{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T05:49:09Z","timestamp":1784180949554,"version":"3.55.0"},"publisher-location":"Cham","reference-count":29,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783030992521","type":"print"},{"value":"9783030992538","type":"electronic"}],"license":[{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T00:00:00Z","timestamp":1648512000000},"content-version":"vor","delay-in-days":87,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>By abstracting over well-known properties of De Bruijn\u2019s representation with nameless dummies, we design a new theory of syntax with variable binding and capture-avoiding substitution. We propose it as a simpler alternative to Fiore, Plotkin, and Turi\u2019s approach, with which we establish a strong formal link. We also show that our theory easily incorporates simple types and equations between terms.<\/jats:p>","DOI":"10.1007\/978-3-030-99253-8_20","type":"book-chapter","created":{"date-parts":[[2022,3,28]],"date-time":"2022-03-28T20:02:48Z","timestamp":1648497768000},"page":"389-408","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Variable binding and substitution for (nameless) dummies"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2523-1481","authenticated-orcid":false,"given":"Andr\u00e9","family":"Hirschowitz","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7220-4067","authenticated-orcid":false,"given":"Tom","family":"Hirschowitz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9299-641X","authenticated-orcid":false,"given":"Ambroise","family":"Lafont","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4380-7691","authenticated-orcid":false,"given":"Marco","family":"Maggesi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2022,3,29]]},"reference":[{"key":"20_CR1","doi-asserted-by":"publisher","unstructured":"Allais, G., Atkey, R., Chapman, J., McBride, C., McKinna, J.: A type and scope safe universe of syntaxes with binding: their semantics and proofs. Proceedings of the ACM on Programming Languages 2(ICFP), 90:1\u201390:30 (2018). https:\/\/doi.org\/10.1145\/3236785","DOI":"10.1145\/3236785"},{"key":"20_CR2","doi-asserted-by":"publisher","unstructured":"Altenkirch, T., Chapman, J., Uustalu, T.: Monads need not be endofunctors. Logical Methods in Computer Science 11(1) (2015). https:\/\/doi.org\/10.2168\/LMCS-11(1:3)2015","DOI":"10.2168\/LMCS-11(1:3)2015"},{"key":"20_CR3","doi-asserted-by":"publisher","unstructured":"Arkor, N., McDermott, D.: Abstract clones for abstract syntax. In: Kobayashi, N. (ed.) Proc. 6th International Conference on Formal Structures for Computation and Deduction. Leibniz International Proceedings in Informatics (LIPIcs), vol.\u00a0195, pp. 30:1\u201330:19. Schloss Dagstuhl - Leibniz-Zentrum f\u00fcr Informatik (2021). https:\/\/doi.org\/10.4230\/LIPIcs.FSCD.2021.30","DOI":"10.4230\/LIPIcs.FSCD.2021.30"},{"key":"20_CR4","doi-asserted-by":"publisher","unstructured":"Berghofer, S., Urban, C.: A head-to-head comparison of de bruijn indices and names. Electronic Notes in Theoretical Computer Science 174(5), 53\u201367 (2007). https:\/\/doi.org\/10.1016\/j.entcs.2007.01.018","DOI":"10.1016\/j.entcs.2007.01.018"},{"key":"20_CR5","doi-asserted-by":"publisher","unstructured":"Bird, R.S., Paterson, R.: De bruijn notation as a nested datatype. Journal of Functional Programming 9(1), 77\u201391 (1999). https:\/\/doi.org\/10.1017\/S0956796899003366","DOI":"10.1017\/S0956796899003366"},{"key":"20_CR6","doi-asserted-by":"publisher","unstructured":"Borthelle, P., Hirschowitz, T., Lafont, A.: A cellular Howe theorem. In: Hermanns, H., Zhang, L., Kobayashi, N., Miller, D. (eds.) Proc. 35th ACM\/IEEE Symposium on Logic in Computer Science ACM (2020). https:\/\/doi.org\/10.1145\/3373718.3394738","DOI":"10.1145\/3373718.3394738"},{"key":"20_CR7","unstructured":"Fiore, M.P., Hur, C.K.: Second-order equational logic. In: Proceedings of the 19th EACSL Annual Conference on Computer Science Logic (CSL 2010) (2010)"},{"key":"20_CR8","doi-asserted-by":"crossref","unstructured":"Fiore, M., Hur, C.K.: On the construction of free algebras for equational systems. Theoretical Computer Science 410, 1704\u20131729 (2009)","DOI":"10.1016\/j.tcs.2008.12.052"},{"key":"20_CR9","doi-asserted-by":"publisher","unstructured":"Fiore, M., Szamozvancev, D.: Formal metatheory of second-order abstract syntax. Proceedings of the ACM on Programming Languages 6(POPL) (2022). https:\/\/doi.org\/10.1145\/3498715","DOI":"10.1145\/3498715"},{"key":"20_CR10","doi-asserted-by":"publisher","unstructured":"Fiore, M.P.: Second-order and dependently-sorted abstract syntax. In: LICS. pp. 57\u201368. IEEE (2008). https:\/\/doi.org\/10.1109\/LICS.2008.38","DOI":"10.1109\/LICS.2008.38"},{"key":"20_CR11","unstructured":"Fiore, M.P., Plotkin, G.D., Turi, D.: Abstract syntax and variable binding. In: Proc. 14th Symposium on Logic in Computer Science IEEE (1999)"},{"key":"20_CR12","unstructured":"Gabbay, M.J., Pitts, A.M.: A new approach to abstract syntax involving binders. In: Proc. 14th Symposium on Logic in Computer Science IEEE (1999)"},{"key":"20_CR13","doi-asserted-by":"publisher","unstructured":"Gheri, L., Popescu, A.: A formalized general theory of syntax with bindings: Extended version. Journal of Automated Reasoning 64(4), 641\u2013675 (2020). https:\/\/doi.org\/10.1007\/s10817-019-09522-2","DOI":"10.1007\/s10817-019-09522-2"},{"key":"20_CR14","doi-asserted-by":"publisher","unstructured":"Hirschowitz, A., Hirschowitz, T., Lafont, A.: Modules over monads and operational semantics. In: Ariola, Z.M. (ed.) Proc. 5th International Conference on Formal Structures for Computation and Deduction. Leibniz International Proceedings in Informatics (LIPIcs), vol.\u00a0167, pp. 12:1\u201312:23. Schloss Dagstuhl - Leibniz-Zentrum f\u00fcr Informatik (2020). https:\/\/doi.org\/10.4230\/LIPIcs.FSCD.2020.12","DOI":"10.4230\/LIPIcs.FSCD.2020.12"},{"key":"20_CR15","doi-asserted-by":"crossref","unstructured":"Hirschowitz, A., Hirschowitz, T., Lafont, A.: Modules over monads and operational semantics (2021), submitted expanded version of\u00a0[14]","DOI":"10.46298\/lmcs-18(3:3)2022"},{"key":"20_CR16","doi-asserted-by":"crossref","unstructured":"Hirschowitz, A., Hirschowitz, T., Lafont, A., Maggesi, M.: Variable binding and substitution for (nameless) dummies (2021), https:\/\/amblafont.github.io\/articles\/debruijn-extended.pdf, preprint","DOI":"10.1007\/978-3-030-99253-8_20"},{"key":"20_CR17","doi-asserted-by":"publisher","unstructured":"Hirschowitz, A., Maggesi, M.: Modules over monads and linearity. In: Proc. 14th International Workshop on Logic, Language, Information and Computation LNCS, vol.\u00a04576, pp. 218\u2013237. Springer (2007). https:\/\/doi.org\/10.1007\/3-540-44802-0_3","DOI":"10.1007\/3-540-44802-0_3"},{"key":"20_CR18","doi-asserted-by":"publisher","unstructured":"Hirschowitz, A., Maggesi, M.: Modules over monads and initial semantics. Information and Computation 208(5), 545\u2013564 (2010). https:\/\/doi.org\/10.1016\/j.ic.2009.07.003","DOI":"10.1016\/j.ic.2009.07.003"},{"key":"20_CR19","unstructured":"Hofmann, M.: Semantical analysis of higher-order abstract syntax. In: Proc. 14th Symposium on Logic in Computer Science IEEE (1999)"},{"key":"20_CR20","unstructured":"Lafont, A.: Initial algebra semantics for de Bruijn monads in Coq. https:\/\/github.com\/amblafont\/binding-debruijn (2021)"},{"key":"20_CR21","unstructured":"Mac Lane, S.: Categories for the Working Mathematician. No.\u00a05 in Graduate Texts in Mathematics, Springer, 2nd edn. (1998)"},{"key":"20_CR22","unstructured":"Maggesi, M.: Initial algebra semantics for de Bruijn monads in HOL Light. https:\/\/github.com\/maggesi\/dbmonad\/tree\/master\/De_Bruijn (2021)"},{"key":"20_CR23","unstructured":"Plotkin, G.: An illative theory of relations. In: Cooper, R., et\u00a0al. (eds.) Situation Theory and its Applications. p. 133\u2013146. No.\u00a022 in CSLI Lecture Notes, Stanford University (1990)"},{"key":"20_CR24","doi-asserted-by":"publisher","unstructured":"Power, J.: Abstract syntax: Substitution and binders: Invited address. Electronic Notes in Theoretical Computer Science 173, 3\u201316 (04 2007). https:\/\/doi.org\/10.1016\/j.entcs.2007.02.024","DOI":"10.1016\/j.entcs.2007.02.024"},{"key":"20_CR25","unstructured":"Sangiorgi, D., Walker, D.: The $$\\pi $$-calculus \u2013 A Theory of Mobile Processes. Cambridge University Press (2001)"},{"key":"20_CR26","doi-asserted-by":"publisher","unstructured":"Sch\u00e4fer, S., Tebbi, T., Smolka, G.: Autosubst: Reasoning with de Bruijn terms and parallel substitutions. In: Urban, C., Zhang, X. (eds.) Proc. 6th International Conference on Interactive Theorem Proving. LNCS, vol.\u00a09236, pp. 359\u2013374. Springer (2015). https:\/\/doi.org\/10.1007\/978-3-319-22102-1_24","DOI":"10.1007\/978-3-319-22102-1_24"},{"key":"20_CR27","doi-asserted-by":"publisher","unstructured":"Stark, K., Sch\u00e4fer, S., Kaiser, J.: Autosubst 2: reasoning with multi-sorted de bruijn terms and vector substitutions. In: Mahboubi, A., Myreen, M.O. (eds.) Proc. 8th International Conference on Certified Programs and Proofs. pp. 166\u2013180. ACM (2019). https:\/\/doi.org\/10.1145\/3293880.3294101","DOI":"10.1145\/3293880.3294101"},{"key":"20_CR28","doi-asserted-by":"publisher","unstructured":"Szlach\u00e1nyi, K.: Skew-monoidal categories and bialgebroids. Advances in Mathematics 231, 1694\u20131730 (2012). https:\/\/doi.org\/10.1016\/j.aim.2012.06.027","DOI":"10.1016\/j.aim.2012.06.027"},{"key":"20_CR29","unstructured":"Trnkov\u00e1, V.: Some properties of set functors. Commentationes Mathematic\u00e6 Universitatis Carolin\u00e6 10(2), 323\u2013352 (1969)"}],"container-title":["Lecture Notes in Computer Science","Foundations of Software Science and Computation Structures"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-99253-8_20","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,30]],"date-time":"2023-01-30T13:52:43Z","timestamp":1675086763000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-99253-8_20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022]]},"ISBN":["9783030992521","9783030992538"],"references-count":29,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-99253-8_20","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022]]},"assertion":[{"value":"29 March 2022","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"FoSSaCS","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Foundations of Software Science and Computation Structures","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Munich","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Germany","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2022","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"4 April 2022","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"6 April 2022","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"25","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"fossacs2022","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/etaps.org\/2022\/fossacs","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"77","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"23","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"30% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"9","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}