Industrial-Strength Documentation for ACL2

The ACL2 theorem prover is a complex system. Its libraries are vast. Industrial verification efforts may extend this base with hundreds of thousands of lines of additional modeling tools, specifications, and proof scripts. High quality documentation is vital for teams that are working together on projects of this scale. We have developed XDOC, a flexible, scalable documentation tool for ACL2 that can incorporate the documentation for ACL2 itself, the Community Books, and an organization's internal formal verification projects, and which has many features that help to keep the resulting manuals up to date. Using this tool, we have produced a comprehensive, publicly available ACL2+Books Manual that brings better documentation to all ACL2 users. We have also developed an extended manual for use within Centaur Technology that extends the public manual to cover Centaur's internal books. We expect that other organizations using ACL2 will wish to develop similarly extended manuals.Comment: In Proceedings ACL2 2014, arXiv:1406.123

A Vernacular for Coherent Logic

We propose a simple, yet expressive proof representation from which proofs for different proof assistants can easily be generated. The representation uses only a few inference rules and is based on a frag- ment of first-order logic called coherent logic. Coherent logic has been recognized by a number of researchers as a suitable logic for many ev- eryday mathematical developments. The proposed proof representation is accompanied by a corresponding XML format and by a suite of XSL transformations for generating formal proofs for Isabelle/Isar and Coq, as well as proofs expressed in a natural language form (formatted in LATEX or in HTML). Also, our automated theorem prover for coherent logic exports proofs in the proposed XML format. All tools are publicly available, along with a set of sample theorems.Comment: CICM 2014 - Conferences on Intelligent Computer Mathematics (2014

On Automated Lemma Generation for Separation Logic with Inductive Definitions

Separation Logic with inductive definitions is a well-known approach for deductive verification of programs that manipulate dynamic data structures. Deciding verification conditions in this context is usually based on user-provided lemmas relating the inductive definitions. We propose a novel approach for generating these lemmas automatically which is based on simple syntactic criteria and deterministic strategies for applying them. Our approach focuses on iterative programs, although it can be applied to recursive programs as well, and specifications that describe not only the shape of the data structures, but also their content or their size. Empirically, we find that our approach is powerful enough to deal with sophisticated benchmarks, e.g., iterative procedures for searching, inserting, or deleting elements in sorted lists, binary search tress, red-black trees, and AVL trees, in a very efficient way

Automating Change of Representation for Proofs in Discrete Mathematics (Extended Version)

Representation determines how we can reason about a specific problem. Sometimes one representation helps us find a proof more easily than others. Most current automated reasoning tools focus on reasoning within one representation. There is, therefore, a need for the development of better tools to mechanise and automate formal and logically sound changes of representation. In this paper we look at examples of representational transformations in discrete mathematics, and show how we have used Isabelle's Transfer tool to automate the use of these transformations in proofs. We give a brief overview of a general theory of transformations that we consider appropriate for thinking about the matter, and we explain how it relates to the Transfer package. We show our progress towards developing a general tactic that incorporates the automatic search for representation within the proving process

Automating Inductive Proofs using Theory Exploration

HipSpec is a system for automatically deriving and proving properties about functional programs. It uses a novel approach, combining theory exploration, counterexample testing and inductive theorem proving. HipSpec automatically generates a set of equational theorems about the available recursive functions of a program. These equational properties make up an algebraic specification for the program and can in addition be used as a background theory for proving additional user-stated properties. Experimental results are encouraging: HipSpec compares favourably to other inductive theorem provers and theory exploration systems

Program Improvement by Automatic Redistribution of Intermediate Results

This paper was originally a Ph.D. thesis proposal.The problem of automatically improving the performance of computer programs has many facets. A common source of program inefficiency is the use of abstraction techniques in program design: general tools used in a specific context often do unnecessary or redundant work. Examples include needless copy operations, redundant subexpressions, multiple traversals of the same datastructure and maintenance of overly complex data invariants. I propose to focus on one broadly applicable way of improving a program's performance: redistributing intermediate results so that computation can be avoided. I hope to demonstrate that this is a basic principle of optimization from which many of the current approaches to optimization may be derived. I propose to implement a system that automatically finds and exploits opportunities for redistribution in a given program. In addition to the program source, the system will accept an explanation of correctness and purpose of the code. Beyond the specific task of program improvement, I anticipate that the research will contribute to our understanding of the design and explanatory structure of programs. Major results will include (1) definition and manipulation of representation of correctness and purpose of a program's implementation, and (2) definition, construction, and use of a representation of a program's dynamic behavior.MIT Artificial Intelligence Laborator