William M. Farmer

Security for Mobile Agents: Authentication and State Appraisal

Mobile agents are processes which can autonomously migrate to new hosts. Despite its many practical benefits, mobile agent technology results in significant new security threats from malicious agents and hosts. The primary added complication is that, as an agent traverses multiple hosts that are trusted to different degrees, its state can change in ways that adversely impact its functionality. In this paper, we discuss achievable security goals for mobile agents, and we propose an architecture to achieve these goals. The architecture models the trust relations between the principals of mobile agent systems. A unique aspect of the architecture is a “state appraisal” mechanism that protects users and hosts from attacks via state modifications and that provides users with flexible control over the authority of their agents.

IMPS: an interactive mathematical proof system

IMPS is an interactive mathematical proof system intended as a general-purpose tool for formulating and applying mathematics in a familiar fashion. The logic of IMPS is based on a version of simple type theory with partial functions and subtypes. Mathematical specification and inference are performed relative to axiomatic theories, which can be related to one another via inclusion and theory interpretation. IMPS provides relatively large primitive inference steps to facilitate human control of the deductive process and human comprehension of the resulting proofs. An initial theory library containing over a thousand repeatable proofs covers significant portions of logic, algebra, and analysis and provides some support for modeling applications in computer science.

A Partial Functions Version of Church's Simple Theory of Types

Churchs simple theory of types is a system of higher-order logic in which functions are assumed to be total. We present in this paper a version of Churchs system called PF in which functions may be partial. The semantics of PF , which is based on Henkins general-models semantics, allows terms to be nondenoting but requires formulas to always denote a standard truth value. We prove that PF is complete with respect to its semantics. The reasoning mechanism in PF for partial functions corresponds closely to mathematical practice, and the formulation of PF adheres tightly to the framework of Churchs system.

A unification algorithm for second-order monadic terms

Abstract This paper presents an algorithm that, given a finite set E of pairs of second-order monadic terms, returns a finite set U ( E ) of ‘substitution schemata’ such that a substitution unifies E iff it is an instance of some member of U ( E ). Moreover, E is unifiable precisely if U ( E ) is not empty. The algorithm terminates on all inputs, unlike the unification algorithms for second-order monadic terms developed by G. Huet and G. Winterstein. The substitution schemata in U ( E ) use expressions (called ‘parametric terms’) which represent sets of terms that differ only in how many times designated strings of (monadic) function constants follow themselves. The substitution schemata may contain unresolved ‘identity restrictions’; consequently, the members of U ( E ) generally do not characterize all the unifiers of E in a completely explicit way. The algorithm is particularly useful for investigating the complexity of formal proofs.

The seven virtues of simple type theory

Simple type theory, also known as higher-order logic, is a natural extension of first-order logic which is simple, elegant, highly expressive, and practical. This paper surveys the virtues of simple type theory and attempts to show that simple type theory is an attractive alternative to first-order logic for practical-minded scientists, engineers, and mathematicians. It recommends that simple type theory be incorporated into introductory logic courses offered by mathematics departments and into the undergraduate curricula for computer science and software engineering students.

Theory Interpretation in Simple Type Theory

Theory interpretation is a logical technique for relating one axiomatic theory to another with important applications in mathematics and computer science as well as in logic itself. This paper presents a method for theory interpretation in a version of simple type theory, called lutins, which admits partial functions and subtypes. The method is patterned on the standard approach to theory interpretation in first-order logic. Although the method is based on a nonclassical version of simple type theory, it is intended as a guide for theory interpretation in classical simple type theories as well as in predicate logics with partial functions.

A simple type theory with partial functions and subtypes

Farmer, W.M., A simple type theory with partial functions and subtypes, Annals of Pure and Applied Logic 64 (1993) 21 l-240. Simple type theory is a higher-order predicate logic for reasoning about truth values, individuals, and simply typed total functions. We present in this paper a version of simple type theory, called PF*, in which functions may be partial and types may have subtypes. We define both a Henkin-style general models semantics and an axiomatic system for PF*, and we prove that the axiomatic system is complete with respect to the general models semantics. We also define a notion of an interpretation of one PF* theory in another. PF* is intended as a foundation for mechanized mathematics. It is the basis for the logic of IMPS, an Interactive Mathematical Proof System developed at The MITRE Corporation.

REDEX CAPTURING IN TERM GRAPH REWRITING

Term graphs are a natural generalization of terms in which structure sharing is allowed. Structure sharing makes term graph rewriting a time- and space-efficient method for implementing term rewrite systems. Certain structure sharing schemes can lead to a situation in which a term graph component is rewritten to another component that contains the original. This phenomenon, called redex capturing, introduces cycles into the term graph which is being rewritten—even when the graph and the rule themselves do not contain cycles. In some applications, redex capturing is undesirable, such as in contexts where garbage collectors require that graphs be acyclic. In other applications, for example in the use of the fixed-point combinator Y, redex capturing acts as a rewriting optimization. We show, using results about infinite rewritings of trees, that term graph rewriting with arbitrary structure sharing (including redex capturing) is sound for left-linear term rewrite systems.

An Infrastructure for Intertheory Reasoning

The little theories method, in which mathematical reasoning is distributed across a network of theories, is a powerful technique for describing and analyzing complex systems. This paper presents an infrastructure for intertheory reasoning that can support applications of the little theories method. The infrastructure includes machinery to store theories and theory interpretations, to store known theorems of a theory with the theory, and to make definitions in a theory by extending the theory in place. The infrastructure is an extension of the intertheory infrastructure employed in the IMPS Interactive Mathematical Proof System.

IMPS: An Interactive Mathematical Proof System

imps is an Interactive Mathematical Proof System intended as a general purpose tool for formulating and applying mathematics in a familiar fashion. The logic of imps is based on a version of simple type theory with partial functions and subtypes. Mathematical specication and inference are performed relative to axiomatic theories, which can be related to one another via inclusion and theory interpretation. imps provides relatively large primitive inference steps to facilitate human control of the deductive process and human comprehension of the resulting proofs. An initial theory library containing almost a thousand repeatable proofs covers signicant portions of logic, algebra and analysis, and provides some support for modeling applications in computer science.