We discuss the problem of incorporating into a heuristic theorem prover a decision procedure for a fragment of the logic. An obvious goal when incorporating such a procedure is to reduce the search space explored by the heuristic component of the system, as would be achieved by eliminating from the system’s data base some explicitly stated axioms. For example, if a decision procedure for linear inequalities is added, one would hope to eliminate the explicit consideration of the transitivity axioms. However, the decision procedure must then be used in all the ways the eliminated axioms might have been. The difficulty of achieving this degree of integration is more dependent upon the complexity of the heuristic component than upon that of the decision procedure. The view of the decision procedure as a "black box " is frequently destroyed by the need pass large amounts of search strategic information back and forth between the two components. Finally, the efficiency of the decision procedure may be virtually irrelevant; the efficiency of the final system may depend most heavily on how easy it is to communicate between the two components. This paper is a case study of how we integrated a linear arithmetic procedure into a heuristic theorem prover. By linear arithmetic here we mean the decidable subset of number theory dealing with universally quantified formulas composed of the logical connectives, the identity relation, the Peano "less than " relation, the Peano addition and subtraction functions, Peano constants,

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: Our ultimate goal is to provide a framework and a methodology which will allow users, and not only system developers, to construct complex reasoning systems by composing existing modules, or to add new modules to existing systems, in a "plug and play" manner. These modules and systems might be based on different logics; have different domain models; use different vocabularies and data structures; use different reasoning strategies; and have different interaction capabilities. This paper makes two main contributions towards our goal. First, it proposes a general architecture for a class of reasoning systems called Open Mechanized Reasoning Systems (OMRSs). An OMRS has three components: a reasoning theory component which is the counterpart of the logical notion of formal system, a control component which consists of a set of inference strategies, and an interaction component which provides an OMRS with the capability of interacting with other systems, including OMRSs and hum...

contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of Computational Logic, Inc., the Defense Advanced Research Projects Agency or the U.S. Government. This paper briefly describes a programming language, its implementation on a microprocessor via a compiler and link-assembler, and the mechanically checked proof of the correctness of the implementation. The programming language, called Piton, is a high-level assembly language designed for verified applications and as the target language for high-level language compilers. It provides execute-only programs, recursive subroutine call and return, stack based parameter passing, local variables, global variables and arrays, a user-visible stack for intermediate results, and seven abstract data types including integers, data addresses, program addresses and subroutine names. Piton is formally specified by an interpreter written for it in the computational logic of Boyer and Moore. Piton has been implemented on the FM8502, a general purpose microprocessor whose gate-level design has been mechanically proved to implement its machine code interpreter. The FM8502 implementation of Piton is via a function in the Boyer-Moore logic which maps a Piton initial state into an FM8502 binary core image. The compiler and link-assembler are all defined as functions in the logic. The implementation requires approximately 36K bytes and 1,400 lines of prettyprinted source code in the Pure Lisp-like syntax of the logic. The implementation has been mechanically proved correct. In particular, if a Piton state can be run to completion without error, then the final values of all the global data structures can be ascertained from an inspection of an FM8502 core image obtained by running the core image produced by the compiler and link-assembler. Thus, verified Piton programs running on FM8502 can be thought of as having been verified down to the gate level. 1.

. The so-called "Boyer-Moore Theorem Prover" (otherwise known as "Nqthm") has been used to perform a variety of verification tasks for two decades. We give an overview of both this system and an interactive enhancement of it, "Pc-Nqthm," from a number of perspectives. First we introduce the logic in which theorems are proved. Then we briefly describe the two mechanized theorem proving systems. Next, we present a simple but illustrative example in some detail in order to give an impression of how these systems may be used successfully. Finally, we give extremely short descriptions of a large number of applications of these systems, in order to give an idea of the breadth of their uses. This paper is intended as an informal introduction to systems that have been described in detail and similarly summarized in many other books and papers; no new results are reported here. Our intention here is merely to present Nqthm to a new audience. This research was supported in part by ONR Contract N...

A new algorithm is presented for determining which, if any, of an arbitrary number of candidates has received a majority of the votes cast in an election. The number of comparisons required is at most twice the number of votes. Furthermore, the algorithm uses storage in a way that permits an efficient use of magnetic tape. A Fortran version of the algorithm is exhibited. The Fortran code has been proved correct by a mechanical verification system for Fortran. The system and the proof are discussed. 1 The work described here was conducted in the Computer Science Laboratory of SRI International and suported in part by NASA Contract NAS1-15528, NSF Grant MCS7904081, and ONR Contract N00014-75-C-0816 1981. A brief history of this work is given in the concluding section. 106 Robert S. Boyer and J Strother Moore 5.1 Introduction Reliability may be obtained by redundant computation and voting in critical hardware systems. What is the best way to determine the majority, if any, of a mult...

A new algorithm is presented for determining which, if any, of an arbitrary number of candidates has received a majority of the votes cast in an election. The number of comparisons required is at most twice the number of votes. Furthermore, the algorithm uses storage in a way that permits an efficient use of magnetic tape.

We briefly review a mechanical theorem-prover for a logic of recursive functions over finitely generated objects including the integers, ordered pairs, and symbols. The prover, known both as NQTHM and as the Boyer-Moore prover, contains a mechanized principle of induction and implementations of linear resolution, rewriting, and arithmetic decision procedures. We describe some applications of the prover, including a proof of the correct implementation of a higher level language on a microprocessor defined at the gate level. We also describe the ongoing project of recoding the entire prover as an applicative function within its own logic.