## Integrating External Deduction Tools with ACL2 (2006)

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Venue: | Sutcliffe (Eds.), Proceedings of the 6th International Workshop on Implementation of Logics (IWIL 2006 |

Citations: | 7 - 5 self |

### BibTeX

@INPROCEEDINGS{Kaufmann06integratingexternal,

author = {Matt Kaufmann and J Strother Moore and Ip Ray and Erik Reeber},

title = {Integrating External Deduction Tools with ACL2},

booktitle = {Sutcliffe (Eds.), Proceedings of the 6th International Workshop on Implementation of Logics (IWIL 2006},

year = {2006},

pages = {7--26}

}

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### Abstract

We present an interface connecting the ACL2 theorem prover with external deduction tools. The logic of ACL2 contains several constructs intended to facilitate structuring of interactive proof development, which complicates the design of such an interface. We discuss some of these complexities and develop a precise specification of the requirements from external tools for sound connection with ACL2. We also develop constructs within ACL2 to enable the developers of external tools to satisfy our specifications. 1

### Citations

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202 |
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Citation Context ...; this mechanism has been used to integrate model checkers and arithmetic decision procedures with Isabelle [MN95, BF00]. Oracles are also used in the HOL family of higher order logic theorem provers =-=[GM93]-=-; for instance, the PROSPER project [DCN + 00] uses the HOL98 theorem prover as a uniform and logically-based coordination mechanism between several verification tools. The most recent incarnation of ... |

103 |
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Citation Context ...roving theorems in the target domain. In fact, ACL2 currently provides a way for users to augment its built-in term simplifier with their own customized reasoning code, via the so-called “meta rules” =-=[BM81]-=-. However, such rules essentially augment the reasoning engine of ACL2 without providing the user control to manipulate a specific subgoal arising during a proof. Furthermore, meta rules only allow re... |

93 | An Integration of Model-Checking with Automated Proof Checking - Rajan, Shankar, et al. - 1995 |

62 | Isabelle's reference manual
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Citation Context ...tools with interactive theorem proving. The PVS theorem prover provides connections with several decision procedures such as model checkers and SAT solvers [RSS95, Sha01]. The Isabelle theorem prover =-=[Pau]-=- uses unverified external tools as oracles for checking formulas as theorems during a proof search; this mechanism has been used to integrate model checkers and arithmetic decision procedures with Isa... |

49 | Structured Theory Development for a Mechanized Logic
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(Show Context)
Citation Context ...ther hand, it is not trivial to connect ACL2 with an external deduction tool. The logic of ACL2 is complicated by the presence of several constructs intended to facilitate effective proof structuring =-=[KM01]-=-. It is therefore imperative (i) to determine under what logical constraints a conjecture certified by a combination of the theorem prover and other tools can be claimed to be a valid theorem, and (ii... |

47 | Combining model checking and deduction for I/O-Automata - Müller, Nipkow - 1995 |

41 | The PROSPER toolkit - Dennis, Collins, et al. - 2003 |

39 | Trace Table Based Approach for Pipeline Microprocessor Verification
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Citation Context ...orola CAP DSP [BH97], separation properties for the Rockwell Collins AAMP7 TM processor [GRW04], and a non-trivial pipelined machine with interrupts, exceptions, and speculative instruction execution =-=[SH97]-=-. However, the applicability of ACL2 (as in fact that of any theorem prover) is often limited by the amount of user expertise required to drive the theorem prover; indeed, the verification projects re... |

37 | Design goals for ACL2
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Citation Context ...ver, with that prover. ACL2 [KMM00, KM06] is an industrial-strength interactive theorem proving system. It consists of an efficient programming interface based on an applicative subset of Common Lisp =-=[KM94]-=-, and a first-order, inductive theorem prover for a logic of recursive functions. The ACL2 theorem prover supports several deduction mechanisms such as congruence-based conditional rewriting, well-fou... |

34 | An LCF-Style Interface between HOL and First-Order Logic
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Citation Context ...tagging of unverified clause processors. There has also been work on using an external tool to search for a proof that can then be checked by the theorem prover without assistance from the tool. Hurd =-=[Hur02]-=- describes such an interface connecting HOL with first-order logic. McCune and Shumsky [MS00] present a system called Ivy which uses Otter to search for first-order proofs of equational theories and t... |

30 | A mechanically checked proof of IEEE compliance of a register-transferlevel specification of the AMD-K7 floating-point multiplication, division, and square root instructions - Russinoff - 1998 |

29 | IVY: A preprocessor and proof checker for first-order logic
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Citation Context ... search for a proof that can then be checked by the theorem prover without assistance from the tool. Hurd [Hur02] describes such an interface connecting HOL with first-order logic. McCune and Shumsky =-=[MS00]-=- present a system called Ivy which uses Otter to search for first-order proofs of equational theories and then invokes ACL2 to check such proof objects. Meng and Paulson [MP04] interface Isabelle with... |

28 | Experiments on supporting interactive proof using resolution
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Citation Context ...gic. McCune and Shumsky [MS00] present a system called Ivy which uses Otter to search for first-order proofs of equational theories and then invokes ACL2 to check such proof objects. Meng and Paulson =-=[MP04]-=- interface Isabelle with a resolution theorem prover. Several ACL2 users have integrated external tools with ACL2; but without the disciplined mechanisms of this paper, such integration has essentiall... |

23 | Combining WS1S and HOL - Basin, Friedrich - 2000 |

23 | Automatic Verification of Safety and Liveness for XScale-Like Processor Models Using WEB refinements - Manolios, Srinivasan - 2004 |

21 |
Programming combinations of deduction and BDD-based symbolic calculation
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Citation Context ...st recent incarnation of this family of theorem provers, HOL4, uses an external oracle interface to decide large Boolean formulas through connections to state-of-the-art BDD and SAT-solving libraries =-=[Gor02]-=-, and also uses that oracle interface to connect HOL4 with ACL2 as discussed in the next section.sThe primary basis for interfacing external tools with theorem provers for higherorder logic (specifica... |

20 | A summary of intrinsic partitioning verification
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Citation Context ...on, division, and square root algorithms of AMD processors [MLK98, Rus98, RF00, FKR + 02], microcode for the Motorola CAP DSP [BH97], separation properties for the Rockwell Collins AAMP7 TM processor =-=[GRW04]-=-, and a non-trivial pipelined machine with interrupts, exceptions, and speculative instruction execution [SH97]. However, the applicability of ACL2 (as in fact that of any theorem prover) is often lim... |

17 |
Formally specifying and mechanically verifying programs for the Motorola complex arithmetic processor DSP
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Citation Context ... by DARPA under Contract No. NBCH30390004.sthe floating point multiplication, division, and square root algorithms of AMD processors [MLK98, Rus98, RF00, FKR + 02], microcode for the Motorola CAP DSP =-=[BH97]-=-, separation properties for the Rockwell Collins AAMP7 TM processor [GRW04], and a non-trivial pipelined machine with interrupts, exceptions, and speculative instruction execution [SH97]. However, the... |

16 | Refinement maps for efficient verification of processor models - MANOLIOS, SRINIVASAN |

15 |
A Proposed Interface Logic for Verification Environments
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(Show Context)
Citation Context ...p of external tools has been widely recognized in the theorem proving community. Some early ideas for connecting different theorem provers are discussed in a proposal for so-called “interface logics” =-=[Gut91]-=-, with the goal to connect automated reasoning tools by defining a single logic L such that the logics of the individual tools can be viewed as sub-logics of L. More recently, with the success of mode... |

13 | Certifying compositional model checking algorithms in ACL2
- Ray, Matthews, et al.
- 2003
(Show Context)
Citation Context ...h ACL2; but without the disciplined mechanisms of this paper, such integration has essentially involved implementation hacks on the ACL2 source code. Ray, Matthews, and Tuttle integrate ACL2 with SMV =-=[RMT03]-=-. Reeber and Hunt connect ACL2 with the Zchaff satisfiability solver [RH06], and Sawada and Reeber provide a connection with SixthSense [SR06]. Manolios and Srinivasan connect ACL2 with UCLID [MS04, M... |

10 |
Adding External Decision Procedures to HOL90 Securely
- Gunter
- 1998
(Show Context)
Citation Context ....sThe primary basis for interfacing external tools with theorem provers for higherorder logic (specifically HOL and Isabelle) involves the concept of “theorem tagging”, introduced by Gunter for HOL90 =-=[Gun98]-=-. The idea is to introduce a tag in the logic for each oracle and view a theorem certified by the oracle as an implication with the tag corresponding to the certifying oracle as a hypothesis. This app... |

9 | An Integration of HOL and ACL2 - Gordon, Reynolds, et al. - 2006 |

8 |
A SAT-Based Decision Procedure for the Subclass of Unrollable
- Reeber, Hunt
- 2006
(Show Context)
Citation Context ...on has essentially involved implementation hacks on the ACL2 source code. Ray, Matthews, and Tuttle integrate ACL2 with SMV [RMT03]. Reeber and Hunt connect ACL2 with the Zchaff satisfiability solver =-=[RH06]-=-, and Sawada and Reeber provide a connection with SixthSense [SR06]. Manolios and Srinivasan connect ACL2 with UCLID [MS04, MS05]. 7 Conclusion and Future Work Different deduction tools bring in diffe... |

7 | An embedding of the ACL2 logic in HOL - Gordon, Hunt, et al. - 2006 |

6 |
A Precise Description
- Kaufmann, Moore
- 1997
(Show Context)
Citation Context ...ocumentation together with references to several books and papers. 2.1 The logic The kernel of the ACL2 logic consists of a formal syntax, some rules of inference, and some axioms. Kaufmann and Moore =-=[KM97]-=- provide a precise description of the kernel logic. The logic supported by the theorem prover is an extension of the kernel logic. The kernel syntax describes terms composed of variables, constants, a... |

5 | A Mechanically Checked Proof of the Kernel of the AMD5K86 Floating-point Division Algorithm - Moore, Lynch, et al. - 1998 |

5 |
ACL2SIX: A hint used to integrate a theorem prover and an automated verification tool
- Sawada, Reeber
(Show Context)
Citation Context ...ed properties of the interpreter to establish the correctness of the design. The above approach has shown promise in scaling formal verification to industrial designs. For instance, Sawada and Reeber =-=[SR06]-=- have recently verified an industrial VHDL floating-point multiplier using a combination of ACL2 and an IBM internal verification tool called SixthSense [MBP + 04]. They introduce two functions, sigbi... |

4 | RTL Verification: A Floating Point Multiplier - Russinoff, Flatau - 2000 |

4 | The Correctness Problem in Computer Science - Moore - 2000 |

3 | Formal Verification of Microprocessors at AMD - Flatau, Kaufmann, et al. - 2002 |

3 | Using Decision Procedures with Higher Order Logics - Shankar - 2001 |

2 | Scalable Automated Verification via Exper-System Guided Transformations, in - Mony, Baumgartner, et al. - 2004 |

1 |
Should We Begin a Stanrdization Process for Interface Logics
- Kaufmann, Moore
- 1992
(Show Context)
Citation Context ...ing ACL2 with external deduction tools, but we have merely scratched the surface. It is well-known that developing an effective interface between two or more deduction tools is a complicated exercise =-=[KM92]-=-. It remains to be seen how to effectively decompose theorem proving problems so as tosmake effective use of clause processors to provide the requisite automation. Some researchers have criticized our... |