Haniel Barbosa, J. Blanchette, Simon Cruanes, Daniel El Ouraoui, P. Fontaine
Satisfiability modulo theories (SMT) solvers have throughout the years been able to cope with increasingly expressive formulas, from ground logics to full first-order logic modulo theories. Nevertheless, higher-order logic within SMT is still little explored. One main goal of the Matryoshka project, which started inMarch 2017, is to extend the reasoning capabilities of SMT solvers and other automatic provers beyond first-order logic. In this preliminary report, we report on an extension of the SMT-LIB language, the standard input format of SMT solvers, to handle higher-order constructs. We also discuss how to augment the proof format of the SMT solver veriT to accommodate these new constructs and the solving techniques they require.
{"title":"Language and Proofs for Higher-Order SMT (Work in Progress)","authors":"Haniel Barbosa, J. Blanchette, Simon Cruanes, Daniel El Ouraoui, P. Fontaine","doi":"10.4204/EPTCS.262.3","DOIUrl":"https://doi.org/10.4204/EPTCS.262.3","url":null,"abstract":"Satisfiability modulo theories (SMT) solvers have throughout the years been able to cope with increasingly expressive formulas, from ground logics to full first-order logic modulo theories. Nevertheless, higher-order logic within SMT is still little explored. One main goal of the Matryoshka project, which started inMarch 2017, is to extend the reasoning capabilities of SMT solvers and other automatic provers beyond first-order logic. In this preliminary report, we report on an extension of the SMT-LIB language, the standard input format of SMT solvers, to handle higher-order constructs. We also discuss how to augment the proof format of the SMT solver veriT to accommodate these new constructs and the solving techniques they require.","PeriodicalId":422279,"journal":{"name":"International Workshop on Proof Exchange for Theorem Proving","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125146337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Quite often, verification tasks for distributed systems are accomplished via counter abstractions. Such abstractions can sometimes be justified via simulations and bisimulations. In this work, we supply logical foundations to this practice, by a specifically designed technique for second order quantifier elimination. Our method, once applied to specifications of verification problems for parameterized distributed systems, produces integer variables systems that are ready to be model-checked by current SMT-based tools. We demonstrate the feasibility of the approach with a prototype implementation and first experiments.
{"title":"Counter Simulations via Higher Order Quantifier Elimination: a preliminary report","authors":"S. Ghilardi, E. Pagani","doi":"10.4204/EPTCS.262.5","DOIUrl":"https://doi.org/10.4204/EPTCS.262.5","url":null,"abstract":"Quite often, verification tasks for distributed systems are accomplished via counter abstractions. Such abstractions can sometimes be justified via simulations and bisimulations. In this work, we supply logical foundations to this practice, by a specifically designed technique for second order quantifier elimination. Our method, once applied to specifications of verification problems for parameterized distributed systems, produces integer variables systems that are ready to be model-checked by current SMT-based tools. We demonstrate the feasibility of the approach with a prototype implementation and first experiments.","PeriodicalId":422279,"journal":{"name":"International Workshop on Proof Exchange for Theorem Proving","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128323853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We implement a user-extensible ad hoc connection between the Lean proof assistant and the computer algebra system Mathematica. By reflecting the syntax of each system in the other and providing a flexible interface for extending translation, our connection allows for the exchange of arbitrary information between the two systems. We show how to make use of the Lean metaprogramming framework to verify certain Mathematica computations, so that the rigor of the proof assistant is not compromised.
{"title":"An Extensible Ad Hoc Interface between Lean and Mathematica","authors":"R. Lewis","doi":"10.4204/EPTCS.262.4","DOIUrl":"https://doi.org/10.4204/EPTCS.262.4","url":null,"abstract":"We implement a user-extensible ad hoc connection between the Lean proof assistant and the computer algebra system Mathematica. By reflecting the syntax of each system in the other and providing a flexible interface for extending translation, our connection allows for the exchange of arbitrary information between the two systems. We show how to make use of the Lean metaprogramming framework to verify certain Mathematica computations, so that the rigor of the proof assistant is not compromised.","PeriodicalId":422279,"journal":{"name":"International Workshop on Proof Exchange for Theorem Proving","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129707238","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We describe the first results of a project of analyzing in which theories formal proofs can be expressed. We use this analysis as the basis of interoperability between proof systems.
{"title":"Analyzing Individual Proofs as the Basis of Interoperability between Proof Systems","authors":"Gilles Dowek","doi":"10.4204/EPTCS.262.1","DOIUrl":"https://doi.org/10.4204/EPTCS.262.1","url":null,"abstract":"We describe the first results of a project of analyzing in which theories formal proofs can be expressed. We use this analysis as the basis of interoperability between proof systems.","PeriodicalId":422279,"journal":{"name":"International Workshop on Proof Exchange for Theorem Proving","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131150292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article shows that theory exploration arises naturally from the need to progressively modify applied formal theories, especially those underpinning deployed systems that change over time or need to be attack-tolerant. Such formal theories require us to explore a problem space with a proof assistant and are naturally dynamic. The examples in this article are from our on-going decade-long eort to formally synthesize critical components of modern distributed systems. Using the Nuprl proof assistant we created event logic and its protocol theories. I also mention the impact over this period of extensions to the constructive type theory implemented by Nuprl. One of them led to our solution of a long standing open problem in constructive logic. Proof exchange among theorem provers is promising for improving the super tactics" that provide domain specic reasoners our protocol theories. Both theory exploration and proof exchange illustrate the dynamic nature of applied formal theories built using modern proof assistants. These activities dispel the false impression that formal theories are rigid and brittle artifacts that become less relevant over time in a fast moving eld like computer science.
{"title":"Proof Assistants and the Dynamic Nature of Formal Theories","authors":"R. Constable","doi":"10.29007/d2df","DOIUrl":"https://doi.org/10.29007/d2df","url":null,"abstract":"This article shows that theory exploration arises naturally from the need to progressively modify applied formal theories, especially those underpinning deployed systems that change over time or need to be attack-tolerant. Such formal theories require us to explore a problem space with a proof assistant and are naturally dynamic. The examples in this article are from our on-going decade-long eort to formally synthesize critical components of modern distributed systems. Using the Nuprl proof assistant we created event logic and its protocol theories. I also mention the impact over this period of extensions to the constructive type theory implemented by Nuprl. One of them led to our solution of a long standing open problem in constructive logic. Proof exchange among theorem provers is promising for improving the super tactics\" that provide domain specic reasoners our protocol theories. Both theory exploration and proof exchange illustrate the dynamic nature of applied formal theories built using modern proof assistants. These activities dispel the false impression that formal theories are rigid and brittle artifacts that become less relevant over time in a fast moving eld like computer science.","PeriodicalId":422279,"journal":{"name":"International Workshop on Proof Exchange for Theorem Proving","volume":"75 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114032479","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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