This paper presents a technique for translating common comprehension expressions (sum, count, product, min, and max) into verification conditions that can be tackled by two off-the-shelf first-order SMT solvers. Since a first-order SMT solver does not directly support the bound variables that occur in comprehension expressions, the challenge is to provide a sound axiomatisation that is strong enough to prove interesting programs and, furthermore, that can be used automatically by the SMT solver. The technique has been implemented in the Spec# program verifier. The paper also reports on the experience of using Spec# to verify several challenging programming examples drawn from a textbook by Dijkstra and Feijen.<\/p>\n","protected":false},"excerpt":{"rendered":"
This paper presents a technique for translating common comprehension expressions (sum, count, product, min, and max) into verification conditions that can be tackled by two off-the-shelf first-order SMT solvers. Since a first-order SMT solver does not directly support the bound variables that occur in comprehension expressions, the challenge is to provide a sound axiomatisation that […]<\/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":"","footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[13560],"msr-publication-type":[193716],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-343340","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-programming-languages-software-engineering","msr-locale-en_us"],"msr_publishername":"","msr_edition":"SAC\u201909 March 8-12, 2009, Honolulu, Hawaii, U.S.A.","msr_affiliation":"","msr_published_date":"2009-03-08","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"","msr_chapter":"","msr_isbn":"","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":"343343","msr_publicationurl":"","msr_doi":"","msr_publication_uploader":[{"type":"file","title":"Reasoning about Comprehensions with First-Order SMT Solvers","viewUrl":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2016\/12\/rmkrml183.pdf","id":343343,"label_id":0},{"type":"file","title":"Reasoning about Comprehensions with First-Order SMT Solvers (Slides)","viewUrl":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2016\/12\/Comprehensions-SAC-2009.pptx","id":344282,"label_id":0}],"msr_related_uploader":"","msr_attachments":[{"id":344282,"url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2016\/12\/Comprehensions-SAC-2009.pptx"},{"id":343343,"url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2016\/12\/rmkrml183.pdf"}],"msr-author-ordering":[{"type":"user_nicename","value":"leino","user_id":32639,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=leino"},{"type":"text","value":"Rosemary Monahan","user_id":0,"rest_url":false}],"msr_impact_theme":[],"msr_research_lab":[],"msr_event":[],"msr_group":[144812],"msr_project":[169833],"publication":[],"video":[],"download":[],"msr_publication_type":"inproceedings","related_content":{"projects":[{"ID":169833,"post_title":"Spec#","post_name":"spec","post_type":"msr-project","post_date":"2004-06-11 11:30:47","post_modified":"2017-06-19 09:32:43","post_status":"publish","permalink":"https:\/\/www.microsoft.com\/en-us\/research\/project\/spec\/","post_excerpt":"Spec# is a formal language for API contracts (influenced by JML, AsmL, and Eiffel), which extends C# with constructs for non-null types, preconditions, postconditions, and object invariants. 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