracing facility. Experience

suggests that these improvements would reduce the number of computer

runs to debug a program a third to a half.

A formal theory is given concerning situations. causality and the possibility and effects of actions is given. The theory is intended to be used by the Advice Taker, a computer program that is to decide what to do by reasoning. Some simple examples are given of descriptions of situations and deductions that certain

goals can be achieved.