{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/138965"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/138965","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Parametric Inversion of Programs","abstract":"Programmers and mathematicians often find themselves in situations where they must solve an inverse problem for a particular function. Solving an inverse problem generally means determining the input that produced a given output. However, this is ambiguous for most functions since the function may have multiple inputs that produce an output. Parametric inversion takes a new approach to solving inverse problems by proposing a method to make a non-injective (many-to-one) function invertible through a parameter. This parameter is used to distinguish between elements in the input space of a function that produced a given output. The existing parametric inversion theory primarily describes inverting mathematical functions. This work extends the theory to encompass inversion of programs. Specifically, we introduce a language, IR, and address problems related to inversion of a simple code block, control flow, and re-use of variables. This includes a practical implementation in Julia that is able to correctly invert a suite of sample programs.","abstract_html":"Programmers and mathematicians often find themselves in situations where they must solve an inverse problem for a particular function. Solving an inverse problem generally means determining the input that produced a given output. However, this is ambiguous for most functions since the function may have multiple inputs that produce an output. Parametric inversion takes a new approach to solving inverse problems by proposing a method to make a non-injective (many-to-one) function invertible through a parameter. This parameter is used to distinguish between elements in the input space of a function that produced a given output. The existing parametric inversion theory primarily describes inverting mathematical functions. This work extends the theory to encompass inversion of programs. Specifically, we introduce a language, IR, and address problems related to inversion of a simple code block, control flow, and re-use of variables. This includes a practical implementation in Julia that is able to correctly invert a suite of sample programs.","abstract_has_math":false,"creators":["Morejon, David"],"institution":"Massachusetts Institute of Technology","degree_name":"Master","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science","school":null,"contributors":[],"advisors":["Tavares, Zenna","Solar-Lezama, Armando"],"committee_chairs":[],"committee_members":[],"year":2021,"date_issued":"2021-06","date_published":"2021-06","updated_at":"2026-07-22T22:22:02Z","subjects":[],"languages":[],"rights":["In Copyright - Educational Use Permitted","Copyright MIT"],"rights_urls":["http://rightsstatements.org/page/InC-EDU/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/1721.1/138965","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Tavares, Zenna","Solar-Lezama, Armando"]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science"]},{"key":"dc:creator","label":"Author","values":["Morejon, David"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2022-01-14T14:41:38Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2022-01-14T14:41:38Z"]},{"key":"dc:date.issued","label":"Date","values":["2021-06"]},{"key":"dc:publisher","label":"Institution","values":["Massachusetts Institute of Technology"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master","Master of Engineering in Electrical Engineering and Computer Science"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright - Educational Use Permitted","Copyright MIT"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/page/InC-EDU/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/1721.1/138965"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Programmers and mathematicians often find themselves in situations where they must solve an inverse problem for a particular function. Solving an inverse problem generally means determining the input that produced a given output. However, this is ambiguous for most functions since the function may have multiple inputs that produce an output. Parametric inversion takes a new approach to solving inverse problems by proposing a method to make a non-injective (many-to-one) function invertible through a parameter. This parameter is used to distinguish between elements in the input space of a function that produced a given output. The existing parametric inversion theory primarily describes inverting mathematical functions. This work extends the theory to encompass inversion of programs. Specifically, we introduce a language, IR, and address problems related to inversion of a simple code block, control flow, and re-use of variables. This includes a practical implementation in Julia that is able to correctly invert a suite of sample programs."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["M.Eng."]},{"key":"dc:title","label":"Title","values":["Parametric Inversion of Programs"]}]}],"canonical_facts":{"dc:contributor.advisor":["Tavares, Zenna","Solar-Lezama, Armando"],"dc:contributor.department":["Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science"],"dc:creator":["Morejon, David"],"dc:date.accessioned":["2022-01-14T14:41:38Z"],"dc:date.available":["2022-01-14T14:41:38Z"],"dc:date.issued":["2021-06"],"dc:description.abstract":["Programmers and mathematicians often find themselves in situations where they must solve an inverse problem for a particular function. Solving an inverse problem generally means determining the input that produced a given output. However, this is ambiguous for most functions since the function may have multiple inputs that produce an output. Parametric inversion takes a new approach to solving inverse problems by proposing a method to make a non-injective (many-to-one) function invertible through a parameter. This parameter is used to distinguish between elements in the input space of a function that produced a given output. The existing parametric inversion theory primarily describes inverting mathematical functions. This work extends the theory to encompass inversion of programs. Specifically, we introduce a language, IR, and address problems related to inversion of a simple code block, control flow, and re-use of variables. This includes a practical implementation in Julia that is able to correctly invert a suite of sample programs."],"dc:description.degree":["M.Eng."],"dc:identifier.uri":["https://hdl.handle.net/1721.1/138965"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["In Copyright - Educational Use Permitted","Copyright MIT"],"dc:rights.uri":["http://rightsstatements.org/page/InC-EDU/1.0/"],"dc:title":["Parametric Inversion of Programs"],"dc:type":["Thesis"],"thesis:degree_name":["Master","Master of Engineering in Electrical Engineering and Computer Science"]},"updated_at":"2026-07-22T22:22:02Z"}