{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T12:05:10Z","timestamp":1648555510840},"reference-count":30,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2009,3,4]],"date-time":"2009-03-04T00:00:00Z","timestamp":1236124800000},"content-version":"unspecified","delay-in-days":5390,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[1994,6]]},"abstract":"<jats:p>We define a categorical framework, based on the notion of <jats:italic>sketch<\/jats:italic>, for specification and evaluation in the senses of algebraic specifications and algebraic programming. This framework goes far beyond our initial motivation, which was to specify computation with algebraic numbers. We begin by redefining sketches in order to deal explicitly with programs. Expressions and terms are carefully defined and studied, then <jats:italic>quasi-projective sketches<\/jats:italic> are introduced. We describe <jats:italic>static evaluation<\/jats:italic> in these sketches: we propose a rigorous basis for evalution in the corresponding structures. These structures admit an initial model, but are not necessarily equational. In Part II (Duval and Reynaud 1994), we study a more general process, called <jats:italic>dynamic evaluation<\/jats:italic>, for structures that may have no initial model.<\/jats:p>","DOI":"10.1017\/s0960129500000438","type":"journal-article","created":{"date-parts":[[2009,3,4]],"date-time":"2009-03-04T04:01:15Z","timestamp":1236139275000},"page":"185-238","source":"Crossref","is-referenced-by-count":6,"title":["Sketches and computation \u2013 I: basic definitions and static evaluation"],"prefix":"10.1017","volume":"4","author":[{"given":"Dominique","family":"Duval","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jean-Claude","family":"Reynaud","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,3,4]]},"reference":[{"key":"S0960129500000438_ref030","first-page":"238","article-title":"A Bibliography on Sketches from the Computer Science Point of View","volume":"45","author":"Perm wall","year":"1991","journal-title":"Bulletin of the European Association for Theoretical Computer Science"},{"key":"S0960129500000438_ref028","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-9839-7"},{"key":"S0960129500000438_ref026","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0077116"},{"key":"S0960129500000438_ref025","volume-title":"Cours de troisi\u00e9me cycle","author":"Lair","year":"1986"},{"key":"S0960129500000438_ref023","volume-title":"Diagrammes 7","author":"Guitart","year":"1982"},{"key":"S0960129500000438_ref029","volume-title":"Accessible categories: The foundations of categorical model theory","author":"Makkai","year":"1987"},{"key":"S0960129500000438_ref022","volume-title":"Diagrammes","author":"Guitart","year":"1980"},{"key":"S0960129500000438_ref021","unstructured":"Gomez-Diaz T. (1993) Examples of using dynamic constructible closure. Proceedings of IMACS\u201993."},{"key":"S0960129500000438_ref020","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-12896-4_366"},{"key":"S0960129500000438_ref018","article-title":"Esquisses et types de structures alg\u00e9briques","volume":"14","author":"Ehresmann","year":"1968","journal-title":"Bulletin de l\u2019lnstitut Polytechnique"},{"key":"S0960129500000438_ref017","unstructured":"Duval D. and S\u00e9n\u00e9chaud P. (to appear) Sketches and parametrization. Theoretical Computer Science."},{"key":"S0960129500000438_ref013","unstructured":"Duval D. and Gonzalez-Vega L. (1993) Dynamic evaluation and real closure. Proceedings of IMACS\u201993."},{"key":"S0960129500000438_ref011","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-51084-2_41"},{"key":"S0960129500000438_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-0021-0"},{"key":"S0960129500000438_ref024","volume-title":"Diagrammes","author":"Lair","year":"1983"},{"key":"S0960129500000438_ref014","first-page":"15","article-title":"Esquisses et Calcul","volume":"VII","author":"Duval","year":"1989","journal-title":"Annales Universit\u00e9 de Caen"},{"key":"S0960129500000438_ref027","volume-title":"Diagrammes","author":"Lellahi","year":"1989"},{"key":"S0960129500000438_ref015","unstructured":"Duval D. and Reynaud J.-C. (1991) Sketches and computation. Rapport de recherche RR871-I-IMAG-123-LIFIA, Institut National Polytechnique de Grenoble."},{"key":"S0960129500000438_ref019","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-69962-7"},{"key":"S0960129500000438_ref006","volume-title":"Diagrammes","author":"Coppey","year":"1984"},{"key":"S0960129500000438_ref010","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-15984-3_279"},{"key":"S0960129500000438_ref003","first-page":"1","article-title":"The formal description of data types using sketches","volume":"298","author":"Barr","year":"1988","journal-title":"Springer-Verlag Lecture Notes in Computer Science"},{"key":"S0960129500000438_ref012","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-9647-5_36"},{"key":"S0960129500000438_ref016","first-page":"239","article-title":"Sketches and computation - Part II: Dynamic Evaluation and Applications","volume":"4","author":"Duval","year":"1994","journal-title":"MSCS"},{"key":"S0960129500000438_ref001","volume-title":"Structure des logiques et logique des structures","author":"Ageron","year":"1991"},{"key":"S0960129500000438_ref008","volume-title":"Calcul formel","author":"Davenport","year":"1987"},{"key":"S0960129500000438_ref004","article-title":"Categories of sketched structures","volume":"13","author":"Bastiani","year":"1972","journal-title":"Cahiers de topologie et g\u00e9om\u00e9trie diff\u00e9rentielle"},{"key":"S0960129500000438_ref005","doi-asserted-by":"publisher","DOI":"10.1017\/S0960129500000232"},{"key":"S0960129500000438_ref007","volume-title":"Diagrammes","author":"Coppey","year":"1988"},{"key":"S0960129500000438_ref009","volume-title":"Handbook of Theoretical Computer Science","author":"Dershowitz","year":"1989"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129500000438","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,14]],"date-time":"2019-05-14T23:49:40Z","timestamp":1557877780000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129500000438\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,6]]},"references-count":30,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1994,6]]}},"alternative-id":["S0960129500000438"],"URL":"https:\/\/doi.org\/10.1017\/s0960129500000438","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,6]]}}}