{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T23:00:14Z","timestamp":1648854014460},"reference-count":18,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2019,6]]},"abstract":"<jats:p> This paper establishes a finite axiomatization of possibly non-halting computer programs and tests, with the if-then-else\u00a0operation. The model is a two-sorted algebra, with one sort being the programs and the other being the tests. The main operation on programs is composition, and 1 and 0 represent the programs skip and loop (i.e. never halts) respectively. Programs are modeled as partial functions on some state space [Formula: see text], with tests modeled as partial predicates on [Formula: see text]. <\/jats:p><jats:p> The operations on the tests are the usual logical connectives \u2227, \u2228, [Formula: see text], [Formula: see text] and [Formula: see text]. In addition, there is the hybrid operation of if-then-else, and the test-valued operation [Formula: see text] on programs which is true when a program halts, and undefined otherwise. The halting operation [Formula: see text] implies that operations of domain [Formula: see text] and domain join \u2228 may also be expressed. <\/jats:p><jats:p> When tests are assumed to be possibly non-halting, the evaluation strategy of the logical connectives affects the result. Here we model parallel evaluation, as opposed to the common sequential (or short-circuit) evaluation strategy. For example, we view [Formula: see text] as false if either [Formula: see text] or [Formula: see text] is false, even if the other does not halt. <\/jats:p>","DOI":"10.1142\/s0218196719500255","type":"journal-article","created":{"date-parts":[[2019,1,25]],"date-time":"2019-01-25T08:29:05Z","timestamp":1548404945000},"page":"743-759","source":"Crossref","is-referenced-by-count":0,"title":["Algebraic properties of <tt>if-then-else<\/tt> and commutative three-valued tests"],"prefix":"10.1142","volume":"29","author":[{"given":"Kh\u00ed-U\u00ed","family":"Soo","sequence":"first","affiliation":[{"name":"Department of Computer Science, The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand"}]},{"given":"Tim","family":"Stokes","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, The University of Waikato, Private Bag 3105, Hamilton, 3240, New Zealand"}]}],"member":"219","published-online":{"date-parts":[[2019,6,18]]},"reference":[{"key":"S0218196719500255BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/BF01190851"},{"key":"S0218196719500255BIB002","doi-asserted-by":"publisher","DOI":"10.1137\/0212047"},{"key":"S0218196719500255BIB003","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1975-0357259-4"},{"key":"S0218196719500255BIB004","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511809088"},{"key":"S0218196719500255BIB005","doi-asserted-by":"publisher","DOI":"10.1145\/1183278.1183285"},{"key":"S0218196719500255BIB006","doi-asserted-by":"publisher","DOI":"10.1137\/0216025"},{"key":"S0218196719500255BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/s002330010032"},{"key":"S0218196719500255BIB008","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196709005354"},{"key":"S0218196719500255BIB009","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196711006844"},{"key":"S0218196719500255BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/j.jlamp.2014.08.007"},{"key":"S0218196719500255BIB011","doi-asserted-by":"publisher","DOI":"10.2307\/2267778"},{"key":"S0218196719500255BIB012","doi-asserted-by":"publisher","DOI":"10.1145\/256167.256195"},{"key":"S0218196719500255BIB013","doi-asserted-by":"publisher","DOI":"10.1007\/BF01190447"},{"key":"S0218196719500255BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)72018-4"},{"key":"S0218196719500255BIB015","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196717500138"},{"issue":"8","key":"S0218196719500255BIB016","volume":"79","author":"Panicker G.","year":"2018","journal-title":"Algebra Universalis"},{"key":"S0218196719500255BIB017","doi-asserted-by":"publisher","DOI":"10.1137\/0220049"},{"issue":"138","key":"S0218196719500255BIB018","first-page":"71","volume":"11","author":"Trokhimenko V. 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