Joshua S. Hodas

Efficient resource management for linear logic proof search

The design of linear logic programming languages and theorem provers opens a number of new implementation challenges not present in more traditional logic languages such as Horn clauses (Prolog) and hereditary Harrop formulas (λProlog and Elf). Among these, the problem of efficiently managing the linear context when solving a goal is of crucial importance for the use of these systems in non-trivial applications. This paper studies this problem in the case of Lolli [10], though its results have application to other systems including those based on linear type theory. We first give a proof-theoretic presentation of the operational semantics of this language as a resolution calculus. We then present a series of resource management systems designed to eliminate the non-determinism in the distribution of linear formulas that undermines the efficiency of a direct implementation of this system.

Efficient Resource Management for Linear Logic Proof Search

The design of linear logic programming languages and theorem provers opens a number of new implementation challenges not present in more traditional logic languages such as Horn clauses (Prolog) and hereditary Harrop formulas (λProlog). Among these, the problem of efficiently managing the linear context when solving a goal is of crucial importance for the use of these systems in non-trivial applications. This paper studies this problem in the case of Lolli [6] (though its results have application to other systems). We first give a proof-theoretic presentation of the operational semantics of this language as a resolution calculus. We then present a series of resource management systems designed to eliminate the non-determinism in the distribution of linear formulas that undermines the efficiency of a direct implementation of this system.

A Tag-Frame System of Resource Management for Proof Search in Linear-Logic Programming

In programming languages based on linear logic, the program can grow and shrink in a nearly arbitrary manner over the course of execution. Since the introduction of the I/O model of proof search [11, 12], a number of refinements have been proposed with the intention of reducing its degree of non-determinism [3, 4, 12, 13, 14]. Unfortunately each of these systems has had some limitations. In particular, while the resource management systems of Cervesato et al. [3, 4] and the frame system of Lopez and Pimentel [14] obtained the greatest degree of determinism, they required global operations on the set of clauses which were suitable only for interpreter-based implementations. In contrast the level-tags system of Hodas, et al. relied only on relabeling tags attached to individual formulas, and was hence appropriate as the specification of an abstract machine. However it retained more non-determinism than the resource management systems. This led to a divergence in the operational semantics of the interpreted and compiled versions of the language Lolli. In this paper we propose a tag-frame system which recaptures the behavior of the resource management systems, while being appropriate as a foundation of a compiled implementation.

Forum as a Logic Programming Language: Preliminary Report

Abstract When Miller introduced Forum he called it a specification logic, rather than a logic programming language. In this paper we outline those features that create problems in attempting to implement an interpreter for the language, and describe solutions to those problems. We show how techniques used in the implementation of Lolli can be extended naturally to Forum. Finally, we show two Forum programs in order to demonstrate some of the paradigms that arise in using the language.

Isolating Resource Consumption in Linear Logic Proof Search (extended abstract)

This work presents an extension of the Tag-Frame resource management system previously developed by the authors. The extended proof system is able to isolate the consumption of a given goal/clause without incurring significant extra runtime costs. We believe this feature may have a number of applications, in particular for debugging linear logic programs and specifications in a proof-theoretic setting. This point is illustrated by means of a simple example.

NOVeLLA: A Multi-Modal Electronic-Book Reader With Visual and Auditory Interfaces

While significant growth in the popularity of electronic books seems likely over the next few years, current systems and near-term proposals from major vendors have shown little foresight in leveraging the equally inevitable increase in processing power available to such systems. In this note we describe a prototype electronic-book reader, NOVeLLA, whose design takes as its starting point the assumption that computing power equivalent to todays high-end desktop systems will be available in hand-held formats within just a few years. It proposes interesting ways in which that power might be utilized, in particular by delivering a powerful speech-based user interface. A secondary goal of the project was to implement the system using off-the-shelf software technologies and Application Programming Interfaces (APIs) available freely or cheaply today, testing whether those technologies and related standards were adequate to the task. Finally, NOVeLLA is the first generally available reader compatible with the unencoded version of the new Open Ebook Document Structure.

A Linear Logic Treatment of Phrase Structure Grammars for Unbounded Dependencies

A number of researchers have proposed applications of Girards Linear Logic [7] to computational linguistics. Most have focused primarily on the connection between linear logic and categorial grammars. In this work we show how linear logic can be used to provide an attractive encoding of phrase structure grammars for parsing structures involving unbounded dependencies. The resulting grammars are closely related to Generalized Phrase Structure Grammars [4, 5]. As part of the presentation we show how a variety of issues, such as island and coordination constraints can be dealt with in this model.

Logic Programming with Multiple Context Management Schemes

Two years experience with programming in Linear Logic has shown that while some problems require the full power of linear context management, for many this much control is too much. In such cases a restriction on either weakening or contraction, but not both, is most appropriate. In this article we introduce a refinement of the system proposed by Hodas and Miller in which each of these constraints is independently available. This enables programs to be more succinct, understandable, and efficient.