{"title":"Combining Higher-Order Logic with Set Theory Formalizations.","authors":"Cezary Kaliszyk, Karol Pąk","doi":"10.1007/s10817-023-09663-5","DOIUrl":"10.1007/s10817-023-09663-5","url":null,"abstract":"<p><p>The Isabelle Higher-order Tarski-Grothendieck object logic includes in its foundations both higher-order logic and set theory, which allows importing the libraries of Isabelle/HOL and Isabelle/Mizar. The two libraries, however, define all the basic concepts independently, which means that the results in the two are disconnected. In this paper, we align significant parts of these two libraries, by defining isomorphisms between their concepts, including the real numbers and algebraic structures. The isomorphisms allow us to transport theorems between the foundations and use the results from the libraries simultaneously.</p>","PeriodicalId":15082,"journal":{"name":"Journal of Automated Reasoning","volume":"67 2","pages":"20"},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10209288/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9545317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Alessandro Abate, Haniel Barbosa, Clark Barrett, Cristina David, Pascal Kesseli, Daniel Kroening, Elizabeth Polgreen, Andrew Reynolds, Cesare Tinelli
{"title":"Synthesising Programs with Non-trivial Constants.","authors":"Alessandro Abate, Haniel Barbosa, Clark Barrett, Cristina David, Pascal Kesseli, Daniel Kroening, Elizabeth Polgreen, Andrew Reynolds, Cesare Tinelli","doi":"10.1007/s10817-023-09664-4","DOIUrl":"10.1007/s10817-023-09664-4","url":null,"abstract":"<p><p>Program synthesis is the mechanised construction of software. One of the main difficulties is the efficient exploration of the very large solution space, and tools often require a user-provided syntactic restriction of the search space. While useful in general, such syntactic restrictions provide little help for the generation of programs that contain non-trivial constants, unless the user is able to provide the constants in advance. This is a fundamentally difficult task for state-of-the-art synthesisers. We propose a new approach to the synthesis of programs with non-trivial constants that combines the strengths of a counterexample-guided inductive synthesiser with those of a theory solver, exploring the solution space more efficiently without relying on user guidance. We call this approach CEGIS(<math><mi>T</mi></math>), where <math><mi>T</mi></math> is a first-order theory. We present two exemplars, one based on Fourier-Motzkin (FM) variable elimination and one based on first-order satisfiability. We demonstrate the practical value of CEGIS(<math><mi>T</mi></math>) by automatically synthesising programs for a set of intricate benchmarks. Additionally, we present a case study where we integrate CEGIS(<math><mi>T</mi></math>) within the mature synthesiser CVC4 and show that CEGIS(<math><mi>T</mi></math>) improves CVC4's results.</p>","PeriodicalId":15082,"journal":{"name":"Journal of Automated Reasoning","volume":"67 2","pages":"19"},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10182957/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9476445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Unifying Splitting.","authors":"Gabriel Ebner, Jasmin Blanchette, Sophie Tourret","doi":"10.1007/s10817-023-09660-8","DOIUrl":"https://doi.org/10.1007/s10817-023-09660-8","url":null,"abstract":"<p><p>AVATAR is an elegant and effective way to split clauses in a saturation prover using a SAT solver. But is it refutationally complete? And how does it relate to other splitting architectures? To answer these questions, we present a unifying framework that extends a saturation calculus (e.g., superposition) with splitting and that embeds the result in a prover guided by a SAT solver. The framework also allows us to study <i>locking</i>, a subsumption-like mechanism based on the current propositional model. Various architectures are instances of the framework, including AVATAR, labeled splitting, and SMT with quantifiers.</p>","PeriodicalId":15082,"journal":{"name":"Journal of Automated Reasoning","volume":"67 2","pages":"16"},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10147822/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9757154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Aart Middeldorp, Alexander Lochmann, Fabian Mitterwallner
{"title":"First-Order Theory of Rewriting for Linear Variable-Separated Rewrite Systems: Automation, Formalization, Certification.","authors":"Aart Middeldorp, Alexander Lochmann, Fabian Mitterwallner","doi":"10.1007/s10817-023-09661-7","DOIUrl":"https://doi.org/10.1007/s10817-023-09661-7","url":null,"abstract":"<p><p>The first-order theory of rewriting is decidable for linear variable-separated rewrite systems. We present a new decision procedure which is the basis of FORT, a decision and synthesis tool for properties expressible in the theory. The decision procedure is based on tree automata techniques and verified in Isabelle. Several extensions make the theory more expressive and FORT more versatile. We present a certificate language that enables the output of FORT to be certified by the certifier FORTify generated from the formalization, and we provide extensive experiments.</p>","PeriodicalId":15082,"journal":{"name":"Journal of Automated Reasoning","volume":"67 2","pages":"14"},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10079773/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9274582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}