{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T01:27:24Z","timestamp":1772242044591,"version":"3.50.1"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2017,3,17]],"date-time":"2017-03-17T00:00:00Z","timestamp":1489708800000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2017,3,17]],"date-time":"2017-03-17T00:00:00Z","timestamp":1489708800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2017,3,17]],"date-time":"2017-03-17T00:00:00Z","timestamp":1489708800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"funder":[{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"crossref","award":["676547"],"award-info":[{"award-number":["676547"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"crossref","award":["640954"],"award-info":[{"award-number":["640954"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>We present a computer-checked generic implementation for solving finite-horizon sequential decision problems. This is a wide class of problems, including inter-temporal optimizations, knapsack, optimal bracketing, scheduling, etc. The implementation can handle time-step dependent control and state spaces, and monadic representations of uncertainty (such as stochastic, non-deterministic, fuzzy, or combinations thereof). This level of genericity is achievable in a programming language with dependent types (we have used both Idris and Agda). Dependent types are also the means that allow us to obtain a formalization and computer-checked proof of the central component of our implementation: Bellman's principle of optimality and the associated backwards induction algorithm. The formalization clarifies certain aspects of backwards induction and, by making explicit notions such as viability and reachability, can serve as a starting point for a theory of controllability of monadic dynamical systems, commonly encountered in, e.g., climate impact research.<\/jats:p>\n                  <jats:p>Comment: 23 pages, 2 figures<\/jats:p>","DOI":"10.23638\/lmcs-13(1:7)2017","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T13:31:40Z","timestamp":1743687100000},"source":"Crossref","is-referenced-by-count":3,"title":["Sequential decision problems, dependent types and generic solutions"],"prefix":"10.23638","volume":"Volume 13, Issue 1","author":[{"given":"Nicola","family":"Botta","sequence":"first","affiliation":[]},{"given":"Patrik","family":"Jansson","sequence":"additional","affiliation":[]},{"given":"Cezar","family":"Ionescu","sequence":"additional","affiliation":[]},{"given":"David R.","family":"Christiansen","sequence":"additional","affiliation":[]},{"given":"Edwin","family":"Brady","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2017,3,17]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1610.07145v5","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1610.07145v5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T13:31:40Z","timestamp":1743687100000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/3191"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3,17]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-13(1:7)2017","relation":{"has-preprint":[{"id-type":"arxiv","id":"1610.07145v2","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1610.07145","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1610.07145","asserted-by":"subject"}],"is-cited-by":[{"id-type":"doi","id":"10.1007\/978-3-030-81701-5_3","asserted-by":"object"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,3,17]]},"article-number":"3191"}}