Dcpos can be presented by a preorder of generators and inequational relations expressed as covers. Algebraic operations on the generators (possibly with their results being ideals of generators) can be extended to the dcpo presented, provided the covers are “stable” for the operations. The resulting dcpo algebra has a natural universal characterization and satisfies all the inequational laws sa...

A dcpo P is continuous if and only if the lattice C(P ) of all Scottclosed subsets of P is completely distributive. However, in the case where P is a non-continuous dcpo, little is known about the order structure of C(P ). In this paper, we study the order-theoretic properties of C(P ) for general dcpo’s P . The main results are: (i) every C(P ) is C-continuous; (ii) a complete lattice L is iso...

Our interest is in automated termination proofs of higher-order rewrite rules in presence of dependent types modulo a theory T on base types. We first describe an original transformation to a type discipline without type dependencies which preserves non-termination. Since the user must reason on expressions of the transformed language, we then introduce an extension of the computability path or...

The canonical extension of a lattice is in an essential way a two-sided completion. Domain theory, on the contrary, is primarily concerned with one-sided completeness. In this paper, we show two things. Firstly, that the canonical extension of a lattice can be given an asymmetric description in two stages: a free co-directed meet completion, followed by a completion by selected directed joins. ...

The canonical extension of a lattice is in an essential way a two-sided completion. Domain theory, on the contrary, is primarily concerned with one-sided completeness. In this paper, we show two things. Firstly, that the canonical extension of a lattice can be given an asymmetric description in two stages: a free co-directed meet completion, followed by a completion by selected directed joins. ...

The paper deals with special types of $L$-ordered sets, $L$-fuzzy complete lattices, and fuzzy directed complete posets.First, a theorem for constructing monotone maps is proved, a characterization for monotone maps on an $L$-fuzzy complete lattice is obtained, and it's proved that if $f$ is a monotone map on an $L$-fuzzy complete lattice $(P;e)$, then the least fixpoint of $f$ is meet of a spe...

We establish sufficient and necessary conditions for a natural sink to be a colimit in DCPO. Based on these conditions we show how to construct a colimit for any functor F from a small category „ into the category DCPO. This demonstrates that the category DCPO is cocomplete. We also investigate under what conditions the colimit object is algebraic. 0 Introduction Colimits play an important role...