[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82177-en":3,"doc-seo-82177-105":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},82177,687197207057,"Sage","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Agentic Proof and Property-Based Testing via Property Templates in Data Intensive Computing","AI-driven code generation shifts software engineering’s bottleneck to intent specification and validation. Addressing this durability crisis requires validating each candidate property in two complementary ways: formally proved against a system model and empirically exercised on the real implementation. Scaling this approach demands both verifying property correctness and operationalizing property-based testing without hallucinated intent. This work proposes property templates—recurring, parameterized property patterns—to support dual-track validation in Apache Spark, evaluated with Lean 4 proofs and executable PBTs.","Agentic Proof and Property-Based Testing via Property-Templates in Data-Intensive Computing  \nSeongmin Lee*  \nUniversity of California, Los Angeles Los Angeles, CA, USA [seongminlee@g.ucla.edu](seongminlee@g.ucla.edu)  \nYaoxuan Wu*  \nUniversity of California, Los Angeles Los Angeles, CA, USA [thaddywu@cs.ucla.edu](thaddywu@cs.ucla.edu)  \nMiryung Kim  \nUniversity of California, Los Angeles Los Angeles, CA, USA [miryung@cs.ucla.edu](miryung@cs.ucla.edu)  \narXiv :2607 .09072v 1 [ cs . SE] 10 Jul 2026  \nAbstract—As the cost of code generation becomes cheaper with AI, the new bottleneck in software engineering has shifted to intent specification and validation. Overcoming this durability crisis of AI-driven coding requires more than traditional fuzzing: each candidate property must be both proven correct over a model of the system and shown to hold on the real implementation, making formal proof and systematic property-based testing (PBT) complementary. However, validating properties this way at scale requires solving two core subproblems: (1) verifying that candidate properties are indeed correct, and (2) operationalizing PBT without AI hallucination. We hypothesize that recurring property patterns, cast as property templates—abstract, parameterized forms with holes—address both subproblems at once.  \nThis paper investigates the value of recurring property patterns in a target system, Apache Spark. In data-intensive scalable computing systems, numerous correctness properties arise from the principles of data partition, computation decomposition, and data-flow computation. For instance, a classic recurring pattern is aggregation decomposition, where, for all data D and workloads Q, a global function executed on the entire dataset relates to a local function followed by a recombiner. We design an agentic, dual-track validation framework that uses property templates to formally verify their correctness in the Lean 4 theorem prover, and instantiate PBT templates as concretized executable PBTs. Our evaluation shows that property templates increase agentic proof engineering success by up to 2.6 × (avg: 1.6 ×) and reduce proof hallucinations by 59%. Template-guided PBT synthesis reduces intent misalignments from 22 to 1 and cuts synthesis cost by up to 5.7 × (avg: 3 .8 ×). Template-guided synthesis further exceeds a state-of-the-art Spark fuzzer and approaches unguided LLM-based PBT on code coverage. Finally, comparing the two tracks is informative: for example, when a proof succeeds yet a PBT finds a counterexample, the mismatch identifies a gap between the formal model and the implementation.  \nI. INTRODUCTION  \nEstablishing that a software system behaves as intended restson two complementary validation techniques. This behavior is captured as a specification—a conjectured property the system should satisfy. Formal proof [1] mathematically verifies it against a model of the system, while property-based testing (PBT) [2], [3], [4] exercises the real implementation on many generated inputs. The two are complementary: a proof determines whether the property is in fact correct, while PBT tests whether the implementation actually obeys it. Applying both therefore yields far stronger evidence than either alone.  \n* Seongmin Lee and Yaoxuan Wu contributed equally to this work.  \nA real software system’s correctness hinges on complex, endto-end properties of its behavior. For example, a query should return the same results whether or not the engine optimizesit, for every input dataset, rather than merely producing the correct output for a single function. Many such properties must be validated, including the correctness of each optimization, rewrite, and equivalence on which the engine relies. Validating even one property through a machine-checked proof, an executable test, or both is laborious. Repeating this process by hand, property after property, does not scale. Language models can now propose candidate properties at scale [5], [6], but t","cbCaibzmmEJUa6dy","https://ap.wps.com/l/cbCaibzmmEJUa6dy","pdf",743945,2,1,12,"English","en",105,"# Abstract\n# I. Introduction\n## Formal proof vs property-based testing\n## Recurring correctness properties in data-intensive systems","[{\"question\":\"Why is validating AI-generated intent a bottleneck in software engineering?\",\"answer\":\"As code generation becomes cheaper, the main challenge becomes specifying and validating the developer’s intent. Candidate properties can be subtly wrong, and generated tests may check weaker conditions than intended.\"},{\"question\":\"What problem does the paper address at scale?\",\"answer\":\"The paper addresses how to validate many proposed correctness properties by confirming each property’s correctness and exercising it as intended. It targets both verifying candidate properties and making property-based testing operational without hallucinated intent.\"},{\"question\":\"How do property templates improve the validation process in Apache Spark?\",\"answer\":\"The approach exploits recurring property patterns by encoding family structure once using parameterized property templates. It then uses an agentic dual-track framework to (1) formally verify template instances in Lean 4 and (2) instantiate executable PBTs, improving proof success, reducing hallucinations, and reducing intent misalignments.\"}]",1784178609,30,{"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},"agentic-proof-and-property-based-testing-via-property-templates-in-data-intensive-computing","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,47,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":20},"https://docshare.wps.com/document/","Document",{"item":48,"name":12,"@type":43,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/agentic-proof-and-property-based-testing-via-property-templates-in-data-intensive-computing/82177/",4,{"url":51,"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","2026-07-19","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},"Why is validating AI-generated intent a bottleneck in software engineering?","Question",{"text":75,"@type":76},"As code generation becomes cheaper, the main challenge becomes specifying and validating the developer’s intent. Candidate properties can be subtly wrong, and generated tests may check weaker conditions than intended.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What problem does the paper address at scale?",{"text":80,"@type":76},"The paper addresses how to validate many proposed correctness properties by confirming each property’s correctness and exercising it as intended. It targets both verifying candidate properties and making property-based testing operational without hallucinated intent.",{"name":82,"@type":73,"acceptedAnswer":83},"How do property templates improve the validation process in Apache Spark?",{"text":84,"@type":76},"The approach exploits recurring property patterns by encoding family structure once using parameterized property templates. It then uses an agentic dual-track framework to (1) formally verify template instances in Lean 4 and (2) instantiate executable PBTs, improving proof success, reducing hallucinations, and reducing intent misalignments.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,122,127,130,134],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"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":29,"slug":121},"research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]