By Robert S. Boyer
This e-book is a user's advisor to a computational common sense. A "computational common sense"
is a mathematical common sense that's either orientated in the direction of dialogue of computation
and mechanized in order that proofs could be checked via computation. The
computational common sense mentioned during this guide is that constructed via Boyer and Moore.
This instruction manual incorporates a particular and entire description of our good judgment and a
detailed reference consultant to the linked mechanical theorem proving process.
In addition, the instruction manual features a primer for the common sense as a sensible
programming language, an creation to proofs within the common sense, a primer for the
mechanical theorem prover, stylistic suggestion on tips on how to use the common sense and theorem
prover successfully, and lots of examples.
The good judgment used to be final defined thoroughly in our ebook A Computational
Logic, , released in 1979. the most objective of the publication used to be to explain in
detail how the theory prover labored, its association, evidence options,
heuristics, and so forth. One degree of the luck of the publication is that we all know of 3
independent winning efforts to build the concept prover from the booklet.
Read Online or Download A Computational Logic Handbook PDF
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Additional info for A Computational Logic Handbook
For example, what is (FN 1 2) ? Violating restriction 3, as in "Definition. " (FN X) = Y may yield "definitions" of "functions" that seem to return many different values for the same input. For example, if the equation above were admitted as an axiom then, by instantiation, we could prove (FN 1) = T. But we could also prove (FN 1) = F. Thus, we could prove T=F, which is not true. Here are some examples of simple function definitions: Definitions. (NLISTP X) = (NOT (LISTP X)) (FIRST X) = (CAR X) (REST X) = (CDR X) (NULL X) = (EQUAL X NIL) (SECOND X) = (FIRST (REST X)) (THIRD X) = (FIRST (REST (REST X))) These definitions illustrate one reason to define a function: to package, under a memorable name, a commonly used nest of function applications.
But whatever the value of Y, the value of (APPEND NIL Y) is the same as that of Y. That is, (EQUAL (APPEND NIL Y) Y) has the value T, regardless of the value of Y. 57 58 A Computational Logic Handbook Similarly, the value of (EQUAL (APPEND (APPEND X Y) Z) (APPEND X (APPEND Y Z))) is T, regardless of the values of X, Y, and Z. " It is easy to test these asser tions by executing the given expressions under sample assignments to the vari ables. But is it possible to demonstrate that the value must always be T?
Our usage of the terms is entirely consistent with everyday practice in programming—not a very strong recommendation of a convention at odds with mathematics... The power of recursive definitions comes at a price. Consider the following derivation from the equation "defining" LEN above: (LEN 0) = (ADD1 (LEN (REST 0))) = (ADD1 (LEN (CDR 0))) = (ADD1 (LEN 0)) (NULL 0) = F REST is CDR (CDR 0) = 0 If the equation "defining" LEN is available as an axiom, we can show that (LEN 0) is one greater than itself !