{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/121403"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/121403","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Matching μ-Logic","abstract":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-12-04 without embargo terms","abstract_html":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-12-04 without embargo terms","abstract_has_math":false,"creators":["Chen, Xiaohong"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":["Roşu, Grigore","Meseguer, José","Parthasarathy, Madhusudan","Veanes, Margus"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2023,"date_issued":"2023-08","date_published":"2023-08","updated_at":"2026-07-22T22:24:57Z","subjects":["Logic","Completeness","Theorem Proving","Proof Generation","Proof Checking"],"languages":["en","eng"],"rights":["Copyright 2023 Xiaohong Chen"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/121403","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Roşu, Grigore","Meseguer, José","Parthasarathy, Madhusudan","Veanes, Margus"]},{"key":"dc:creator","label":"Author","values":["Chen, Xiaohong"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2023-08","2023-05-26"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computer Science"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Logic","Completeness","Theorem Proving","Proof Generation","Proof Checking"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2023 Xiaohong Chen"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/121403"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-12-04 without embargo terms","The student, Xiaohong Chen, accepted the attached license on 2023-05-24 at 18:13.","The student, Xiaohong Chen, submitted this Dissertation for approval on 2023-05-24 at 18:24.","This Dissertation was approved for publication on 2023-05-26 at 09:11.","DSpace SAF Submission Ingestion Package generated from Vireo submission #19392 on 2023-12-04 at 16:59:48","We present matching μ-logic, which is a unifying logic for specifying and reasoning about programs and programming languages. Matching μ-logic uses its formulas, called patterns, to uniformly express programs’ static structures, dynamic behaviors, and logical constraints. Programming languages can be formally defined as matching μ-logic theories, which include patterns as axioms. The correctness of programming language implementations and tools can be proved using a fixed proof system. These proofs can be encoded as proof objects and automatically checked using a small proof checker. An important feature of matching μ-logic is its μ operator, which provides direct support for specifying fixpoints and thus enables to specify and reason about induction and recursion. We study the proof theory of matching μ-logic and prove a few important completeness results. We study the expressive power of matching μ-logic and show that many important logics, calculi, and foundations of computations, especially those featuring fixpoints/induction/recursion, can be defined as matching μ-logic theories. We study automated reasoning for matching μ-logic, with a focus on fixpoint reasoning. We propose a set of high-level automated proof rules that can be applied to many matching μ-logic theories, and thus enable automated reasoning in them. We propose applicative matching μ-logic, abbreviated as AML, as a simple instance of matching μ-logic that retains all of its expressive power. AML is a fragment of matching μ-logic where we eliminate sorts and many-sorted symbols from matching μ-logic, because they are definable using axioms and theories. We present an encoding of matching μ-logic into AML and implement a 200-line proof checker for AML using Metamath. We study proof-certifying program execution and formal verification, where the correctness of an execution/verification task is established by an AML proof object, serving as a machine-checkable correctness certificate. Our approach is based on the K formal language semantics framework. We design and implement procedures that output AML proof objects for the language-agnostic program interpreter and formal verifier of K, which are parametric in the formal semantics of a programming language. This way, we reduce checking the correctness of a language task (i.e., executing or verifying a program) to checking the corresponding AML proof objects using the proof checker. We hope to demonstrate that matching μ-logic can serve as a unifying foundation for programming, where programming languages are defined as theories, and the correctness of language tools is established by machine-checkable proof objects."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Matching μ-Logic"]}]}],"canonical_facts":{"dc:contributor":["Roşu, Grigore","Meseguer, José","Parthasarathy, Madhusudan","Veanes, Margus"],"dc:creator":["Chen, Xiaohong"],"dc:date":["2023-08","2023-05-26"],"dc:description":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-12-04 without embargo terms","The student, Xiaohong Chen, accepted the attached license on 2023-05-24 at 18:13.","The student, Xiaohong Chen, submitted this Dissertation for approval on 2023-05-24 at 18:24.","This Dissertation was approved for publication on 2023-05-26 at 09:11.","DSpace SAF Submission Ingestion Package generated from Vireo submission #19392 on 2023-12-04 at 16:59:48","We present matching μ-logic, which is a unifying logic for specifying and reasoning about programs and programming languages. Matching μ-logic uses its formulas, called patterns, to uniformly express programs’ static structures, dynamic behaviors, and logical constraints. Programming languages can be formally defined as matching μ-logic theories, which include patterns as axioms. The correctness of programming language implementations and tools can be proved using a fixed proof system. These proofs can be encoded as proof objects and automatically checked using a small proof checker. An important feature of matching μ-logic is its μ operator, which provides direct support for specifying fixpoints and thus enables to specify and reason about induction and recursion. We study the proof theory of matching μ-logic and prove a few important completeness results. We study the expressive power of matching μ-logic and show that many important logics, calculi, and foundations of computations, especially those featuring fixpoints/induction/recursion, can be defined as matching μ-logic theories. We study automated reasoning for matching μ-logic, with a focus on fixpoint reasoning. We propose a set of high-level automated proof rules that can be applied to many matching μ-logic theories, and thus enable automated reasoning in them. We propose applicative matching μ-logic, abbreviated as AML, as a simple instance of matching μ-logic that retains all of its expressive power. AML is a fragment of matching μ-logic where we eliminate sorts and many-sorted symbols from matching μ-logic, because they are definable using axioms and theories. We present an encoding of matching μ-logic into AML and implement a 200-line proof checker for AML using Metamath. We study proof-certifying program execution and formal verification, where the correctness of an execution/verification task is established by an AML proof object, serving as a machine-checkable correctness certificate. Our approach is based on the K formal language semantics framework. We design and implement procedures that output AML proof objects for the language-agnostic program interpreter and formal verifier of K, which are parametric in the formal semantics of a programming language. This way, we reduce checking the correctness of a language task (i.e., executing or verifying a program) to checking the corresponding AML proof objects using the proof checker. We hope to demonstrate that matching μ-logic can serve as a unifying foundation for programming, where programming languages are defined as theories, and the correctness of language tools is established by machine-checkable proof objects."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/121403"],"dc:language":["en","eng"],"dc:rights":["Copyright 2023 Xiaohong Chen"],"dc:subject":["Logic","Completeness","Theorem Proving","Proof Generation","Proof Checking"],"dc:title":["Matching μ-Logic"],"dc:type":["text"],"thesis:degree_discipline":["Computer Science"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:57Z"}