LogScheme: Integrating logic programming into Scheme

We have recently defined a framework for Narrowing-driven Partial Evaluation (NPE) of functional logic programs. This method is as powerful as partial deduction of logic programs and positive supercompilation of functional programs. Although it is possible to treat complex terms containing primitive functions (e.g. conjunctions or equations) in the NPE framework, its basic control mechanisms do not allow for effective polygenetic specialization of these complex expressions. We introduce a sophisticated unfolding rule endowed with a dynamic narrowing strategy which permits flexible scheduling of the elements (in conjunctions) which are reduced during specialization. We also present a novel abstraction operator which extends some partitioning techniques defined in the framework of conjunctive partial deduction. We provide experimental results obtained from an implementation using the Indy system which demonstrate that the control refinements produce better specializations.KeywordsLogic ProgramFunction SymbolPartial EvaluationPrimitive FunctionImprove ControlThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Languages that integrate functional and logic programming with a complete operational semantics are based on narrowing, a unification-based goal-solving mechanism which subsumes the reduction principle of functional languages and the resolution principle of logic languages. In this article, we present a partial evaluation scheme for functional logic languages based on an automatic unfolding algorithm which builds narrowing trees. The method is formalized within the theoretical framework established by Lloyd and Shepherdson for the partial deduction of logic programs, which we have generalized for dealing with functional computations. A generic specialization algorithm is proposed which does not depend on the eager or lazy nature of the narrower being used. To the best of our knowledge, this is the first generic algorithm for the specialization of functional logic programs. We also discuss the relation to work on partial evaluation in functional programming, term-rewriting systems, and logic programming. Finally, we present some experimental results with an implementation of the algorithm which show in practice that the narrowing-driven partial evaluator effectively combines the propagation of partial data structures (by means of logical variables and unification) with better opportunities for optimization (thanks to the functional dimension).

In functional logic programs, rules are applicable independently of textual order, i.e., any rule can potentially be used to evaluate an expression. This is similar to logic languages and contrary to functional languages, e.g., Haskell enforces a strict sequential interpretation of rules. However, in some situations it is convenient to express alternatives by means of compact default rules. Although default rules are often used in functional programs, the non-deterministic nature of functional logic programs does not allow to directly transfer this concept from functional to functional logic languages in a meaningful way. In this paper we propose a new concept of default rules for Curry that supports a programming style similar to functional programming while preserving the core properties of functional logic programming, i.e., completeness, non-determinism, and logic-oriented uses of functions. We discuss the basic concept and sketch an initial implementation of it which exploits advanced features of functional logic languages.

In functional logic programs, rules are applicable independently of textual order, i.e., any rule can potentially be used to evaluate an expression. This is similar to logic languages and contrary to functional languages, e.g., Haskell enforces a strict sequential interpretation of rules. However, in some situations it is convenient to express alternatives by means of compact default rules. Although default rules are often used in functional programs, the non-deterministic nature of functional logic programs does not allow to directly transfer this concept from functional to functional logic languages in a meaningful way. In this paper, we propose a new concept of default rules for Curry that supports a programming style similar to functional programming while preserving the core properties of functional logic programming, i.e., completeness, non-determinism, and logic-oriented use of functions. We discuss the basic concept and propose an implementation which exploits advanced features of functional logic languages.

A new declarative programming paradigm, constraint functional logic programming (CFLP) is presented, which unifies systematically all features of constraint, functional and logic programming. CFLP extends constraint functional programming (CFP), which supports equation solving over a functional program, to general constraint programming permitting the use of constraints for programming as well as for posing queries. It also generalises constraint logic programming (CLP), by admitting user-defined functions as a purely functional subsystem of a CLP language. This paper presents the motivation for designing CFLP and its semantics. Programming examples are given in the concrete CFLP language Falcon.KeywordsLogic ProgramLogic ProgrammingConstraint ProgrammingConstraint SystemFunctional ProgrammingThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Currently available programming and database systems are insufficient for engineering applications. The authors contend that a logical progression from a formal conceptual model of the engineering domain to a computational model will lead to new programming paradigms capable of directly supporting engineering applications in a rigorous, concise manner. A formal domain model devised by the authors, theHybrid Model (HM) of design information, is briefly introduced. It is an extension of axiomatic set theory and is discussed in detail elsewhere. HM forms the basis ofDesigner, a prototype-based object-oriented programming language supporting a signature-based canonical message-passing mechanism and multiple inheritance. Designer is implemented using the Scheme programming language. Because Designer satisfies a formal conceptual model, and because it is based on a formally specified language, its robustness and logical validity are superior to those of other languages not founded on formal principles. Designer combines concepts of functional and object-oriented programming to provide the formal rigor and flexibility to capture the complex and strongly interrelated information that designers use. Examples demonstrate how Designer represents design information. The results of the authors' research indicate that Designer can capture design information (including aspects of functional requirements and design intent) effectively and efficiently.

Saraswat recently introduced the framework of concurrent constraint programming [14]. The essence of the framework is that computations consist of concurrent agents interacting by communicating constraints. Several concurrent constraint programming languages have been defined. They differ in the kinds of constraints that can be used as well as the kinds of operations on constraints which are available. In this paper we introduce a very simple concurrent constraint language we call Lucy, designed to closely mimic the actor model of computation. Agents can communicate only by the posting of constraints upon bags (un-ordered collections possibly with duplicate elements). This very impoverished concurrent constraint language is a syntactic subset of Janus, a concurrent constraint language which closely resembles concurrent logic programming languages such as Guarded Horn Clauses [21], Strand [5], Parlog [2] and Flat Concurrent Prolog [13]. By identifying the subset of Janus which is an actor language, we elucidate the relationship between actors and concurrent logic programming (and its generalization as concurrent constraint programming). Lucy is best not thought of as a unification of logic and constraint programming with actor and object-oriented programming, but as the missing link between these programming language genera.

The deductive layer is based on the deductive paradigm, which integrates logic programming with database facilities. The term ‘deductive’ highlights the ability to perform deductions concerning the content of the database.

Typing rule-based transformations over topological collections

The basics of logic programming, as embodied by Prolog, are generally well-known in the programming language community. However, more advanced techniques, such as tabling, answer subsumption and probabilistic logic programming fail to attract the attention of a larger audience. The cause for the community's seemingly limited interest lies with the presentation of these features: the literature frequently focuses on implementations and examples that do little to aid the understanding of non-experts in the field. The key point is that many of these advanced logic programming features can be characterised in more generally known, more accessible terms. In my research I try to reconcile these advanced concepts from logic programming (Tabling, Answer subsumption and probabilistic programming) with concepts from functional programming (effects, monads and applicative functors).

Multiple policy strategies exist to promote equity and inclusion in education and training systems. Across countries, the provision of additional resources to students with special educational needs is a common strategy; previous research indicates that providing extra resources to students with special educational needs can help those students make progress in schools. The purpose of this article is threefold: first, it will discuss the Organisation for Economic Cooperation and Development (OECD) tripartite categorisation system for describing how different countries serve and differentiate between students with diverse special needs. The authors rely upon the OECD's work in an attempt to characterise the international special needs student population and to synthesise some of the progress that has been made toward understanding what education for students with disabilities, learning difficulties, and disadvantages looks like. Next, the article presents new lenses for viewing policies that target additional resources to disadvantaged youth. The authors intend for the lenses proposed to facilitate more fruitful international comparisons. Finally, the article will discuss the challenges inherent to making such comparisons and will conclude with suggestions for addressing those challenges.

In his 1977 ACM Turing Award Lecture, John Backus identified the word-at-a-time style of programming, inherited from the underlying hardware and dubbed the "von Neumann bottleneck", as a major obstacle to the advancement of programming. In this keynote, I argue that the functional programming he advocated introduced its own bottleneck: that everything produced by a computation (including nothing) must be encoded as a single value. This "obligation to singularity" is foreign to modelling, where single values sit collegially between no values and two values. Exploring diverse examples, I will argue that adopting a modelling (de facto: relational) style of programming eliminates the functional bottleneck, and with it many of the data-to-control flow escapes that Backus originally sought to avoid.

If you look at the examples and exercises presented so far in this book you can see that we fluctuate between two styles of programming: [statement1] // do something [statement2] // do something [statement3] // do something …

Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this article, we will survey the use ofstructural proof theoryas an alternative foundation. Researchers have been using this foundation for the past 35 years to elevate logic programming from its roots in first-order classical logic into higher-order versions of intuitionistic and linear logic. These more expressive logic programming languages allow for capturing stateful computations and rich forms of abstractions, including higher-order programming, modularity, and abstract data types. Term-level bindings are another kind of abstraction, and these are given an elegant and direct treatment within both proof theory and these extended logic programming languages. Logic programming has also inspired new results in proof theory, such as those involving polarity and focused proofs. These recent results provide a high-level means for presenting the differences between forward-chaining and backward-chaining style inferences. Anchoring logic programming in proof theory has also helped identify its connections and differences with functional programming, deductive databases, and model checking.

A meta-program, regardless of the nature of the programming language, is a program whose data denotes another (object) program. The importance of meta-programming can be gauged from its large number of applications. These include compilers, interpreters, program analysers, and program transformers. Furthermore, if the object program is a logic or functional program formalizing some knowledge, then the meta-program may be regarded as a meta-reasoner for reasoning about this knowledge. In this chapter, the meta-program is assumed to be a logic program. The object program does not have to be a logic program although much of the work in this chapter assumes this. We have identified three major topics for consideration. These are the theoretical foundations of meta-programming, the suitability of the alternative meta-programming techniques for different applications, and methods for improving the efficiency of meta-programs. As with logic programs generally, meta-programs have declarative and procedural semantics. The theoretical study of meta-programming shows that both aspects of the semantics depend crucially on the manner in which object programs are represented as data in a meta-program. The second theme of the paper is the problem of designing and choosing appropriate ways of specifying important meta-programming problems, including dynamic metaprogramming and problems involving self-application. The third theme concerns efficient implementation of meta-programs. Meta-programming systems require representations with facilities that minimize the overhead of interpreting the object program. In addition, efficiency can be gained by transforming the meta-program, specializing it for the particular object program it is reasoning about. This chapter, which concentrates on these aspects of meta-programming, is not intended to be a survey of the field. A more complete survey of meta-programming for logic programming can be found in [Barklund, 1995]. Many issues in meta-programming have their roots in problems in logic which have been studied for several decades. This chapter emphasizes meta-programming solutions. It is not intended to give a full treatment of the underlying logical problems, though we try to indicate some connections to wider topics in meta-logic. The meta-programs in this chapter are logic programs based on first order logic.