A Theory About First-Order Terms in ACL2

We describe the development in ACL2 of a library of results about first-order terms. In particular, we present the formalization of some of the main properties of the complete lattice of first-order terms with respect to the subsumption relation. As a byproduct, verified executable implementations are obtained for some basic operations on firstorder terms, including matching, renaming, unification and anti-unification. This work can be seen as a basis for further studies about the formal properties of automated reasoning and symbolic computation systems.Ministerio de Ciencia y Tecnología TIC2000-1368-CO3-0

Formal proofs about rewriting using ACL2

We present an application of the ACL2 theorem prover to reason about rewrite systems theory. We describe the formalization and representation aspects of our work using the firstorder, quantifier-free logic of ACL2 and we sketch some of the main points of the proof effort. First, we present a formalization of abstract reduction systems and then we show how this abstraction can be instantiated to establish results about term rewriting. The main theorems we mechanically proved are Newman’s lemma (for abstract reductions) and Knuth–Bendix critical pair theorem (for term rewriting).Ministerio de Educación y Ciencia TIC2000-1368-CO3-0

The use of proof plans in tactic synthesis

We undertake a programme of tactic synthesis. We first formalize the notion of a tactic as a rewrite rule, then give a correctness criterion for this by means of a reflection mechanism in the constructive type theory OYSTER. We further formalize the notion of a tactic specification, given as a synthesis goal and a decidability goal. We use a proof planner. CIAM. to guide the search for inductive proofs of these, and are able to successfully synthesize several tactics in this fashion. This involves two extensions to existing methods: context-sensitive rewriting and higher-order wave rules. Further, we show that from a proof of the decidability goal one may compile to a Prolog program a pseudo- tactic which may be run to efficiently simulate the input/output behaviour of the synthetic tacti

Investigation, Development, and Evaluation of Performance Proving for Fault-tolerant Computers

A number of methodologies for verifying systems and computer based tools that assist users in verifying their systems were developed. These tools were applied to verify in part the SIFT ultrareliable aircraft computer. Topics covered included: STP theorem prover; design verification of SIFT; high level language code verification; assembly language level verification; numerical algorithm verification; verification of flight control programs; and verification of hardware logic

Compiling Unit Clauses for the Warren Abstract Machine

This thesis describes the design, development, and installation of a computer program which compiles unit clauses generated in a Prolog-based environment at Argonne National Laboratories into Warren Abstract Machine (WAM) code. The program enhances the capabilities of the environment by providing rapid unification and subsumption tests for the very significant class of unit clauses. This should improve performance substantially for large programs that generate and use many unit clauses

Formal methods and digital systems validation for airborne systems

This report has been prepared to supplement a forthcoming chapter on formal methods in the FAA Digital Systems Validation Handbook. Its purpose is as follows: to outline the technical basis for formal methods in computer science; to explain the use of formal methods in the specification and verification of software and hardware requirements, designs, and implementations; to identify the benefits, weaknesses, and difficulties in applying these methods to digital systems used on board aircraft; and to suggest factors for consideration when formal methods are offered in support of certification. These latter factors assume the context for software development and assurance described in RTCA document DO-178B, 'Software Considerations in Airborne Systems and Equipment Certification,' Dec. 1992

Discovery and Reasoning in Mathematics

We discuss the automation of mathematical reasoning, surveying the abilities displayed by human mathematicians and the computational techniques available for automating these abilities. We argue the importance of the simultaneous study of these techniques, because problems inherent in one technique can often be solved if it is able to interact with others