Complete axioms for categorical fixed-point operators Export

@proceedings{citeulike:1856628, abstract = {We give an axiomatic treatment of fixed-point operators in categories. A notion of iteration operator is defined embodying the equational properties of iteration theories. We prove a general completeness theorem for iteration operators, relying on a new, purely syntactic characterisation of the free iteration theory. We then show how iteration operators arise in axiomatic domain theory. One result derives them from the existence of sufficiently many bifree algebras (exploiting the universal property Freyd introduced in his notion of algebraic compactness). Another result shows that, in the presence of a parameterized natural numbers object and an equational lifting monad, any uniform fixed-point operator is necessarily an iteration operator}, author = {Simpson, A. and Plotkin, G.}, booktitle = {Logic in Computer Science, 2000. Proceedings. 15th Annual IEEE Symposium on}, citeulike-article-id = {1856628}, citeulike-linkout-0 = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=855753}, citeulike-linkout-1 = {http://citeseer.ist.psu.edu/simpson00complete.html}, journal = {Logic in Computer Science, 2000. Proceedings. 15th Annual IEEE Symposium on}, keywords = {category-theory, domain-theory}, pages = {30--41}, posted-at = {2007-11-02 16:06:25}, priority = {4}, title = {Complete axioms for categorical fixed-point operators}, url = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=855753}, year = {2000} }

TY - CONF ID - citeulike:1856628 L3 - citeulike-article-id:1856628 N2 - We give an axiomatic treatment of fixed-point operators in categories. A notion of iteration operator is defined embodying the equational properties of iteration theories. We prove a general completeness theorem for iteration operators, relying on a new, purely syntactic characterisation of the free iteration theory. We then show how iteration operators arise in axiomatic domain theory. One result derives them from the existence of sufficiently many bifree algebras (exploiting the universal property Freyd introduced in his notion of algebraic compactness). Another result shows that, in the presence of a parameterized natural numbers object and an equational lifting monad, any uniform fixed-point operator is necessarily an iteration operator JF - Logic in Computer Science, 2000. Proceedings. 15th Annual IEEE Symposium on EP - 41 TI - Complete axioms for categorical fixed-point operators T2 - Logic in Computer Science, 2000. Proceedings. 15th Annual IEEE Symposium on SP - 30 KW - category-theory KW - domain-theory AU - Simpson, A AU - Plotkin, G PY - 2000/// UR - http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=855753 ER -