Posted in Logic

By Robert S. Boyer

This ebook is a user's advisor to a computational common sense. A "computational good judgment"
is a mathematical good judgment that's either orientated in the direction of dialogue of computation
and mechanized in order that proofs should be checked by way of computation. The
computational good judgment mentioned during this instruction manual is that built by means of Boyer and Moore.
This guide incorporates a special and whole description of our good judgment and a
In addition, the guide contains 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 tips to use the good judgment and theorem
prover successfully, and lots of examples.
The common sense used to be final defined thoroughly in our ebook A Computational
Logic, [4], released in 1979. the most objective of the ebook used to be to explain in
detail how the concept prover labored, its association, facts suggestions,
heuristics, and so on. One degree of the good fortune of the booklet is that we all know of 3
independent profitable efforts to build the theory prover from the e-book.

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Extra resources for A Computational Logic Handbook

Example text

In fact, the QUOTE notation makes this similarity strikingly obvious. We call ' (PLUS X Y) the "quotation" of the term (PLUS X Y) and will eventually define a function, called EVAL\$, with the property that the EVAL\$ of ' (PLUS X Y), in a suitable environment, is equal to (PLUS X Y). We will illustrate functions for manipulating these conventional data struc­ tures after we have discussed the definitional principle. 6. Defining Functions The user can define new functions by adding equations that permit calls of the new functions to be reduced to calls of old ones.

EQUAL FLG ' L I S T ) ; If FLG is ' LIST, X is a list of terms and we substitute ; NEW for VAR in each element of X and return the resulting ; list of terms. (IF (NLISTP X) NIL (CONS (SUBST T NEW VAR (CAR X)) (SUBST 'LIST NEW VAR (CDR X)))) ; Otherwise, X is a term. (IF (NLISTP X) ; If X is not a list, it is a variable symbol. Is it VAR? (IF (EQUAL X VAR) NEW X) ; If so, ; return NEW; ; otherwise, return X. ; Otherwise, X is the application of its CAR to the list ; of terms in its CDR. Substitute into each of the argument ; terms with SUBST ' LIST and put the function symbol on ; the front.

But how can an inductive instance of a theorem about f give a hypothesis about g? It can't, unless the "theorem about f " is actually a general theorem about fg. That is, the formal statement of sufficiently general inductively provable conjectures about mutually recursive functions frequently involve explicit mention of the intertwined function. 40 A Computational Logic Handbook SUBSTITUTE-LIST calls SUBSTITUTE and SUBSTITUTE-LIST. 9 Following the paradigm in which we introduced f and g by defining f g, we now introduce SUBSTITUTE and SUBSTITUTE-LIST by defining the single function SUBST.