[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83902-en":3,"doc-seo-83902-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},83902,8796095461610,"Oliver","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","Towards Quantifier-Free Interpolation in Array Languages with Unbounded Data Specifications","This paper studies quantifier-free interpolation for fragments extending the extensional theory of arrays, focusing on expressive specifications over unbounded domains. It establishes general quantifier-free interpolation for combinatory array logic with iterated diffs and proves the uniform interpolation property for the simple flat array fragment. The results provide, to the authors’ knowledge, the first positive quantifier-free interpolation outcomes for array theories whose specifications capture rich unbounded data behavior.","arXiv :2607 .05 126v 1 [ cs .LO] 6 Jul 2026  \nTOWARDS QUANTIFIER-FREE INTERPOLATION IN ARRAY LANGUAGES WITH UNBOUNDED DATA SPECIFICATIONS  \nRODRIGO RAYA  a AND CHRISTOPHE RINGEISSEN  ba Technical University of Madrid, 28031 Madrid, Spain  \nb Universit´e de Lorraine, CNRS, Inria, LORIA, F-54000 Nancy, France  \nAbstract. We investigate quantifier-free interpolation properties for several fragments generalising the extensional theory of arrays. Our results include the (general) quantifierfree interpolation properties of combinatory array logic with iterated diffs and the uniform interpolation property of the simple flat array fragment. To our knowledge, these are the first positive quantifier-free interpolation results obtained for theories of arrays featuring expressive specifications over unbounded domains.  \n1. Introduction  \nSoftware model checkers employ a variety of automated reasoning techniques to develop correct programs. One of the challenges in model checking software, as opposed to hardware specifications, is the need to handle infinite domains. In this setting, one usually needs to work with a suitable abstraction of the system, specified in a decidable logical fragment. Upon certifying the correctness of the abstraction, a variety of program synthesis techniques can be used to produce source code in a programming language of interest.  \nOne application of interpolation algorithms is to accelerate the discovery of program invariants, which are essential to approximate the semantics of programming patterns such as loops or function calls. For instance, in CEGAR-based model checkers, interpolation algorithms are used to refine abstractions based on the analysis of spurious error traces [KMZ06] . When these traces and their interpolants are given by quantifier-free formulas, model checkers can make use of fast decision procedures implemented in Satisfiability Modulo Theories (SMT) solvers. Among the most expressive theories supported by these solvers are data structures theories. Unfortunately, not all data structure theories admit quantifier-free interpolation [HS19, GGKN23], which limits the class of systems for which safety properties can be shown with the help of interpolation.  \nAnother application of interpolation is program synthesis under the assumption that certain components of the system are known [KB13] .  \nThis paper addresses the property of (general and uniform) quantifier-free interpolation in data structure theories that generalise the extensionality axiom [McC93] to functions  \nKey words and phrases: formal verification, cardinality constraints, interpolation.  \nThe first author wishes to thank Dr. Tanja Schindler for various discussions regarding the material presented in [RR25a] . Research supported by the Santander Postdoctoral Fellowship SN260020008RRC.  \nPreprint submitted to © R. Raya and C. Ringeissen  \nLogical Methods in Computer Science ⃝CC Creative Commons  \nand relation symbols. This extension of the quantifier-free theory of arrays is particularly useful in the verification of parametrised systems or distributed protocols [DHV+14 , DHZ16 , GBR16 , AGP17 , DDMW19 , KKT19 , GP20], where one is often interested in guaranteeing that a certain property holds at every component of the system. It turns out that supporting such generalisation incurs only a mild overhead with respect to the extensional fragment [dMB09] . Moreover, recent work shows that the theory can be combined with cardinality constraints, preserving decidability [GP20, RK22] . Further extensions supporting regular relations and aggregation constraints are described in [RK24] .  \nIn [RR25a], we developed the observation that the decision procedures in [RK22, RK24] rely on a kind of reduction to the index and element theory of the data structure, analogous to the reduction approach found in the method of interpolation of [KMZ06] . We used this observation to show weak quantifier-free interpolation properties of combinatory array l","cbCaifhdWdyO2nYw","https://ap.wps.com/l/cbCaifhdWdyO2nYw","pdf",532955,4,1,25,"English","en",105,"# Introduction\n## Interpolation in program verification and synthesis\n## Related work and prior interpolation frameworks\n## Scope and contributions of the paper","[{\"question\":\"What interpolation property does the paper focus on, and why is it important?\",\"answer\":\"The paper focuses on (general and uniform) quantifier-free interpolation properties for array-related logical fragments. This is important because quantifier-free interpolants enable efficient reasoning in verification workflows using SMT solvers.\"},{\"question\":\"Which array fragments are shown to satisfy quantifier-free interpolation results?\",\"answer\":\"The paper proves general quantifier-free interpolation for combinatory array logic with iterated diffs and shows uniform interpolation for the simple flat array fragment.\"},{\"question\":\"What challenge does the paper address regarding arrays and unbounded domains?\",\"answer\":\"Many data-structure theories do not admit quantifier-free interpolation, limiting safety proofs. The paper targets array theories with expressive, unbounded data specifications and establishes positive interpolation results despite this challenge.\"}]",1784191330,63,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"towards-quantifier-free-interpolation-in-array-languages-with-unbounded-data-specifications","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":20},"https://docshare.wps.com/document/towards-quantifier-free-interpolation-in-array-languages-with-unbounded-data-specifications/83902/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-27","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What interpolation property does the paper focus on, and why is it important?","Question",{"text":75,"@type":76},"The paper focuses on (general and uniform) quantifier-free interpolation properties for array-related logical fragments. This is important because quantifier-free interpolants enable efficient reasoning in verification workflows using SMT solvers.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Which array fragments are shown to satisfy quantifier-free interpolation results?",{"text":80,"@type":76},"The paper proves general quantifier-free interpolation for combinatory array logic with iterated diffs and shows uniform interpolation for the simple flat array fragment.",{"name":82,"@type":73,"acceptedAnswer":83},"What challenge does the paper address regarding arrays and unbounded domains?",{"text":84,"@type":76},"Many data-structure theories do not admit quantifier-free interpolation, limiting safety proofs. The paper targets array theories with expressive, unbounded data specifications and establishes positive interpolation results despite this challenge.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]