Subtyping constraints in quasi-lattices

Abstract

In this paper, we show the decidability and NP-completeness of the satisfiability problem for non-structural subtyping constraints in quasi-lattices. This problem, first introduced by Smolka in 1989, is important for the typing of logic and functional languages. The decidability result is obtained by generalizing Trifonov and Smith's algorithm over lattices, to the case of quasi-lattices with a complexity in O(mvMvn3), where m (resp. M) stands for the number of minimal (resp. maximal) elements of the quasi-lattice, v is the number of unbounded variables and n is the number of constraints. Similarly, we extend Pottier's algorithm for computing explicit solutions to the case of quasi-lattices. Finally we evoke some applications of these results to type inference in constraint logic programming and functional programming languages. © Springer-Verlag Berlin Heidelberg 2003.