By Robert S. Boyer

This booklet is a user's advisor to a computational good judgment. A "computational common sense"
is a mathematical good judgment that's either orientated in the direction of dialogue of computation
and mechanized in order that proofs might be checked by means of computation. The
computational good judgment mentioned during this instruction manual is that constructed by means of Boyer and Moore.
This guide features a distinct and whole description of our common sense and a
detailed reference advisor to the linked mechanical theorem proving approach.
In addition, the guide features a primer for the good judgment as a practical
programming language, an advent to proofs within the common sense, a primer for the
mechanical theorem prover, stylistic recommendation on find out how to use the good judgment and theorem
prover successfully, and plenty of examples.
The good judgment was once final defined thoroughly in our publication A Computational
Logic, [4], released in 1979. the most function of the ebook was once to explain in
detail how the theory prover labored, its association, facts strategies,
heuristics, and so forth. One degree of the good fortune of the e-book is that we all know of 3
independent winning efforts to build the theory prover from the ebook.

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From this example it should be clear that the QUOTE notation does encourage the use of the traditional convention for representing lists! Literal atoms are commonly used to represent symbolic data such as names, operators, and attributes. For example, in an application in which the days of the week are relevant, one might choose to denote each day with a number. , 'MONDAY for the first work day, ' TUESDAY for the second, etc. ' MONDAY is, of course, 30 A Computational Logic Handbook (PACK ' (77 79 78 68 65 89 .

Thus, 'ABC is an abbreviation of (PACK (CONS 65 67 0 ) ) ) ) . ' NIL, which is an abbreviation for (CONS 66 (CONS (PACK (CONS 78 (CONS 73 (CONS 76 0)))), is further abbreviated NIL. Recall that the symbol NIL is not a variable sym­ bol. Note that the object NIL is a LITATOM and, hence, is not F. Thus, to the surprise of many Lisp programmers, (IF NIL Y Z) = Y. (LIST χ χ x 2 . . x n ) is an abbreviation for (CONS χ χ (LIST x 2 . . xn) ) . (LIST) is an abbreviation for NIL. Finally, we provide a convention for abbreviating certain LISTP constants.

But the argument list is arbitrarily long, so we must use recursion to describe the process: if the argument list is empty, return the empty list; otherwise, SUBSTITUTE new for v a r into the first argument and cons that onto the result of recursively substituting new for v a r into the rest of the argument list. Let us call SUBSTITUTE-LIST the function that SUBSTITUTES into each term in the argument list. Then we have a mutually recursive pair of functions, SUBSTITUTE calls SUBSTITUTE-LIST and This may look like an unattractive solution that could be cured by some syntactic sugar that hides f g from the user.

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