New PDF release: A Computational Logic Handbook

By Robert S. Boyer

ISBN-10: 0121229521

ISBN-13: 9780121229528

This e-book is a user's consultant 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 could be checked by way of computation. The
computational common sense mentioned during this instruction manual is that constructed by means of Boyer and Moore.
This instruction manual features a designated and whole description of our good judgment and a
detailed reference consultant to the linked mechanical theorem proving approach.
In addition, the guide contains 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 recommendation on tips to use the good judgment and theorem
prover successfully, and plenty of examples.
The good judgment used to be final defined thoroughly in our booklet A Computational
Logic, [4], released in 1979. the most objective of the e-book used to be to explain in
detail how the theory prover labored, its association, facts recommendations,
heuristics, and so forth. One degree of the luck of the booklet is that we all know of 3
independent winning efforts to build the theory prover from the booklet.

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However, it can be proved that the EVAL$ expression is equal to 4. Our definition of EVAL$ is attractive because for functions which always terminate, such as PLUS, we get theorems of the form: (EQUAL (EVAL$ T (LIST 'PLUS X Y) A) (PLUS (EVAL$ T X A) (EVAL$ T Y A))) The advantage of this will become apparent later. 51 A Primer for the Logic EVAL$ and V&C$ are extremely powerful programming tools as they permit one to pass around ''terms" as objects in the language. One can define many useful general purpose functions using EVAL$ or V&C$.

If FLG is ' LIST, X is treated as a list of terms, each is evaluated in the environment ALIST, and the list of results is returned. 50 A Computational Logic Handbook It is convenient to have a version of the interpreter that deals just with values and not value-cost pairs. We define the following two functions which are analogous to V&C-APPLY$ and V&C$: (APPLY$ FN ARGS) FN is assumed to be a function name (a SUBRP or non-SUBRP), and ARGS is a list of values. Apply FN to ARGS and return the result.

5) ) = ' (1 2 3 4 5) Finally, let us illustrate how we deal with the prohibition of mutual recursion. First, what is mutual recursion? We say f and g are defined mutually recursively if the definition of f involves calls of f and g, and the definition of g involves calls of f and g. This might be written Definitions. (f x) = φ ( ( ί (a x ) ) , (g (b x ) ) ) (g x) = y ( ( f (ex)), (g (d x) ) ) . Observe that if we define f first and then g, then by the time the definition of g 39 A Primer for the Logic is presented, g is no longer "new;" it is involved in the axiom for f.

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A Computational Logic Handbook by Robert S. Boyer


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