Countable Lawvere Theories and Computational Effects Export

@article{citeulike:4537738, abstract = {Lawvere theories have been one of the two main category theoretic formulations of universal algebra, the other being monads. Monads have appeared extensively over the past fifteen years in the theoretical computer science literature, specifically in connection with computational effects, but Lawvere theories have not. So we define the notion of (countable) Lawvere theory and give a precise statement of its relationship with the notion of monad on the category Set . We illustrate with examples arising from the study of computational effects, explaining how the notion of Lawvere theory keeps one closer to computational practice. We then describe constructions that one can make with Lawvere theories, notably sum, tensor, and distributive tensor, reflecting the ways in which the various computational effects are usually combined, thus giving denotational semantics for the combinations.}, author = {Power, J.}, citeulike-article-id = {4537738}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/j.entcs.2006.04.025}, citeulike-linkout-1 = {http://linkinghub.elsevier.com/retrieve/pii/S1571066106004002}, day = {31}, doi = {10.1016/j.entcs.2006.04.025}, issn = {15710661}, journal = {Electronic Notes in Theoretical Computer Science}, keywords = {category-theory, lawvere-theories, monads}, month = {August}, pages = {59--71}, posted-at = {2009-11-14 15:29:54}, priority = {2}, title = {Countable Lawvere Theories and Computational Effects}, url = {http://dx.doi.org/10.1016/j.entcs.2006.04.025}, volume = {161}, year = {2006} }

TY - JOUR ID - citeulike:4537738 L3 - citeulike-article-id:4537738 N2 - Lawvere theories have been one of the two main category theoretic formulations of universal algebra, the other being monads. Monads have appeared extensively over the past fifteen years in the theoretical computer science literature, specifically in connection with computational effects, but Lawvere theories have not. So we define the notion of (countable) Lawvere theory and give a precise statement of its relationship with the notion of monad on the category Set . We illustrate with examples arising from the study of computational effects, explaining how the notion of Lawvere theory keeps one closer to computational practice. We then describe constructions that one can make with Lawvere theories, notably sum, tensor, and distributive tensor, reflecting the ways in which the various computational effects are usually combined, thus giving denotational semantics for the combinations. JF - Electronic Notes in Theoretical Computer Science SN - 15710661 EP - 71 TI - Countable Lawvere Theories and Computational Effects VL - 161 SP - 59 KW - category-theory KW - lawvere-theories KW - monads AU - Power, J PY - 2006/08/31/ UR - http://dx.doi.org/10.1016/j.entcs.2006.04.025 ER -