A Logical Interpretation of Powerdomains

This paper characterizes the powerdomain constructions which have been used in the semantics of programming languages in terms of formulas of first order logic under a pre-ordering of provable implication. The goal is to reveal the basic logical significance of the powerdomains by casting them in the right setting. Such a treatment may contribute to a better understanding of their potential uses in areas which deal with concepts of sets and partial information such as databases and artificial intelligence. Extended examples relating powerdomains to databases are provided. A new powerdomain is introduced and discussed in comparison with a similar operator from database theory. The new powerdomain is motivated by the logical characterizations of the three well-known powerdomains and is itself characterized by formulas of first order logic

Representing Powerdomain Elements as Monadic Second Order Predicates

This report characterizes the powerdomain constructions which have been used in the semantics of programming languages in terms of formulas of first order logic under a preordering of provable implication. This provides an intuitive representation which suggests a new form of powerdomain - called the mixed powerdomain - which expresses data in a different way from the well-known constructions from programming semantics. It can be shown that the mixed powerdomain has many of the properties associated with the convex powerdomain such as the possibility of solving recursive equations and a simple algebraic characterization

The Mixed Powerdomain

This paper introduces an operator M called the mixed powerdomain which generalizes the convex (Plotkin) powerdomain. The construction is based on the idea of representing partial information about a set of data items using a pair of sets, one representing partial information in the manner of the upper (Smyth) powerdomain and the other in the manner of the lower (Hoare) powerdomain where the components of such pairs are required to satisfy a consistency condition. This provides a richer family of meaningful partial descriptions than are available in the convex powerdomain and also makes it possible to include the empty set in a satisfactory way. The new construct is given a rigorous mathematical treatment like that which has been applied to the known powerdomains. It is proved that M is a continuous functor on bifinite domains which is left adjoint to the forgetful functor from a category of continuous structures called mix algebras. For a domain D with a coherent Scott topology, elements of M D can be represented as pairs (U, V) where U ⊆ D is a compact upper set, V ⊆ D is a closed set and the downward closure of U ∩ V is equal to V. A Stone dual characterization of M is also provided

Forms of Semantic Specification

The way to specify a programming language has been a topic of heated debate for some decades and at present there is no consensus on how this is best done. Real languages are almost always specified informally; nevertheless, precision is often enough lacking that more formal approaches could benefit both programmers and language implementors. My purpose is to look at a few of these formal approaches in hope of establishing some distinctions or at least stirring some discussion

The Mixed Powerdomain

This paper characterizes the powerdomain constructions which have been used in the semantics of programming languages in terms of formulas of first order logic under a preordering of provable implication. The goal is to reveal the basic logical significance of the powerdomain elements by casting them in the right setting. Such a treatment may contribute to a better understanding of their potential uses in areas which deal with concepts of sets and partial information such as databases and computational linguistics. This way of viewing powerdomain elements suggests a new form of powerdomain - called the mixed powerdomain - which expresses data in a different way from the well-known constructions from programming semantics. It is shown that the mixed powerdomain has many of the properties associated with the convex powerdomain such as the possiblity of solving recursive equations and a simple algebraic characterization

Nets as Tensor Theories

This report is intended to describe and motivate a relationship between a class of nets and the fragment of linear logic built from the tensor connective. In this fragment of linear logic a net may be represented as a theory and a computation on a net as a proof. A rigorous translation is described and a soundness and completeness theorem is stated. The translation suggests connecticns between concepts from concurrency such as causal dependency and concepts from proof theory such as cut elimination. The main result of this report is a cut reduction theorem which establishes that any proof of a sequent can be transformed into another proof of the same sequent with the property that all cuts are essential . A net-theoretic reading of this result tells that unnecessary dependencies from a computation can be eliminated resulting in a maximally concurrent computation. We note that it is possible to interpret proofs as arrows in the strictly symmetric strict monoidal category freely generated by a net and establish soundness of our proof reduction rules under this interpretation. Finally, we discuss how other linear connectives may be related to the concepts of internal and external choice

Policy-Directed Certificate Retrieval

Any large scale security architecture that uses certificates to provide security in a distributed system will need some automated support for moving certificates around in the network. We believe that for efficiency, this automated support should be tied closely to the consumer of the certificates: the policy verifier. As a proof of concept, we have built QCM, a prototype policy language and verifier that can direct a retrieval mechanism to obtain certificates from the network. Like previous verifiers, QCM takes a policy and certificates supplied by a requester and determines whether the policy is satisfied. Unlike previous verifiers, QCM can take further action if the policy is not satisfied: QCM can examine the policy to decide what certificates might help satisfy it and obtain them from remote servers on behalf of the requester. This takes place automatically, without intervention by the requester; there is no additional burden placed on the requester or the policy writer for the retrieval service we provide. We present examples that show how our technique greatly simplifies certificate-based secure applications ranging from key distribution to ratings systems, and that QCM policies are simple to write. We describe our implementation, and illustrate the operation of the prototype