This paper introduces a propositional encoding for lexicographic path orders (LPOs) and the corresponding LPO termination property of term rewrite systems. Given this encoding, termination analysis can be performed using a state-of-the-art Boolean satisfiability solver. Experimental results are unequivocal, indicating orders of magnitude speedups in comparison with previous implementations for LPO termination. The results of this paper have already had a direct impact on the design of several major termination analyzers for term rewrite systems. The contribution builds on a symbol-based approach towards reasoning about partial orders. The symbols in an unspecified partial order are viewed as variables that take integer values and are interpreted as indices in the order. For a partial order statement on n symbols, each index is represented in ⌈log 2 n ⌉ propositional variables and partial order constraints between symbols are modeled on the bit representations. The proposed encoding is general and relevant to other applications which involve propositional reasoning about partial orders.

Abstract. We construct a readable, compact and efficient implementation of Dijkstra’s shortest path algorithm and Fibonacci heaps using Constraint Handling Rules (CHR), which is increasingly used as a high-level rule-based general-purpose programming language. We measure its performance in different CHR systems, investigating both the theoretical asymptotic complexity and the constant factors realized in practice. 1

Abstract. We propose an extension of Constraint Handling Rules (CHR) with aggregates such as sum, count, findall, and min. This new feature significantly improves the conciseness and expressiveness of the language. In this paper, we describe an implementation based on source-to-source transformations to CHR (extended with some low-level compiler directives). We allow user-defined aggregates and nested aggregate expressions over arbitrary guarded conjunctions of constraints. Both an on-demand and an incremental aggregate computation strategy are supported. 1

Abstract. Size-change termination analysis is a simple and powerful technique successfully applied for a variety of programming paradigms. A main advantage is that termination for size-change graphs is decidable and based on simple linear ranking functions. A main disadvantage is that the size-change termination problem is PSPACE-complete. Proving size change termination may have to consider exponentially many size change graphs. This paper is concerned with the representation of large sets of size-change graphs. The approach is constraint based and the novelty is that sets of size-change graphs are represented as disjunctions of size-change constraints. A constraint solver to facilitate size-change termination analysis is obtained by interpreting size-change constraints over a sufficiently large but finite non-negative integer domain. A Boolean kbit modeling of size change graphs using binary decision diagrams leads to a concise representation. Experimental evaluation indicates that the 2-bit representation facilitates an efficient implementation which is guaranteed complete for our entire benchmark suite. 1

Abstract. In this paper, we address the different conceptual and technical difficulties encountered when embedding CHR into an imperative host language. We argue that a tight, natural integration leads to a powerful programming language extension, intuitive to both CHR and imperative programmers. We show how to compile CHR to highly optimized imperative code. To this end, we first review the well-established CHR compilation scheme, and survey the large body of possible optimizations. We then show that this scheme, when used for compilation to imperative target languages, leads to stack overflows. We therefore introduce new optimizations that considerably improve the performance of recursive CHR programs. Rules written using tail calls are even guaranteed to run in constant space. We implemented systems for both Java and C, following the language design principles and compilation scheme presented in this paper, and show that our implementations outperform other state-of-the-art CHR compilers by several orders of magnitude. 1

In this report, we provide a detailed description of the compilation scheme the K.U.Leuven JCHR system uses to compile CHR to efficient Java code. We start from a relatively straightforward adaptation of the traditional CHR compilation scheme for Prolog, and gradually add all its basic optimizations. Next, we show why this compilation scheme is not suited for compilation to an imperative host language such as Java. We therefore introduce a novel compilation scheme from CHR to Java that uses explicit call stack maintenance and trampoline-style compilation to guarantee that executing recursive CHR programs no longer results in call stack overflows. The empirical evaluation of the improved compilation scheme

We propose an extension of the Constraint Handling Rules language with aggregates like sum, count, findall, and min in the heads of rules. We define the semantics of aggregate expressions formally and informally. Our prototype implementation allows nested aggregate expressions over guarded conjunctions of constraints, using either an ondemand or an incremental computation strategy. Case studies demonstrate that by using aggregates, the program size can be reduced significantly, with an acceptable constant run-time overhead.

Abstract. We extend the Constraint Handling Rules language with aggregates such as sum, count, findall, and min. The proposed extension features nested aggregate expressions over guarded conjunctions of constraints, a series of predefined aggregates, and application-tailored user-defined aggregates. We formally define the operational semantics of aggregates, and show how incremental aggregate computation facilitates efficient implementations. Case studies demonstrate that language support for aggregates significantly reduces program size, thus improving readability and maintainability considerably. 1

Abstract. This paper describes the application of a partial order constraint solver to a telecommunications feature subscription configuration problem. Partial order constraints are encoded to propositional logic and solved using a state-of-the-art Boolean satisfaction solver. The encoding is based on a symbol-based approach: symbols are viewed as variables which take integer values and are interpreted as indices in the order. Experimental evaluation indicates that partial order constraints are a viable alternative to previous solutions which apply constraint programming techniques and integer linear programming. 1

Abstract. Traditional object-oriented programming languages can be difficult to use when working with ontologies, leading to the creation of domain-specific languages designed specifically for ontology processing. Prolog, with its logic-based, declarative semantics offers many advantages as a host programming language for querying and processing OWL2 ontologies. The SWI-Prolog semweb library provides some support for OWL but until now there has been a lack of any library providing direct and comprehensive support for OWL2. We have developed Thea, a library based directly on the OWL2 functionalstyle syntax, allowing storage and manipulation of axioms as a Prolog database. Thea can translate ontologies to Description Logic programs but the emphasis is on using Prolog as an application programming and processing language rather than a reasoning engine. Thea offers the ability to seamless connect to the java OWL API and OWLLink servers. Thea also includes support for SWRL. In this paper we provide examples of using Thea for processing ontologies, and compare the results to alternative methods. Thea is available from GitHub: