[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-665539-105":59,"doc-detail-665539-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","properties-of-a-computational-lambda-calculus-for-higher-order-relational-queries","Properties of a Computational Lambda Calculus for Higher-Order Relational Queries","","We investigate the operational semantics of an untyped computational lambda calculus whose normal forms serve as database queries. The calculus extends a computational core with operations and rewriting rules that transform the monadic computational type into a multiset monad, enabling a representation of tables. Additional comonadic constructs and rewriting rules support tables of tables. Confluence is established using decreasing diagrams, and a Curry-style idempotent intersection type assignment system proves type invariance under conversion.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/properties-of-a-computational-lambda-calculus-for-higher-order-relational-queries/665539/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/properties-of-a-computational-lambda-calculus-for-higher-order-relational-queries/665539.png","ImageObject",300,407,{"name":92,"@type":93},"Danger Angel","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-29",true,{"@type":102,"interactionType":103,"userInteractionCount":19},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What does the paper study in the computational lambda calculus?","Question",{"text":112,"@type":113},"It studies operational semantics of an untyped computational lambda calculus where normal forms represent database queries, including extensions that model tables and tables of tables.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How is multiset behavior introduced for database tables?",{"text":117,"@type":113},"By extending the computational core with operations for empty multisets, multiset union, and rewriting rules that shape computations into a multiset monad.",{"name":119,"@type":110,"acceptedAnswer":120},"What type system result is proven?",{"text":121,"@type":113},"The paper introduces an idempotent intersection type assignment system and proves type invariance under conversion, supporting soundness and completeness relative to termination.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},665539,1793304824,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":19,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":129,"read_time":144},962090769052,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","Properties of a Computational Lambda Calculus for Higher-Order Relational Queries  \nClaudio Sacerdoti Coen 1 , Riccardo Treglia 1 ,*  \n1 Università di Bologna, Bologna, Italy, Mura Anteo Zamboni, 7, 40126 Bologna (BO), Italy  \nAbstract  \nWe study the operational semantics of an untyped computational lambda calculus whose normal forms represent queries on databases. The calculus extends the computational core with additional operations and rewriting rules whose effect is to turn the monadic type of computations into a multiset monad that captures tables. Moreover, we introduce comonadic constructs and additional rewriting rules to be able to form tables of tables. Proving confluence becomes tricky: we succeed exploiting decreasing diagrams. In the second part, we study a Curry style type assignment system for the calculus. We introduce an idempotent intersection type system establishing type invariance under conversion.  \nKeywords  \nLambda calculus, Monads, Confluence, Intersection Types, Databases  \n1. Introduction to the Calculus: Syntax and Reduction Relation  \nThe second author et al. have introduced and studied in [1, 2] the computational core 􀀕© , a 􀀕-calculus inspired by Moggi’s computational one [3], [4] . The calculus differentiates between values and computations, the latter obtained via return/bind constructs for a generic monad. The operational semantics is obtained simply by orienting the monadiclaws, and confluence was proved among other properties.  \nIn this work, we extend 􀀕© with specific additional operations and rewriting rules over computations that turn the generic monad into a multiset monad: the 0-ary operation ∅ represents the empty multiset, ⊎ the union of multisets, and the monadic return, denoted by [·], is now interpreted as forming a singleton. The rewriting rules partially capture the algebraicity of the operations in the sense of Plotkin and Power [5, 6] by letting the operators commute with those rewriting contexts that are built from bind operators, only. Because in 􀀕© , contrary to Moggi’s computational 􀀕-calculus, values and computations are rigidly split, the extension described so far does not allow the formation of multisets of multisets, because multisets are not values. To overcome the issue, we  \nICTCS’23: 24th Italian Conference on Theoretical Computer Science, September 13 –15, 2023, Palermo, Italy  \n* Corresponding author.  \n$ [claudio.sacerdoticoen@unibo.it](claudio.sacerdoticoen@unibo.it) (C. S. Coen); [riccardo.treglia@unibo.it](riccardo.treglia@unibo.it) (R. Treglia)  \n􀂀 https://www.cs.unibo.it/~sacerdot/ (C. S. Coen); [https://sites.google.com/view/riccardotreglia/home](https://sites.google.com/view/riccardotreglia/home)[ ](https://sites.google.com/view/riccardotreglia/home)(R. Treglia)  \n􀀚 0000-0002-4360-6016 (C. S. Coen); 0000-0002-9731-1248 (R. Treglia)  \n© 2023 Copyright © 2023 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0) .  \nCEUR Workshop Proceedings ([CEUR-WS.org](CEUR-WS.org))  \nCEUR ~~  ~~[Workshop](Workshop ceur-ws.org)[ ceur-ws.org](Workshop ceur-ws.org)[ ](Workshop ceur-ws.org)[Proceedings](Proceedings ISSN 1613-0073)[ ISSN 1613-0073](Proceedings ISSN 1613-0073)   \nadd two more co-monadic constructs to reflect computations into values, following ideas by [7] . These constructs are the thunk/force constructs of Levy’s call-by-push-value calculus [8]; however, our calculus is strong, i. e. , it allows reduction inside values as well. Finally, we introduce an equational theory over computations to capture associativity and commutativity of ⊎ and idempotency of ∅: this is the minimal theory that turns the calculus into a confluent one.  \nThe calculus we are going to introduce takes inspiration from the (untyped) NRC􀀕 calculus [9], and it is to it as 􀀕© is to the (untyped) 􀀕-calculus. Indeed, we introduce it with the intent of studying semantic properties of the NRC􀀕-calculus via intersection types, tr","cbCaikWAyACA5eqH","https://ap.wps.com/l/cbCaikWAyACA5eqH","pdf",907450,14,"English","# Introduction to the Calculus: Syntax and Reduction Relation\n## Multiset monad extension and rewriting rules\n## Comonadic constructs and equational theory\n## Motivation from NRC calculus and intersection types\n## Intersection types and idempotent type discipline","[{\"question\":\"What does the paper study in the computational lambda calculus?\",\"answer\":\"It studies operational semantics of an untyped computational lambda calculus where normal forms represent database queries, including extensions that model tables and tables of tables.\"},{\"question\":\"How is multiset behavior introduced for database tables?\",\"answer\":\"By extending the computational core with operations for empty multisets, multiset union, and rewriting rules that shape computations into a multiset monad.\"},{\"question\":\"What type system result is proven?\",\"answer\":\"The paper introduces an idempotent intersection type assignment system and proves type invariance under conversion, supporting soundness and completeness relative to termination.\"}]","Properties of a Computational Lambda Calculus for Higher-Order Relational Queries | PDF",35]