Continuously generated fixed points in Pω¹

Article type: Research Article

Authors: Bracho, Felipe

Affiliations: Mathematical Institute, Oxford

Note: [1] This work was suported by the Institute for Applied Mathematics and Systems of the National University of Mexico (U.N.A.M) and CONACYT.

Abstract: In this paper we investigate the fixed points of functions that can be obtained by continuous fixed point operators in Pω. We also introduce an operator Cgn that generates all of these fixed points for any continuous function. In the last two sections of the paper we study the fixed points of λa.a∘a (retracts) and of λy λf.f((y)(f)) (fixed point operators).

Keywords: programming language semantics, lattice, algebraic lattice, retract, continuous function, fixed points

DOI: 10.3233/FI-1980-3406

Journal: Fundamenta Informaticae, vol. 3, no. 4, pp. 477-489, 1980