## The Combined KEAPPA- IWIL Workshops Proceedings Proceedings of the workshops Knowledge Exchange: Automated Provers and Proof Assistants

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@MISC{Urban_thecombined,

author = {Josef Urban},

title = {The Combined KEAPPA- IWIL Workshops Proceedings Proceedings of the workshops Knowledge Exchange: Automated Provers and Proof Assistants},

year = {}

}

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### Abstract

Existing automated provers and proof assistants are complementary, to the point that their cooperative integration would benefit all efforts in automating reasoning. Indeed, a number of specialized tools incorporating such integration have been built. The issue is, however, wider, as we can envisage cooperation among various automated provers as well as among various proof assistants. This workshop brings together practitioners and researchers who have experimented with knowledge exchange among tools supporting automated reasoning. Organizers: Piotr Rudnicki, Geoff Sutcliffe

### Citations

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Citation Context ...ed proof methods, including rewriting, resolution- and tableau provers, and case-based and inductive reasoning. Adding support for more specialized reasoning tools such as proof-producing SAT solvers =-=[5]-=- or SMT solvers such as haRVey [3] will be similarly helped by existing generic interfaces. The current encoding supports only a core subset of TLA +2 , including propositional and first-order logic, ... |

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Citation Context ...constant formulas. 2.2 TLA + The TLA + language adds the following to the TLA logic: • An underlying logic that is essentially ZFC set theory plus classical untyped first-order logic with Hilbert’s ε =-=[13]-=-. The major difference between this underlying logic and traditional ZFC is that functions are defined axiomatically rather than being represented as sets of ordered pairs. • A mechanism for defining ... |

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Citation Context ...since it is a straightforward generalization of the one used in SAT 106Learning Techniques for Pseudo-Boolean Solving Santos, Manquinho solvers. Moreover, considering the use of lazy data structures =-=[12]-=- for clause manipulation, the overhead of adding a large number of clauses during the search is smaller than with other types of constraints. 4.2 Pseudo-Boolean Constraint Learning The use of PB const... |

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Citation Context ...o small and medium size case studies. Currently, the strategy is applied in a European project called Protocure to verify medical guidelines which can be seen as yet another form of concurrent system =-=[14]-=-. Overall, we believe that the strategy has the potential to make interactive proofs in (linear) temporal logic in general more intuitive and automatic. References [1] K.R. Apt and E.-R. Olderog. Veri... |

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Citation Context ...h rules similar to the ones of Tables4 and 5, we support in KIV operators for Dijkstra’s choice, synchronous parallel execution, and interrupts. Furthermore, we have integrated STATEMATE state charts =-=[3]-=- as well as UML state charts [5] as alternative formalisms to define concurrent systems. For all of our extensions, the strategy of sequencing and induction has remained unchanged and arbitrary tempor... |

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Citation Context ... Constraint Propagation (and possibly other inference methods). If a conflict arises, i.e. a given constraint cannot be satisfied by extending the current partial assignment, then a conflict analysis =-=[11]-=- procedure is carried out to determine the level to which the search process can safely backtrack to. Moreover, a no-good constraint is also added to the set of problem constraints. The main goal of t... |

28 | Translating higher-order clauses to first-order clauses
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Citation Context ... can proofs be mined for strategies that are helpful for speeding up proofs for a class of problems? Interpolation. Proof visualization. Finally, in the context of Isabelle/HOL, it has been suggested =-=[8]-=- to translate HOL formulas (which use polymorphism), into first-order untyped formulas. A potentially unsound translation is then run through first-order provers, but the produced proofs (currently ap... |

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Citation Context ...on wrote a program that computes Gröbner bases to prove polynomial equalities, specially in arithmetics [7]. This program was adapted in Isabelle by Amine Chaieb and Makarius Wenzel for the same task =-=[2]-=-. We show on examples that our tactic is faster. This paper is organized as follow. In section 2 we explain the mathematical method we use to reduce the problem to Gröbner bases computations. In secti... |

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Citation Context ...te often, e.g., for the formulae inferred by Skolemization and splitting steps. These status values can be used for semantic verification of the derivations, as is done by the GDV derivation verifier =-=[17]-=-. While the SZS ontologies are in use and have matured to some extent, it is not claimed that they are comprehensive and perfect. Developers and users of automated reasoning software are invited to pr... |

17 | Faster Proof Checking in the Edinburgh Logical Framework
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Citation Context ...od or satisfiability, a reason why the software could not process the data, etc. For software that works with first-order logic, the de facto standard for expressing logical data is the TPTP language =-=[19]-=- (and it is expected that this will soon extend to higher-order logic [4]). The SZS ontologies that are linked to the TPTP are used by some automated reasoning software to express the status values. T... |

13 |
Rocket-fast proof checking for SMT solvers
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Citation Context ...o support ordinary mathematical reasoning in the underlying logic. Proofs in TLA +2 are natural deduction proofs written in a hierarchical style that we have found to be good for ordinary mathematics =-=[9]-=- and crucial for managing the complexity of correctness proofs of systems [6]. The PM computes proof obligations that establish the correctness of the proof and sends them to one or more back-end prov... |

12 |
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Citation Context ...ng precisely what is known or has been established about logical data. The ontologies can be used for existing logical data, e.g., they are used for the status of problems in the TPTP problem library =-=[21]-=- and solutions in the TSTP solution library [16], and can be used by automated reasoning software to describe their input and output. Already several ATP systems, e.g., Darwin [3], E, Metis [7], Parad... |

4 |
Semantic Derivation Verification: Techniques and Implementation
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(Show Context)
Citation Context ...that a user invokes directly, but rather as embedded components of more complex reasoning systems. For one example, NASA’s certifiable program synthesis system [6] embeds the SSCPA ATP system harness =-=[20]-=-, the ATP systems E [13], SPASS [24], Vampire [12], and the GDV derivation verifier [17]. For another example, SRI’s BioDeducta system [14] embeds the ATP system SNARK [15], and the BioBike integrated... |

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3 | Producing proofs from an arithmetic decision procedure in elliptical lf
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(Show Context)
Citation Context ...ce of resolution steps in a backward traversal of the implication graph can be directly applied to PB formulas [11]. Additionally, techniques such as the detection of Unique Implication Points (UIPs) =-=[11, 18]-=- can also be directly used in PB-SAT conflict analysis. As a result, a new propositional clause is generated and added to the original formula. In the last pseudo-Boolean solver evaluation, some PB so... |

3 | Proof translation and SMT-LIB benchmark certification: A preliminary report
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Citation Context ...sful in identifying the necessary axioms for proving each conjecture, and subsequently obtaining either a proof using EP or an assurance of a proof using iProver [9]. In addition to SRASS, the MANSEX =-=[22]-=- and IDV [23] tools were used during the initial development of the axiomatization, to find the most obvious relationships and to analyze proofs. All automated reasoning and proof processing was done ... |

2 |
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Citation Context ... for interactive use, the effects of the Isar proof commands are not always easily predictable, and this encourages a linear rather than hierarchical proof development style. The Focal Proof Language =-=[1]-=- is essentially a subset of the TLA +2 proof language. Our experience with hierarchical proofs in Focal provides additional confidence in the attractiveness of our approach. We know of no declarative ... |