Abstract We introduce the framework FreeCHR which formalizes the embedding of Constraint Handling Rules (CHR) into a host language, using the concept of initial algebra semantics from category theory. We hereby establish a high-level implementation scheme for CHR as well as a common formalization for both theory and practice. We propose a lifting of the syntax of CHR via an endofunctor in the category Set and a lifting of the very abstract operational semantics of CHR into FreeCHR, using the free algebra, generated by the endofunctor. We give proofs for soundness and completeness with its original definition. We also propose a first abstract execution algorithm and prove correctness with the operational semantics. Finally, we show the practicability of our approach by giving two possible implementations of this algorithm in Haskell and Python. Under consideration in Theory and Practice of Logic Programming.

We present a concise source-to-source transformation that introduces justifications for user-defined constraints into the rule-based Constraint Handling Rules (CHR) programming language. There is no need to introduce a new semantics for justifications. This leads to a conservative extension of the language, as we can show the equivalence of rule applications. A scheme of two rules suffices to allow for logical retraction (deletion, removal) of CHR constraints during computation. Without the need to recompute from scratch, these rules remove the constraint and also undo all its consequences. We prove a confluence result concerning the rule scheme. We prove its correctness in general and tighten the results for confluent programs. We give an implementation, show its correctness, present two classical examples of dynamic algorithms, and improve the implementation. The computational overhead of introducing justifications and of performing logical retraction, i.e. the additional time and space needed, is proportional to the derivation length in the original program. This overhead may increase space complexity, but does not change the worst-case time complexity.

This paper discusses a rule-based approach for visualizing proofs using tableaux techniques. Semantic Tableau is usually used to prove by refutation. In addition, tableaux techniques are commonly studied in different courses. Visualization is an effective teaching methodology. The availability of visualization methods that could be used by instructors is thus important.

Computational psychology has the aim to explain human cognition by computational models of cognitive processes. The cognitive architecture Adaptive Control of Thought--Rational (ACT-R) is popular to develop such models. Although ACT-R has a well-defined psychological theory and has been used to explain many cognitive processes, there are two problems that make it hard to reason formally about its cognitive models: First, ACT-R lacks a computational formalization of its underlying production rule system, and, second, there are many different implementations and extensions of ACT-R with many technical artifacts complicating formal reasoning even more. This article describes a formal operational semantics—the very abstract semantics —that abstracts from as many technical details as possible, keeping it open to extensions and different implementations of the ACT-R theory. In a second step, this semantics is refined to define some of its abstract features that are found in many implementations of ACT-R—called the abstract semantics . It concentrates on the procedural core of ACT-R and is suitable for analysis of the general transition system, since it still abstracts from details like timing, the sub-symbolic layer of ACT-R or conflict resolution. Furthermore, a translation of ACT-R models to the declarative programming language Constraint Handling Rules (CHR) is defined. This makes the abstract semantics an executable specification of ACT-R. CHR has been used successfully to embed other rule-based formalisms like graph transformation systems or functional programming. There are many theoretical results and practical tools that support formal reasoning about and analysis of CHR programs. The translation of ACT-R models to CHR is proven sound and complete w.r.t. the abstract operational semantics of ACT-R. This paves the way to analysis of ACT-R models through CHR analysis results and tools. Therefore, to the best of our knowledge, our abstract semantics is the first abstract formulation of ACT-R suitable for both analysis and execution.

Abstract Constraint Handling Rules (CHR) is both an effective concurrent declarative programming language and a versatile computational logic formalism. In CHR, guarded reactive rules rewrite a multi-set of constraints. Concurrency is inherent, since rules can be applied to the constraints in parallel. In this comprehensive survey, we give an overview of the concurrent, parallel as well as distributed CHR semantics, standard and more exotic, that have been proposed over the years at various levels of refinement. These semantics range from the abstract to the concrete. They are related by formal soundness results. Their correctness is proven as a correspondence between parallel and sequential computations. On the more practical side, we present common concise example CHR programs that have been widely used in experiments and benchmarks. We review parallel and distributed CHR implementations in software as well as hardware. The experimental results obtained show a parallel speed-up for unmodified sequential CHR programs. The software implementations are available online for free download and we give the web links. Due to its high level of abstraction, the CHR formalism can also be used to implement and analyse models for concurrency. To this end, the Software Transaction Model, the Actor Model, Colored Petri Nets and the Join-Calculus have been faithfully encoded in CHR. Finally, we identify and discuss commonalities of the approaches surveyed and indicate what problems are left open for future research.

The paper introduces an approach that allows for detecting interaction with a graphical display in a rule-based declarative approach. It also introduces the possibility of connecting the interaction to a specific animation step to be performed. The two approaches were embedded into an animation system to aid in teaching algorithms.

Trees and graphs are two data structures that are commonly used in representing different kinds of data. They also have many associated algorithms taught in different courses. It is thus beneficial to have a tool that could be used by students, teachers and programmers to visually trace how their algorithms work. The work in this paper presents, CHR-Graph, an easy-to-use platform for animating trees and graphs and their correlated algorithms using Constraint Handling Rules (CHR).

Over the past years, visualization of programs has been widely applied. Algorithm animation was proven to aid in teaching and learning. It provides a convenient medium for beginners to a programming language by giving them the ability to visually discover how their programs are running. It also provides experts of a language with a means to have a visual trace utility. Lately, a new approach for adding visualization features into Constraint Handling Rules (CHR) programs was proposed. The new methodology was a dynamic one able to animate different types of algorithms. The work in this paper aims at introducing a revised extension that is able to embed visualization features into Java programs. With the new extension, Java algorithms could be animated without the need of doing any modifications to the code. In addition, the provided technique is still a general one able to animate different kinds of algorithms.

Recently, a new approach for embedding visualization features into Constraint Handling Rules (CHR) programs has been proposed. It allows CHR programmers to animate and visualize different algorithms implemented in CHR. Such features have become essential with CHR being a general purpose language. In this paper, a new diagrammatic representation for CHR programs is presented. The representation is also able to account for the newly embedded visual features.

A devil's advocate is one who argues against a claim, not as a committed opponent but in order to determine the validity of the claim. We are interested in a devil's advocate that argues against termination of a program. He does so by producing a maleficent program that can cause the non-termination of the original program. By inspecting and running the malicious program, one may gain insight into the potential reasons for non-termination and produce counterexamples for termination.

The popular cognitive architecture ACT-R is used in many cognitive models to explain cognitive features of human-beings. It has a well-defined psychological theory but lacks a formalization of its underlying computational system. This lack allows for technical ad-hoc artifacts in the original reference implementation. More importantly, formal analysis of cognitive models is not possible without a well-defined semantics. In prior work we have defined an abstract operational semantics for ACT-R's production system that is suitable for model analysis. It abstracts from details like timings and conflict resolution methods. However, to describe the behavior of ACT-R implementations a more refined semantics is needed.

Abstract In computational cognitive science, the cognitive architecture ACT-R is very popular. It describes a model of cognition that is amenable to computer implementation, paving the way for computational psychology. Its underlying psychological theory has been investigated in many psychological experiments, but ACT-R lacks a formal definition of its underlying concepts from a mathematical-computational point of view. Although the canonical implementation of ACT-R is now modularized, this production rule system is still hard to adapt and extend in central components like the conflict resolution mechanism (which decides which of the applicable rules to apply next). In this work, we present a concise implementation of ACT-R based on Constraint Handling Rules which has been derived from a formalization in prior work. To show the adaptability of our approach, we implement several different conflict resolution mechanisms discussed in the ACT-R literature. This results in the first implementation of one such mechanism. For the other mechanisms, we empirically evaluate if our implementation matches the results of reference implementations of ACT-R.

Abstract This paper introduces a new constraint domain for reasoning about data with uncertainty. It extends convex modeling with the notion of p-box to gain additional quantifiable information on the data whereabouts. Unlike existing approaches, the p-box envelops an unknown probability instead of approximating its representation. The p-box bounds are uniform cumulative distribution functions (cdf) in order to employ linear computations in the probabilistic domain. The reasoning by means of p-box cdf-intervals is an interval computation which is exerted on the real domain then it is projected onto the cdf domain. This operation conveys additional knowledge represented by the obtained probabilistic bounds. The empirical evaluation of our implementation shows that, with minimal overhead, the output solution set realizes a full enclosure of the data along with tighter bounds on its probabilistic distributions.

Constraint Handling Rules (CHR) is a declarative rule-based programming language that has cut out its niche over the course of the last 20 years. It generalizes concurrent constraint logic programming to multiple heads, thus closing the gap to multiset transformation systems. Its popular extension CHR with Disjunction (CHR∨) is a multiparadigm declarative programming language that allows embedding of Horn programs with SLD resolution. We analyze the assets and the limitations of the classical declarative semantics of CHR∨ and highlight its natural relationship with linear-logic. We furthermore develop two linear-logic semantics for CHR∨ that differ in the reasoning domain for which they are instrumental. We show their idempotence and their soundness and completeness with respect to the operational semantics. We show how to apply the linear-logic semantics to decide program properties and to reason about operational equivalence of CHR∨ programs.

Abstract Riveret et al. have proposed a framework for probabilistic legal reasoning. Their goal is to determine the chance of winning a court case, given the probabilities of the judge accepting certain claimed facts and legal rules. In this paper we tackle the same problem by defining and implementing a new formalism, called probabilistic argumentation logic, which can be seen as a probabilistic generalization of Nute's defeasible logic. Not only does this provide an automation of the — only hand-performed — computations in Riveret et al, it also provides a solution to one of their open problems: a method to determine the initial probabilities from a given body of precedents.

This paper investigates the compilation of a committed-choice rule-based language, Constraint Handling Rules (CHR), to specialized hardware circuits. The developed hardware is able to turn the intrinsic concurrency of the language into parallelism. Rules are applied by a custom executor that handles constraints according to the best degree of parallelism the implemented CHR specification can offer. Our framework deploys the target digital circuits through the Field Programmable Gate Array (FPGA) technology, by first compiling the CHR code fragment into a low level hardware description language. We also discuss the realization of a hybrid CHR interpreter, consisting of a software component running on a general purpose processor, coupled with a hardware accelerator. The latter unburdens the processor by executing in parallel the most computational intensive CHR rules directly compiled in hardware. Finally the performance of a prototype system is evaluated by time efficiency measures.

Abstract Graph transformation systems (GTS) and constraint handling rules (CHR) are non-deterministic rule-based state transition systems. CHR is well known for its powerful confluence and program equivalence analyses, for which we provide the basis in this work to apply them to GTS. We give a sound and complete embedding of GTS in CHR, investigate confluence of an embedded GTS and provide a program equivalence analysis for GTS via the embedding. The results confirm the suitability of CHR-based program analyses for other formalisms embedded in CHR.

Abstract We observe that the various formulations of the operational semantics of Constraint Handling Rules proposed over the years fall into a spectrum ranging from the analytical to the pragmatic. While existing analytical formulations facilitate program analysis and formal proofs of program properties, they cannot be implemented as is. We propose a novel operational semantics ω!, which has a strong analytical foundation, while featuring a terminating execution model. We prove its soundness and completeness with respect to existing analytical formulations and we provide an implementation in the form of a source-to-source transformation to CHR with rule priorities.

Abstract We present in this paper a first-order axiomatization of an extended theory T of finite or infinite trees, built on a signature containing an infinite set of function symbols and a relation finite(t), which enables to distinguish between finite and infinite trees. We show that T has at least one model and prove its completeness by giving not only a decision procedure, but a full first-order constraint solver that gives clear and explicit solutions for any first-order constraint satisfaction problem in T. The solver is given in the form of 16 rewriting rules that transform any first-order constraint ϕ into an equivalent disjunction φ of simple formulas such that φ is either the formula true or the formula false or a formula having at least one free variable, being equivalent neither to true nor to false and where the solutions of the free variables are expressed in a clear and explicit way. The correctness of our rules implies the completeness of T. We also describe an implementation of our algorithm in CHR (Constraint Handling Rules) and compare the performance with an implementation in C++ and that of a recent decision procedure for decomposable theories.

Rule-based programming experiences renaissance due to its applications in areas such as Business Rules, Semantic Web, Computational Biology, Verification and Security. Executable rules are used in declarative programming languages, in program transformation and analysis, and for reasoning in artificial intelligence applications.Constraint Handling Rules (CHR) [6, 8, 11] is a concurrent committed-choice constraint logic programming language consisting of guarded rules that transform multi-sets of atomic formulas (constraints) into simpler ones until exhaustion. CHR was initially developed for solving constraints, but has matured into a general-purpose concurrent constraint language over the last decade, because it can embed many rule-based formalisms and describe algorithms in a declarative way. The clean semantics of CHR facilitates non-trivial program analysis and transformation

Constraint Handling Rules (CHR) is a committed-choice rule-based language that was originally intended for writing constraint solvers. In this paper we show that it is also possible to write the classic union-find algorithm and variants in CHR. The programs neither compromise in declarativeness nor efficiency. We study the time complexity of our programs: they match the almost-linear complexity of the best known imperative implementations. This fact is illustrated with experimental results.

During the last decade, Constraint Handling Rules (CHR) have become a major specification and implementation language for logical, constraint-based algorithms and intelligent applications (as witnessed for example by several hundred publications available online that mention CHR). Algorithms are often specified using inference rules, rewrite rules, sequents, proof rules, or logical axioms that can be almost directly written in CHR.

Soft constraints are a generalization of classical constraints, which allow for the description of preferences rather than strict requirements. In soft constraints, constraints and partial assignments are given preference or importance levels, and constraints are combined according to combinators which express the desired optimization criteria. On the other hand, constraint handling rules (CHR) constitute a high‐level natural formalism to specify constraint solvers and propagation algorithms. We present a framework to design and specify soft constraint solvers by using CHR. In this way, we extend the range of applicability of CHR to soft constraints rather than just classical ones, and we provide a straightforward implementation for soft constraint solvers.

Most cities in Germany regularly publish a booklet called the Mietspiegel. It basically contains a verbal description of an expert system. It allows the calculation of the estimated fair rent for a flat. By hand, one may need a weekend to do this task. With our computerized version, the Munich Rent Advisor, the user just fills in a form in a few minutes, and the rent is calculated immediately. We also extended the functionality and applicability of the Mietspiegel so that the user need not answer all questions on the form. The key to computing with partial information using high-level programming was to use constraint logic programming. We rely on the Internet, and more specifically the World Wide Web, to provide this service to a broad user group, the citizens of Munich and the people who are planning to move to Munich. To process the answers from the questionnaire and return its result, we wrote a small simple stable special-purpose web server directly in ECLiPSe. More than 10,000 people have used our service in the last three years. This article describes the experiences in implementing and using the Munich Rent Advisor. Our results suggest that logic programming with constraints can be an important ingredient in intelligent internet systems.

Optimistic type systems for logic programs are considered. In such systems types are conservative approximations to the success set of the program predicates. The use of logic programs to describe types is proposed. It is argued that this approach unifies the denotational and operational approaches to descriptive type systems and is simpler and more natural than previous approaches. The focus is on the use of unary-predicate programs to describe the types. A proper class of unary-predicate programs is identified, and it is shown that it is expensive enough to express several notions of types. An analogy with two-way automata and a correspondence with alternating algorithms are used to obtain a complexity characterization of type inference and type checking. This characterization is facilitated by the use of logic programs to represent types.>