Theorem proving can be a very useful formal method. However it currently takes a lot of time and study to learn how to use a theorem prover, and proving even apparently simple theorems can be tedious. Theorem proving, and its beneets in software and hardware development , should be accepted more readily and widely if new users can do larger proofs of more complete models earlier in their traini...

The challenges in using theorem proving for verification of parallel systems are to achieve adequate automation, and to allow human guidance to be expressed in terms of the system under examination rather than the mechanisms of the prover. This paper provides an overview of techniques that address these challenges.

We describe the key features of the proof description language of Declare, an experimental theorem prover for higher order logic. We take a somewhat radical approach to proof description: proofs are not described with tactics but by using just three expressive outlining constructs. The language is \declarative" because each step speci es its logical consequences, i.e. the constants and formulae...

In this chapter, we describe the ACL2 theorem proving system and show how it can be used to model and verify hardware using refinement. This is a timely problem, as the ever-increasing complexity of microprocessor designs and the potentially devastating economic consequences of shipping defective products has made functional verification a bottleneck in the microprocessor design cycle, requirin...

Material for the course Automated Theorem Proving at Carnegie Mellon University, Fall 1999. This includes revised versions from the course notes on Linear Logic (Spring 1998) and Computation and Deduction (Spring 1997). Material for this course is available at http://www.cs.cmu.edu/~fp/courses/atp/. Please send comments to [email protected] This material is in rough draft form and is likely to cont...

Focused proof systems provide means for reducing and structuring the non-determinism involved in searching for sequent calculus proofs. We present a focused proof system for a first-order logic with inductive and co-inductive definitions in which the introduction rules are partitioned into an asynchronous phase and a synchronous phase. These focused proofs allow us to naturally see proof search...

ProofPeer We define the concept of collaborative theorem proving and outline our plan to make it a reality. We believe that a successful implementation of collaborative theorem proving is a necessary prerequisite for the formal verification of large systems. 1 The Challenge In today's computerised and scientific era, making our claims indefeasible is more critical and more relevant than ever. W...

Cancellative abelian monoids encompass abelian groups, but also such ubiquitous structures as the natural numbers or multisets. Both the AC axioms and the cancellation law are diicult for a general purpose theorem prover, as they create many variants of clauses which contain sums. We describe a reened superposition calculus for cancellative abelian monoids which requires neither explicit infere...

This paper discusses the challenges of adding symbolic computation capabilities to a computer algebra system. Indeed, a simple expressions such as m × n can be evaluated to a full value when both m and n have known values. However, if one or both of them have no definite value, then most CASs treat them as symbols and a syntactic representation of some kind is returned. Most CASs do this withou...