[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-652814-105":3,"detail-sidebar-cat-0-en-105":80,"doc-detail-652814-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":73,"head_meta":75,"extra_data":77,"updated_unix":79},105,"en","the-isabelleisar-reference-manual-interactive-theorem-proving","The Isabelle/Isar Reference Manual - interactive theorem proving","","The Isabelle system and its Isar language provide structured, machine-checked proof development in higher-order logic. Isabelle offers a generic infrastructure for deductive systems in Standard ML, while Isar introduces an interpreted language environment tailored for theory and proof development. Compared with raw ML, Isar supports a more robust development workflow, including theory development graphs and managed transactions with unlimited undo. 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Isar offers an interpreted, tailored language environment to support theory and proof development through structured documents.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"How does Isar differ from raw ML for proof development?",{"text":67,"@type":63},"Isar provides a more robust and comfortable platform than raw ML by supporting structured theory development graphs and managed transactions with unlimited undo, improving the overall development workflow for proofs.",{"name":69,"@type":60,"acceptedAnswer":70},"What are proper and improper Isar commands?",{"text":71,"@type":63},"Isar commands can be proper document constructors or improper commands. Improper language elements are discouraged for final readable outcomes, but can be helpful during proof development for tasks like diagnostics or emulating old-style tactical proving.","https://schema.org",{"og:url":32,"og:type":74,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":76,"canonical":32},"index,follow",{"doc_id":78,"site_id":7},652814,1792882998,{"code":4,"msg":81,"data":82},"success",[83,87,91,95,100,104,109,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":84,"show_sort_weight":85,"slug":86},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":88,"show_sort_weight":89,"slug":90},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":92,"show_sort_weight":93,"slug":94},"Exam",70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":102,"slug":103},6,50,"technology",{"id":105,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},7,"Healthcare",40,"healthcare",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},8,"Research & Report",30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},19,"General","general",{"code":4,"msg":81,"data":131},{"doc_id":78,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":101,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":22,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":139,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":79,"read_time":144},962093541761,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Isabelle  \nIsar  \n=  \n→  \nλ  \n∀  \nβ  \nα  \nThe Isabelle/Isar Reference Manual  \nMakarius Wenzel  \nWith Contributions by Clemens Ballarin, Stefan Berghofer, Jasmin Blanchette, Timothy Bourke, Lukas Bulwahn, Amine Chaieb, Lucas Dixon, Florian Haftmann, Brian Huffman, Lars Hupel, Gerwin Klein, Alexander Krauss, Ondřej Kunčar, Andreas Lochbihler, Tobias Nipkow, Lars Noschinski, David von Oheimb, Larry Paulson, Sebastian Skalberg, Christian Sternagel, Dmitriy Traytel  \nOctober 24, 2026  \nPreface  \nThe Isabelle system essentially provides a generic infrastructure for building deductive systems (programmed in Standard ML), with a special focus on interactive theorem proving in higher-order logics. Many years ago, even endusers would refer to certain ML functions (goal commands, tactics, tacticalsetc.) to pursue their everyday theorem proving tasks.  \nIn contrast Isar provides an interpreted language environment of its own, which has been specifically tailored for the needs of theory and proof development. Compared to raw ML, the Isabelle/Isar top-level provides a more robust and comfortable development platform, with proper support for theory development graphs, managed transactions with unlimited undo etc. In its pioneering times, the Isabelle/Isar version of the Proof General user interface [2 , 3] has contributed to the success of for interactive theory and proof development in this advanced theorem proving environment, even though it was somewhat biased towards old-style proof scripts. The more recent Isabelle/jEdit Prover IDE [61] emphasizes the document-oriented approach of Isabelle/Isar again more explicitly.  \nApart from the technical advances over bare-bones ML programming, the main purpose of the Isar language is to provide a conceptually different view on machine-checked proofs [58 , 59] . Isar stands for Intelligible semiautomated reasoning. Drawing from both the traditions of informal mathematical proof texts and high-level programming languages, Isar offers a versatile environment for structured formal proof documents. Thus properly written Isar proofs become accessible to a broader audience than unstructured tactic scripts (which typically only provide operational information for the machine) . Writing human-readable proof texts certainly requires some additional efforts by the writer to achieve a good presentation, both of formal and informal parts of the text. On the other hand, human-readable formal texts gain some value in their own right, independently of the mechanic proof-checking process.  \nDespite its grand design of structured proof texts, Isar is able to assimilate the old tactical style as an “improper” sub-language. This provides an easy upgrade path for existing tactic scripts, as well as some means for interactive experimentation and debugging of structured proofs. Isabelle/Isar supports  \nii  \na broad range of proof styles, both readable and unreadable ones.  \nThe generic Isabelle/Isar framework (see chapter 2) works reasonably well for any Isabelle object-logic that conforms to the natural deduction view of the Isabelle/Pure framework. Specific language elements introduced by Isabelle/HOL are described in part III. Although the main language elements are already provided by the Isabelle/Pure framework, examples given in the generic parts will usually refer to Isabelle/HOL.  \nIsar commands may be either proper document constructors, or improper commands. Some proof methods and attributes introduced later are classified as improper as well. Improper Isar language elements, which are marked by “􀀃 ” in the subsequent chapters; they are often helpful when developing proof documents, but their use is discouraged for the final human-readable outcome. Typical examples are diagnostic commands that print terms or theorems according to the current context; other commands emulate oldstyle tactical theorem proving.  \nContents  \nI Basic Concepts 1  \n1 Synopsis 2  \n1. 1 Notepad . . . . . . . . . . . . . . . . . . . . . . . . ","cbCaih7M0CgixSNR","https://ap.wps.com/l/cbCaih7M0CgixSNR","pdf",1828202,365,"English","# Preface\n## Isabelle and Isar: purpose and contrast\n## Human-readable structured proofs\n## Proper vs improper Isar commands\n## Generic Isabelle/Isar framework\n# Contents\n## Basic Concepts\n### Synopsis\n### Notepad\n### Types and terms\n### Facts\n### Block structure\n### Calculational reasoning\n### Induction\n### Natural Deduction\n### Generalized elimination and cases\n## The Isabelle/Isar Framework\n### The Pure framework\n### The Isar proof lang","[{\"question\":\"What are the main roles of the Isabelle system and the Isar language?\",\"answer\":\"Isabelle provides infrastructure for building deductive systems in Standard ML, focusing on interactive theorem proving in higher-order logics. Isar offers an interpreted, tailored language environment to support theory and proof development through structured documents.\"},{\"question\":\"How does Isar differ from raw ML for proof development?\",\"answer\":\"Isar provides a more robust and comfortable platform than raw ML by supporting structured theory development graphs and managed transactions with unlimited undo, improving the overall development workflow for proofs.\"},{\"question\":\"What are proper and improper Isar commands?\",\"answer\":\"Isar commands can be proper document constructors or improper commands. Improper language elements are discouraged for final readable outcomes, but can be helpful during proof development for tasks like diagnostics or emulating old-style tactical proving.\"}]","The Isabelle/Isar Reference Manual - interactive theorem proving | PDF",920]