Jared Davis

Academic Papers

2015

Sol Swords and Jared Davis. Fix your types. In ACL2 2015. October, 2015. EPTCS 192. Pages 3-16.

Abstract. When using existing ACL2 datatype frameworks, many theorems require type hypotheses. These hypotheses slow down the theorem prover, are tedious to write, and are easy to forget. We describe a principled approach to types that provides strong type safety and execution efficiency while avoiding type hypotheses, and we present a library that automates this approach. Using this approach, types help you catch programming errors and then get out of the way of theorem proving.

(See also the FTY Documentation)

Jared Davis and Magnus O. Myreen. The reflective Milawa theorem prover is sound (down to the machine code that runs it). Journal of Automated Reasoning. Springer. August, 2015. Volume 55(2), Pages 117-183.

Official version (Springer) / Author's pre-print version

Abstract. This paper presents, we believe, the most comprehensive evidence of a theorem prover's soundness to date. Our subject is the Milawa theorem prover. We present evidence of its soundness down to the machine code.

Milawa is a theorem prover styled after NQTHM and ACL2. It is based on an idealised version of ACL2's computational logic and provides the user with high-level tactics similar to ACL2's. In contrast to NQTHM and ACL2, Milawa has a small kernel that is somewhat like an LCF-style system.

We explain how the Milawa theorem prover is constructed as a sequence of reflective extensions from its kernel. The kernel establishes the soundness of these extensions during Milawa's bootstrapping process.

Going deeper, we explain how we have shown that the Milawa kernel is sound using the HOL4 theorem prover. In HOL4, we have formalized its logic, proved the logic sound, and proved that the source code for the Milawa kernel (1,700 lines of Lisp) faithfully implements this logic.

Going even further, we have combined these results with the x86 machine-code level verification of the Lisp runtime Jitawa. Our top-level theorem states that Milawa can never claim to prove anything that is false when it is run on this Lisp runtime.

(See also Milawa Documentation and Jitawa's Website)

2014

Jared Davis, Anna Slobodova, and Sol Swords. Microcode Verification—Another Piece of the Microprocessor Verification Puzzle. Invited talk, ITP 2014. Springer, LNCS 8558. July, 2014. Pages 1-16.

Official version (Springer) / Author's pre-print version

Abstract. Despite significant progress in formal hardware verification in the past decade, little has been published on the verification of microcode. Microcode is the heart of every microprocessor and is one of the most complex parts of the design: it is tightly connected to the huge machine state, written in an assembly-like language that has no support for data or control structures, and has little documentation and changing semantics. At the same time it plays a crucial role in the way the processor works.

We describe the method of formal microcode verification we have developed for an x86-64 microprocessor designed at Centaur Technology. While the previous work on high and low level code verification is based on an unverified abstract machine model, our approach is tightly connected with our effort to verify the register-transfer level implementation of the hardware. The same microoperation specifications developed to verify implementation of the execution units are used to define operational semantics for the microcode verification.

While the techniques used in the described verification effort are not inherently new, to our knowledge, our effort is the first interconnection of hardware and microcode verification in context of an industrial size design. Both our hardware and microcode verifications are done within the same verification framework.

Jared Davis and Matt Kaufmann. Industrial Strength Documentation for ACL2. In ACL2 2014. July, 2014. EPTCS 152. Pages 9-25.

Abstract. 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.

(See also the ACL2+Books Manual)

Magnus O. Myreen and Jared Davis. The reflective Milawa theorem prover is sound (down to the machine code that runs it) . In ITP 2014. July, 2014. Springer, LNCS 8558. Pages 421-436.

Note: You may prefer the more comprehensive 2015 journal paper of the same name, see above.

Abstract. Milawa is a theorem prover styled after ACL2 but with a small kernel and a powerful reflection mechanism. We have used the HOL4 theorem prover to formalize the logic of Milawa, prove the logic sound, and prove that the source code for the Milawa kernel (2,000 lines of Lisp) is faithful to the logic. Going further, we have combined these results with our previous verification of an x86 machine-code implementation of a Lisp runtime. Our top-level HOL4 theorem states that when Milawa is run on top of our verified Lisp, it will only print theorem statements that are semantically true. We believe that this top-level theorem is the most comprehensive formal evidence of a theorem prover's soundness to date.

(See also the Milawa Documentation and Jitawa's Website)

(See also Slides from my July 2012 talk at Northeastern University)

2013

Jared Davis and Sol Swords. Verified AIG Algorithms in ACL2. In ACL2 2013. May, 2013. EPTCS 114. Pages 95-110.

Abstract. And-Inverter Graphs (AIGs) are a popular way to represent Boolean functions (like circuits). AIG simplification algorithms can dramatically reduce an AIG, and play an important role in modern hardware verification tools like equivalence checkers. In practice, these tricky algorithms are implemented with optimized C or C++ routines with no guarantee of correctness. Meanwhile, many interactive theorem provers can now employ SAT or SMT solvers to automatically solve finite goals, but no theorem prover makes use of these advanced, AIG-based approaches.

We have developed two ways to represent AIGs within the ACL2 theorem prover. One representation, Hons-AIGs, is especially convenient to use and reason about. The other, Aignet, is the opposite; it is styled after modern AIG packages and allows for efficient algorithms. We have implemented functions for converting between these representations, random vector simulation, conversion to CNF, etc., and developed reasoning strategies for verifying these algorithms.

Aside from these contributions towards verifying AIG algorithms, this work has an immediate, practical benefit for ACL2 users who are using GL to bit-blast finite ACL2 theorems: they can now optionally trust an off-the-shelf SAT solver to carry out the proof, instead of using the built-in BDD package. Looking to the future, it is a first step toward implementing verified AIG simplification algorithms that might further improve GL performance.

Jared Davis. Embedding ACL2 Models in End-User Applications. In Do-Form 2013, AISB 2013, Exeter, UK. April, 2013. Pages 49-56.

Abstract. Formal verification, based on mechanical theorem proving, can provide unique evidence that systems are correct. Unfortunately this promise of correctness is, for most projects, not enough to justify its high cost. Since formal models and proof scripts offer few other direct benefits to system developers and managers, the idea of formal verification is abandoned.

We have developed a way to embed functions from the ACL2 theorem prover into software that is written in mainstream programming languages. This lets us reuse formal ACL2 models to develop applications with features like graphics, networking, databases, etc. For example, we have written a web-based tool for hardware designers in Ruby on top of a 100,000+ line ACL2 codebase.

This is neat: we can reuse the supporting work needed for formal verification to create tools that are useful beyond the formal verification team. The value added by these tools will help to justify the investment in formal verification, and the project as a whole will benefit from the precision of formal modeling and analysis.

2011

Sol Swords and Jared Davis. Bit-Blasting ACL2 Theorems. ACL2 2011. November, 2011. EPTCS 70. Pages 84-102.

Abstract. Interactive theorem proving requires a lot of human guidance. Proving a property involves (1) figuring out why it holds, then (2) coaxing the theorem prover into believing it. Both steps can take a long time. We explain how to use GL, a framework for proving finite ACL2 theorems with BDD- or SAT-based reasoning. This approach makes it unnecessary to deeply understand why a property is true, and automates the process of admitting it as a theorem. We use GL at Centaur Technology to verify execution units for x86 integer, MMX, SSE, and floating-point arithmetic.

(See also ACL2 '11 Slides)

Magnus O. Myreen and Jared Davis. A Verified Runtime for a Verified Theorem Prover. In Interactive Theorem Proving (ITP 2011). August, 2011, Nijmegen, The Netherlands. Springer, LNCS 6898. Pages 265-280.

Abstract. Theorem provers, such as ACL2, HOL, Isabelle and Coq, rely on the correctness of runtime systems for programming languages like ML, OCaml or Common Lisp. These runtime systems are complex and critical to the integrity of the theorem provers.

In this paper, we present a new Lisp runtime which has been formally veried and can run the Milawa theorem prover. Our runtime consists of 7,500 lines of machine code and is able to complete a 4 gigabyte Milawa proof effort. When our runtime is used to carry out Milawa proofs, less unveried code must be trusted than with any other theorem prover.

Our runtime includes a just-in-time compiler, a copying garbage collector, a parser and a printer, all of which are HOL4-veried down to the concrete x86 code. We make heavy use of our previously developed tools for machine-code verication. This work demonstrates that our approach to machine-code verication scales to non-trivial applications.

(See also Milawa Documentation and Jitawa's Website)

(See also ACL2 '11 Rump Session Slides)

Anna Slobadova, Jared Davis, Sol Swords, and Warren A Hunt., Jr. A Flexible Formal Verification Framework for Industrial Scale Validation. Invited talk, Formal Methods and Models for Codesign (MemoCode 2011). July, 2011. Cambridge, UK. Pages 89-97.

Abstract. In recent years, leading microprocessor companies have made huge investments to improve the reliability of their products. Besides expanding their validation and CAD tools teams, they have incorporated formal verification methods into their design flows. Formal verification (FV) engineers require extensive training, and FV tools from CAD vendors are expensive. At first glance, it may seem that FV teams are not affordable by smaller companies. We have not found this to be true. This paper describes the formal verification framework we have built on top of publicly-available tools. This framework gives us the flexibility to work on myriad different problems that occur in microprocessor design.

2010

Warren A. Hunt Jr., Sol Swords, Jared Davis, and Anna Slobadova. Use of Formal Verification at Centaur Technology. In David S. Hardin, editor, Design and Verification of Microprocessor Systems for High Assurance Applications. 2010. Springer. Pages 65-88.

Abstract. We have developed a formal-methods-based hardware verification toolflow to help ensure the correctness of our X86-compatible microprocessors. Our toolflow uses the ACL2 theorem-proving system as a design database and a verification engine. We verify Verilog designs by first translating them into a formally defined hardware description language, and then using a variety of automated verification algorithms controlled by theorem-proving scripts.

In this chapter, we describe our approach to verifying components of VIA Centaur's 64-bit Nano, X86-compatible microprocessor. We have successfully verified a number of media-unit operations, such as the packed addition/subtraction instructions. We have verified the integer multiplication unit, and we are in the process of verifying microcode sequences that perform arithmetic operations.

2009

Jared Davis. A Self-Verifying Theorem Prover. Ph.D. Dissertation. The University of Texas at Austin. December, 2009

Abstract.Programs have precise semantics, so we can use mathematical proof to establish their properties. These proofs are often too large to validate with the usual "social process" of mathematics, so instead we create and check them with theorem proving software. This software must be advanced enough to make the proof process tractable, but this very sophistication casts doubt upon the whole enterprise: who verifies the verifier?

We begin with a simple proof checker, Level 1, that only accepts proofs composed of the most primitive steps, like Instantiation and Cut. This program is so straightforward the ordinary, social process can establish its soundness and the consistency of the logical theory it implements (so we know theorems are "always true").

Next, we develop a series of increasingly capable proof checkers, Level 2, Level 3, etc. Each new proof checker accepts new kinds of proof steps which were not accepted in the previous levels. By taking advantage of these new proof steps, higherlevel proofs can be written more concisely than lower-level proofs, and can take less time to construct and check. Our highest-level proof checker, Level 11, can be thought of as a simplified version of the ACL2 or NQTHM theorem provers. One contribution of this work is to show how such systems can be verified.

To establish that the Level 11 proof checker can be trusted, we first use it, without trusting it, to prove the fidelity of every Level n to Level 1: whenever Level n accepts a proof of some Phi, there exists a Level 1 proof of Phi. We then mechanically translate the Level 11 proof for each Level n into a Level n - 1 proof. That is, we create a Level 1 proof of Level 2's fidelity, a Level 2 proof of Level 3's fidelity, and so on. This layering shows that each level can be trusted, and allows us to manage the sizes of these proofs.

In this way, our system proves its own fidelity, and trusting Level 11 only requires us to trust Level 1.

(See also Milawa Documentation)

2006

Jared Davis. Memories: Array-like Records for ACL2. In ACL2 2006. August, 2006, Seattle, WA, USA.

Abstract. We have written a new records library for modelling fixed-size arrays and linear memories. Our implementation provides fixnum-optimized O(log₂ n) reads and writes from addresses 0, 1, ... , n-1. Space is not allocated until locations are used, so large address spaces can be represented. We do not use single-threaded objects or ACL2 arrays, which frees the user from syntactic restrictions and slow-array warnings. Finally, we can prove the same hypothesis-free rewrite rules found in misc/records for efficient rewriting during theorem proving.

(See also Memory Library Documentation)

Jared Davis. Reasoning about File Input in ACL2. In ACL2 2006. August, 2006, Seattle, WA, USA.

Abstract. We introduce the logical story behind file input in ACL2 and discuss the types of theorems that can be proven about filereading operations. We develop a low level library for reasoning about the primitive input routines. We then develop a representation for Unicode text, and implement efficient functions to translate our representation to and from the UTF-8 encoding scheme. We introduce an efficient function to read UTF-8-encoded files, and prove that when files are well formed, the function produces valid Unicode text which corresponds to the contents of the file.

We find exhaustive testing to be a useful technique for proving many theorems in this work. We show how ACL2 can be directed to prove a theorem by exhaustive testing.

(This is now mostly in the ACL2 Std/IO library)

2004

Jared Davis. Finite Set Theory based on Fully Ordered Lists. In ACL2 2004. November, 2004, Austin, TX, USA.

Abstract. We present a new finite set theory implementation for ACL2 wherein sets are implemented as fully ordered lists. This order unifies the notions of set equality and element equality by creating a unique representation for each set, which in turn enables nested sets to be trivially supported and eliminates the need for congruence rules.

We demonstrate that ordered sets can be reasoned about in the traditional style of membership arguments. Using this technique, we prove the classic properties of set operations in a natural and effotless manner. We then use the exciting new MBE feature of ACL2 to provide linear-time implementations of all basic set operations. These optimizations are made "behind the scenes" and do not adversely impact reasoning ability.

We finally develop a framework for reasoning about quantification over set elements. We also begin to provide common higher-order patterns from functional programming. The net result is an efficient library that is easy to use and reason about.

(This became the ACL2 Std/Osets library)

Gregory L. Wickstrom, Jared Davis, Steve Morrison, Steve Roach, Victor L. Winter. The SSP: An Example of High-Assurance Systems Engineering. In High-Assurance Systems Engineering (HASE 2004). March, 2004, Tampa, FL, USA. IEEE Computer Society 2004, ISBN 0-7695-2094-4.

Abstract. The SSP is a high assurance systems engineering effort spanning both hardware and software. Extensive design review, first principle design, n-version programming, program transformation, verification, and consistency checking are the techniques used to provide assurance in the correctness of the resulting system.