Towards the uniform implementation of declarative languages

Current implementation techniques for functional languages differ considerably from those for logic languages. This complicates the development of flexible and efficient abstract machines that can be used for the compilation of declarative languages combining concepts of functional and logic programming. We propose an abstract machine, called the JUMP-machine, which systematically integrates the operational concepts needed to implement the functional and logic programming paradigm. The use of a tagless representation for heap objects, which originates from the Spineless Tagless G-machine, supports the integration of different concepts. In this paper, we provide a functional logic kernel language and show how to translate it into the abstract machine language of the JUMP-machine. Furthermore, we define the operational semantics of the machine language formally and discuss the mapping of the abstract machine to concrete machine architectures. We tested the approach by writing a compiler for the functional logic language GTML. The obtained performance results indicate that the proposed method allows to implement functional logic languages efficiently.     

Path Dependent Analysis of Logic Programs

This paper presents an abstract semantics that uses information about execution paths to improve precision of data flow analyses of logic programs. The abstract semantics is illustrated by abstracting execution paths using call strings of fixed length and the last transfer of control. Abstract domains that have been developed for logic program analyses can be used with the new abstract semantics without modification.     

Set based logic programming

In a previous paper (Blair et al. 2001), the authors showed that the mechanism underlying Logic Programming can be extended to handle the situation where the atoms are interpreted as subsets of a given space X. The view of a logic program as a one-step consequence operator along with the concepts of supported and stable model can be transferred to such situations. In this paper, we show that we can further extend this paradigm by creating a new one-step consequence operator by composing the old one-step consequence operator with a monotonic idempotent operator (miop) in the space of all subsets of X, 2 ^X . We call this extension set based logic programming. We show that such a set based formalism for logic programming naturally supports a variety of options. For example, if the underlying space has a topology, one can insist that the new one-step consequence operator always produces a closed set or always produces an open set. The flexibility inherent in the semantics of set based logic programs is due to both the range of natural choices available for specifying the semantics of negation, as well as the role of monotonic idempotent operators (miops) as parameters in the semantics. This leads to a natural type of polymorphism for logic programming, i.e. the same logic program can produce a variety of outcomes depending on the miop associated with the semantics. We develop a general framework for set based programming involving miops. Among the applications, we obtain integer-based representations of real continuous functions as stable models of a set based logic program.      

Comparing approaches to free dcpo-algebra constructions

Algebraic structures play an important rôle for the semantics of programming languages. One application is the use of free algebra constructions for modelling computational effects in categorical frameworks for denotational semantics, as proposed by Plotkin and Power. It is well-known that, for abstract reasons, free algebra constructions are available in the category of dcpos and Scott continuous maps. However, only very recently, this construction has been investigated in concrete settings to obtain explicit characterisations of free dcpo algebras. Thereby three approaches have been developed: one order-theoretic approach by Jung, Moshier and Vickers, and two topological approaches, one by Keimel and Lawson the other by Battenfeld. In this paper we compare these approaches. In particular, we show that the order-theoretic approach can be translated into the topological setting where it is generalised by Keimel and Lawson’s approach. Furthermore, we explain the problems in comparing the order-theoretic approach with Battenfeld’s approach. Finally, we show that the two topological approaches differ on a more general scale.     

A suite of abstract domains for static analysis of string values

Strings are widely used in modern programming languages in various scenarios. For instance, strings are used to build up Structured Query Language (SQL) queries that are then executed. Malformed strings may lead to subtle bugs, as well as non‐sanitized strings may raise security issues in an application. For these reasons, the application of static analysis to compute safety properties over string values at compile time is particularly appealing. In this article, we propose a generic approach for the static analysis of string values based on abstract interpretation. In particular, we design a suite of abstract semantics for strings, where each abstract domain tracks a different kind of information. We discuss the trade‐off between efficiency and accuracy when using such domains to catch the properties of interest. In this way, the analysis can be tuned at different levels of precision and efficiency, and it can address specific properties.Copyright © 2013 John Wiley & Sons, Ltd.     

Logical approximation for program analysis

The abstract interpretation of programs relates the exact semantics of a programming language to a finite approximation of those semantics. In this article, we describe an approach to abstract interpretation that is based in logic and logic programming. Our approach consists of faithfully representing a transition system within logic and then manipulating this initial specification to create a logical approximation of the original specification. The objective is to derive a logical approximation that can be interpreted as a terminating forward-chaining logic program; this ensures that the approximation is finite and that, furthermore, an appropriate logic programming interpreter can implement the derived approximation. We are particularly interested in the specification of the operational semantics of programming languages in ordered logic, a technique we call substructural operational semantics (SSOS). We show that manifestly sound control flow and alias analyses can be derived as logical approximations of the substructural operational semantics of relevant languages.     

The ASM Refinement Method

In this paper the abstract state machine (ASM) refinement method is presented. Its characteristics compared to other refinement approaches in the literature are explained. Some frequently occurring forms of ASM refinements are identified and illustrated by examples from the design and verification of architectures and protocols, from the semantics and the implementation of programming languages and from requirements engineering.     

Strong and uniform equivalence of nonmonotonic theories – an algebraic approach

We show that the concepts of strong and uniform equivalence of logic programs can be generalized to an abstract algebraic setting of operators on complete lattices. Our results imply characterizations of strong and uniform equivalence for several nonmonotonic logics including logic programming with aggregates, default logic and a version of autoepistemic logic. This work was partially supported by the NSF grant IIS-0325063.     

Widening operators for powerset domains

The finite powerset construction upgrades an abstract domain by allowing for the representation of finite disjunctions of its elements. While most of the operations on the finite powerset abstract domain are easily obtained by “lifting” the corresponding operations on the base-level domain, the problem of endowing finite powersets with a provably correct widening operator is still open. In this paper we define three generic widening methodologies for the finite powerset abstract domain. The widenings are obtained by lifting any widening operator defined on the base-level abstract domain and are parametric with respect to the specification of a few additional operators that allow all the flexibility required to tune the complexity/precision trade-off. As far as we know, this is the first time that the problem of deriving non-trivial, provably correct widening operators in a domain refinement is tackled successfully. We illustrate the proposed techniques by instantiating our widening methodologies on powersets of convex polyhedra, a domain for which no non-trivial widening operator was previously known.     

Mechanizing some advanced refinement concepts

We describe how the HOL theorem prover can be used to check and apply rules of program refinement. The rules are formulated in the refinement calculus, which is a theory of correctness preserving program transformations. We embed a general command notation with a predicate transformer semantics in the logic of the HOL system. Using this embedding, we express and prove rules for data refinement and superposition refinement of initialized loops. Applications of these proof rules to actual program refinements are checked using the HOL system, with the HOL system generating these conditions. We also indicate how the HOL system is used to prove the verification conditions. Thus, the HOL system can provide a complete mechanized environment for proving program refinements.     

The semantics of the combination of atomized statements and parallel choice

In this paper we define a uniform language that is an extension of the language underlying the process algebraPA. One of the main extensions of this language overPA is given by so-called atomizing brackets. If we place these brackets around a statement then we treat this statement as an atomic action. Put differently, these brackets remove all interleaving points. We present a transition system for the language and derive its operational semantics. We show that there are several options for defining a transition system such that the resulting operational semantics is a conservative extension of the semantics forPA. We define a semantic domain and a denotational model for the language. Next we define a closure operator on the semantic domain and show how to use this closure operator to derive a fully abstract denotational semantics. Then the algebraic theory of the language is considered. We define a collection of axioms and a term rewrite system based on these axioms. Using this term rewrite system we are able to identify normal forms for the language. It is shown that these axioms capture the denotational equality. It follows that if two terms are provably equal then they have the same operational semantics. Finally, we show how to extend the axiomatization in order to axiomatize its operational equivalence.     

含有析取语义循环的不变式生成改进方法

抽象解释为程序不变式的自动化生成提供了通用的框架,但是该框架下的大多数已有数值抽象域只能表达几何上是凸的约束集.因此,对于包含(所对应的约束集是非凸的)析取语义的特殊程序结构,采用传统数值抽象域会导致分析结果不精确.针对显式和隐式含有析取语义的循环结构,提出了基于循环分解和归纳推理的不变式生成改进方法,缓解了抽象解释分析中出现的语义损失问题.实验结果表明:相比已有方法,该方法能为这种包含析取语义的循环结构生成更加精确的不变式,并且有益于一些安全性质的推理.     

Stabilization-Preserving Atomicity Refinement

Program refinements from an abstract to a concrete model empower designers to reason effectively in the abstract and architects to implement effectively in the concrete. For refinements to be useful, they must not only preserve functionality properties but also dependability properties. In this paper, we focus our attention on refinements that preserve the dependability property of stabilization. Specifically, we present a stabilization-preserving refinement of atomicity from an abstract model where a process can atomically access the state of all its neighbors and update its own state, to a concrete model where a process can only atomically access the state of any one of its neighbors or atomically update its own state. Our refinement is sound and complete with respect to the computations admitted by the abstract model, and induces linear step complexity and constant synchronization delay in the computations admitted by the concrete model. It is based on a bounded-space, stabilizing dining philosophers program in the concrete model. The program is readily extended to: (a) solve stabilization-preserving semantics refinement, (b) solve the stabilizing drinking philosophers problem, and (c) allow further refinement into a message-passing model.     

Dualities between alternative semantics for logic programming and nonmonotonic reasoning

The Gelfond-Lifschitz operator associated with a logic program (and likewise the operator associated with default theories by Reiter) exhibits oscillating behavior. In the case of logic programs, there is always at least one finite, nonempty collection of Herbrand interpretations around which the Gelfond-Lifschitz operator bounces around. The same phenomenon occurs with default logic when Reiter's operator is considered. Based on this, a stable class semantics and extension class semantics has been proposed. The main advantage of this semantics was that it was defined for all logic programs (and default theories), and that this definition was modelled using the standard operators existing in the literature such as Reiter's operator. In this paper our primary aim is to prove that there is a very interestingduality between stable class theory and the well-founded semantics for logic programming. In the stable class semantics, classes that were minimal with respect to Smyth's power-domain ordering were selected. We show that the well-founded semantics precisely corresponds to a class that is minimal w.r.t. Hoare's power domain ordering: the well-known dual of Smyth's ordering. Besides this elegant duality, this immediately suggests how to define a well-founded semantics for default logic in such a way that the dualities that hold for logic programming continue to hold for default theories. We show how the same technique may be applied to strong autoepistemic logic: the logic of strong expansions proposed by Marek and Truszczynski.     

动态模糊逻辑程序设计语言探讨

动态模糊问题是普遍存在的,但是现存的程序设计语言中适合解决动态模糊问题的极少,本文试图作这方面的研究,设计一种适合解决动态模糊性问题的程序设计语言.本文仿照监督命令的程序结构,给出动态模糊逻辑程序设计语言的一个抽象模型,其内容包括:动态模糊逻辑程序设计语言的抽象语法、动态模糊语义.     

Consistency properties and set based logic programming

Blair et al. (2001) developed an extension of logic programming called set based logic programming. In the theory of set based logic programming the atoms represent subsets of a fixed universe X and one is allowed to compose the one-step consequence operator with a monotonic idempotent operator O so as to ensure that the analogue of stable models in the theory are always closed under O. Marek et al. (1992, Ann Pure Appl Logic 96:231–276 1999) developed a generalization of Reiter’s normal default theories that can be applied to both default theories and logic programs which is based on an underlying consistency property. In this paper, we show how to extend the normal logic programming paradigm of Marek, Nerode, and Remmel to set based logic programming. We also show how one can obtain a new semantics for set based logic programming based on a consistency property.     

Closures on CPOs Form Complete Lattices

It is well known that closure operators on a complete lattice, ordered pointwise, give rise to a complete lattice, and this basic fact plays an important rôle in many fields of the semantics area, notably in domain theory and abstract interpretation. We strengthen that result by showing that closure operators on any directed-complete partial order (CPO) still form a complete lattice. An example of application in abstract interpretation theory is given.