{"id":151006,"date":"1994-01-01T00:00:00","date_gmt":"1994-01-01T00:00:00","guid":{"rendered":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/msr-research-item\/a-tutorial-on-co-induction-and-functional-programming\/"},"modified":"2018-10-16T20:16:24","modified_gmt":"2018-10-17T03:16:24","slug":"a-tutorial-on-co-induction-and-functional-programming","status":"publish","type":"msr-research-item","link":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/publication\/a-tutorial-on-co-induction-and-functional-programming\/","title":{"rendered":"A Tutorial on Co-induction and Functional Programming"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Co-induction is an important tool for reasoning about unbounded structures. This tutorial explains the foundations of co-induction, and shows how it justifies intuitive arguments about lazy streams, of central importance to lazy functional programmers. We explain from first principles a theory based on a new formulation of bisimilarity for functional programs, which coincides exactly with Morris-style contextual equivalence. We show how to prove properties of lazy streams by co-induction and derive Bird and Wadler&#8217;s Take Lemma, a well-known proof technique for lazy streams.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Co-induction is an important tool for reasoning about unbounded structures. This tutorial explains the foundations of co-induction, and shows how it justifies intuitive arguments about lazy streams, of central importance to lazy functional programmers. We explain from first principles a theory based on a new formulation of bisimilarity for functional programs, which coincides exactly with [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":[{"type":"user_nicename","value":"adg","user_id":"30825"}],"msr_publishername":"Springer London","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"Proceedings of the 1994 Glasgow Workshop on Functional Programming, Ayr, Scotland","msr_editors":"","msr_how_published":"","msr_isbn":"978-3-540-19914-4 (Print) 978-1-4471-3573-9 (Online)","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"78-95","msr_page_range_start":"78","msr_page_range_end":"95","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"Proceedings of the 1994 Glasgow Workshop on Functional Programming, Ayr, Scotland","msr_doi":"10.1007\/978-1-4471-3573-9_6","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"Andrew D. Gordon","msr_other_contributors":"","msr_speaker":"","msr_award":"","msr_affiliation":"","msr_institution":"","msr_host":"","msr_version":"","msr_duration":"","msr_original_fields_of_study":"","msr_release_tracker_id":"","msr_s2_match_type":"","msr_citation_count_updated":"","msr_published_date":"1994-09-12","msr_highlight_text":"","msr_notes":"","msr_longbiography":"","msr_publicationurl":"","msr_external_url":"","msr_secondary_video_url":"","msr_conference_url":"","msr_journal_url":"","msr_s2_pdf_url":"","msr_year":1994,"msr_citation_count":0,"msr_influential_citations":0,"msr_reference_count":0,"msr_s2_match_confidence":0,"msr_microsoftintellectualproperty":true,"msr_s2_open_access":false,"msr_s2_author_ids":[],"msr_pub_ids":[],"msr_hide_image_in_river":0,"footnotes":""},"msr-research-highlight":[],"research-area":[13560],"msr-publication-type":[193716],"msr-publisher":[],"msr-focus-area":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-151006","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-programming-languages-software-engineering","msr-locale-en_us"],"msr_publishername":"Springer London","msr_edition":"Proceedings of the 1994 Glasgow Workshop on Functional Programming, Ayr, Scotland","msr_affiliation":"","msr_published_date":"1994-09-12","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"78-95","msr_chapter":"","msr_isbn":"978-3-540-19914-4 (Print) 978-1-4471-3573-9 (Online)","msr_journal":"","msr_volume":"","msr_number":"","msr_editors":"","msr_series":"","msr_issue":"","msr_organization":"","msr_how_published":"","msr_notes":"","msr_highlight_text":"","msr_release_tracker_id":"","msr_original_fields_of_study":"","msr_download_urls":"","msr_external_url":"","msr_secondary_video_url":"","msr_longbiography":"","msr_microsoftintellectualproperty":1,"msr_main_download":"316508","msr_publicationurl":"","msr_doi":"10.1007\/978-1-4471-3573-9_6","msr_publication_uploader":[{"type":"file","title":"fp94","viewUrl":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/1994\/01\/fp94.pdf","id":316508,"label_id":0},{"type":"doi","title":"10.1007\/978-1-4471-3573-9_6","viewUrl":false,"id":false,"label_id":0}],"msr_related_uploader":"","msr_citation_count":0,"msr_citation_count_updated":"","msr_s2_paper_id":"","msr_influential_citations":0,"msr_reference_count":0,"msr_arxiv_id":"","msr_s2_author_ids":[],"msr_s2_open_access":false,"msr_s2_pdf_url":null,"msr_attachments":[],"msr-author-ordering":[{"type":"user_nicename","value":"adg","user_id":30825,"rest_url":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=adg"}],"msr_impact_theme":[],"msr_research_lab":[],"msr_event":[],"msr_group":[],"msr_project":[],"publication":[],"video":[],"msr-tool":[],"msr_publication_type":"inproceedings","related_content":[],"_links":{"self":[{"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/151006","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item"}],"about":[{"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-research-item"}],"version-history":[{"count":1,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/151006\/revisions"}],"predecessor-version":[{"id":525085,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/151006\/revisions\/525085"}],"wp:attachment":[{"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/media?parent=151006"}],"wp:term":[{"taxonomy":"msr-research-highlight","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-research-highlight?post=151006"},{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=151006"},{"taxonomy":"msr-publication-type","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-publication-type?post=151006"},{"taxonomy":"msr-publisher","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-publisher?post=151006"},{"taxonomy":"msr-focus-area","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-focus-area?post=151006"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=151006"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=151006"},{"taxonomy":"msr-field-of-study","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-field-of-study?post=151006"},{"taxonomy":"msr-conference","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-conference?post=151006"},{"taxonomy":"msr-journal","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-journal?post=151006"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=151006"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=151006"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}