David Scott Warren

XSB as an efficient deductive database engine

This paper describes the XSB system, and its use as an in-memory deductive database engine. XSB began from a Prolog foundation, and traditional Prolog systems are known to have serious deficiencies when used as database systems. Accordingly, XSB has a fundamental bottom-up extension, introduced through tabling (or memoing)[4], which makes it appropriate as an underlying query engine for deductive database systems. Because it eliminates redundant computation, the tabling extension makes XSB able to compute all modularly stratified datalog programs finitely and with polynomial data complexity. For non-stratified programs, a meta-interpreter with the same properties is provided. In addition XSB significantly extends and improves the indexing capabilities over those of standard Prolog. Finally, its syntactic basis in HiLog [2], lends it flexibility for data modelling. The implementation of XSB derives from the WAM [25], the most common Prolog engine. XSB inherits the WAMs efficiency and can take advantage of extensive compiler technology developed for Prolog. As a result, performance comparisons indicate that XSB is significantly faster than other deductive database systems for a wide range of queries and stratified rule sets. XSB is under continuous development, and version 1.3 is available through anonymous ftp.

HILOG: a foundation for higher-order logic programming

Abstract We describe a novel logic, called HiLog, and show that it provides a more suitable basis for logic programming than does traditional predicate logic. HiLog has a higher-order syntax and allows arbitrary terms to appear in places where predicates, functions, and atomic formulas occur in predicate calculus. But its semantics is first-order and admits a sound and complete proof procedure. Applications of HiLog are discussed, including DCG grammars, higher-order and modular logic programming, and deductive databases.

Formal semantics for time in databases

The concept of a historical database is introduced as a tool for modeling the dynamic nature of some part of the real world. Just as first-order logic has been shown to be a useful formalism for expressing and understanding the underlying semantics of the relational database model, intensional logic is presented as an analogous formalism for expressing and understanding the temporal semantics involved in a historical database. The various components of the relational model, as extended to include historical relations, are discussed in terms of the model theory for the logic ILs, a variation of the logic IL formulated by Richard Montague. The modal concepts of intensional and extensional data constraints and queries are introduced and contrasted. Finally, the potential application of these ideas to the problem of natural language database querying is discussed.

Efficient Model Checking Using Tabled Resolution

We demonstrate the feasibility of using the XSB tabled logic programming system as a programmable fixed-point engine for implementing efficient local model checkers. In particular, we present XMC, an XSB-based local model checker for a CCS-like value-passing language and the alternation-free fragment of the modal mu-calculus. XMC is written in under 200 lines of XSB code, which constitute a declarative specification of CCS and the modal mu-calculus at the level of semantic equations.

Xsb: Extending prolog with tabled logic programming

The paradigm of Tabled Logic Programming (TLP) is now supported by a number of Prolog systems, including XSB, YAP Prolog, B-Prolog, Mercury, ALS, and Ciao. The reasons for this are partly theoretical: tabling ensures termination and optimal known complexity for queries to a large class of programs. However, the overriding reasons are practical. TLP allows sophisticated programs to be written concisely and efficiently, especially when mechanisms such as tabled negation and call and answer subsumption are supported. As a result, TLP has now been used in a variety of applications from program analysis to querying over the semantic web. This paper provides a survey of TLP and its applications as implemented in the XSB Prolog, along with discussion of how XSB supports tabling with dynamically changing code, and in a multi-threaded environment.

Automatic mode inference for logic programs

In general, logic programs are undirected, i.e., there is no concept of “input” and “output” arguments to a procedure. An argument may be used either as an input or as an output argument, and programs may be executed either in a “forward” direction or in a “backward” direction. However, it is often the case that in a given program, a predicate is used with some of its arguments used consistently as input arguments and others as output arguments. Such mode information can be used by a compiler to effect various optimizations. This paper considers the problem of automatically inferring the models of the predicates in a program. The dataflow analysis we use is more powerful than approaches relying on syntactic characteristics of programs. Our work differs from that of Mellish in that (1) we give a sound and efficient treatment of variable aliasing in mode inference; (2) by propagating instantiation information using state transformations rather than through dependencies between variables, we achieve greater precision in the treatment of unification, e.g. through =/2; and (3) we describe an efficient implementation based on the dynamic generation of customized mode interpreters. Several optimizations to improve the performance of the mode inference algorithm are described, as are various program optimizations based on mode information.

XSB: A System for Effciently Computing WFS

The well-founded model provides a natural and robust semantics for logic programs with negative literals in rule bodies. We implemented the well-founded semantics in the SLG-WAM of XSB [19]. Performance results indicate that the overhead of delay and simplification to Prolog — or tabled — evaluations is minimal. To compute the well-founded semantics, the SLG-WAM adds to an efficient tabling engine for definite programs three operations — negative loop detection, delay and simplification — which serve to detect, to break and to resolve cycles through negation that might arise in evaluating normal programs. XSB is a full Prolog system that closely approximates the ISO standard; additionally, it supports a tight integration of tabled predicates with nontabled predicates.The well-founded model provides a natural and robust semantics for logic programs with negative literals in rule bodies. We implemented the well-founded semantics in the SLG-WAM of XSB 19]. Performance results indicate that the overhead of delay and simpliica-tion to Prolog | or tabled | evaluations is minimal. To compute the well-founded semantics, the SLG-WAM adds to an eecient tabling engine for deenite programs three operations | negative loop detection, delay and simpliication | which serve to detect, to break and to resolve cycles through negation that might arise in evaluating normal programs. XSB is a full Prolog system that closely approximates the ISO standard; additionally, it supports a tight integration of tabled predicates with nontabled predicates.

Efficient top-down computation of queries under the well-founded semantics

Abstract The well-founded model provides a natural and robust semantics for logic programs with negative literals in rule bodies. Although various procedural semantics have been proposed for query evaluation under the well-founded semantics, the practical issues of implementation for effective and efficient computation of queries have been rarely discussed. This paper investigates two major implementation issues of query evaluation under the well-founded semantics, namely, (a) to ensure that negative literals be resolved only after their positive counterparts have been completely evaluated, and (b) to detect and handle potential negative loops. We present efficient incremental algorithms for maintaining positive and negative dependencies among subgoals in a top-down evaluation. Both completely evaluated subgoals and potential negative loops are detected by inspecting the dependency information of a single subgoal. Our implementation can be viewed as an effective successor to SLDNF resolution, extending Prolog computation in a natural and smooth way.

Efficient access mechanisms for tabled logic programs

Abstract The use of tabling in logic programming allows bottom-up evaluation to be incorporated in a top-down framework, combining advantages of both. At the engine level, tabling also introduces issues not present in pure top-down evaluation, due to the need for subgoals and answers to access tables during resolution. This article describes the design, implementation, and experimental evaluation of data structures and algorithms for high-performance table access. Our approach uses tries as the basis for tables. Tries, a variant of discrimination nets, provide complete discrimination for terms, and permit a lookup and possible insertion to be performed in a single pass through a term. In addition, a novel technique of substitution factoring is proposed. When substitution factoring is used, the access cost for answers is proportional to the size of the answer substitution, rather than to the size of the answer itself. Answer tries can be implemented both as interpreted structures and as compiled WAM-like code. When they are compiled, the speed of computing substitutions through answer tries is competitive with the speed of unit facts compiled or asserted as WAM code. Because answer tries can also be created an order of magnitude more quickly than asserted code, they form a promising alternative for representing certain types of dynamic code, even in Prolog systems without tabling.

Query evaluation under the well-founded semantics

SLD resolution with negation as finite failure (or SLDNF) reflects the procedural interpretation of Horn-clause predicate logic as a programming language and forms the computational basis for prolog systems. Despite its advantages in memory management, SLDNF is often not appropriate for query evaluation for three reasons; a) it may not terminate due to infinite positive recursion; b) it may not terminate due to infinite recursion through negation; and c) it may repeatedly evaluate the same clause body literal, leading to unacceptable performance. We address all three problems for goal-oriented query evaluation of arbitrary programs by presenting an extension of SLDNF, called SLG resolution, with the following distinctive features: (i) SLG resolution is a partial deduction procedure, consisting of several transformations. Each query is transformed step by step into a set of answer clauses; (ii) SLG resolution is sound and ideally complete for all non-floundering queries with respect to all three-valued stable models (including the well founded partial model); (iii) SLG resolution allows an arbitrary computation rule and an arbitrary control strategy for selecting transformations to apply; (iv) SLG resolution avoids both positive and negative loops and always terminates for programs with the bounded-term-size property; (v) SLG resolution has a polynomial time data complexity for well founded negation. Restricted forms of SLG resolution are identified for definite, locally stratified, and modularly stratified programs, thereby shedding light on the role each transformation plays. To provide answers to a query under different three-valued stable models, SLG resolution can be enhanced by further processing of the derived set of answer clauses. SLG resolution makes many more clausal specifications into effective programs. With simple (user or computer generated) annotations, SLDNF resolution and SLG resolution can be fully integrated. Thus a system including SLG resolution can be fully integrated. Thus a system including SLG resolution is naturally upward compatible with Prolog. For all these reasons we believe that SLG resolution will provide the computational basis for the next generation of logic programming systems.