Toward a declarative semantics for infinite objects in logic programming

AbstractA greatest fixed point characterization of the minimal infinite objects computed by a nonterminating logic program is presented, avoiding difficulties experienced by other attempts in the literature. A minimal infinite object is included in the denotation just when (1) it is successively finitely approximated by a fair infinite computation of the program and (2) any nonterminating computation which continually approximates this object in fact constructs it. Minimal objects are the most general constructible by nonterminating computations of the program

(Co-)Inductive semantics for Constraint Handling Rules

In this paper, we address the problem of defining a fixpoint semantics for Constraint Handling Rules (CHR) that captures the behavior of both simplification and propagation rules in a sound and complete way with respect to their declarative semantics. Firstly, we show that the logical reading of states with respect to a set of simplification rules can be characterized by a least fixpoint over the transition system generated by the abstract operational semantics of CHR. Similarly, we demonstrate that the logical reading of states with respect to a set of propagation rules can be characterized by a greatest fixpoint. Then, in order to take advantage of both types of rules without losing fixpoint characterization, we present an operational semantics with persistent. We finally establish that this semantics can be characterized by two nested fixpoints, and we show the resulting language is an elegant framework to program using coinductive reasoning.Comment: 17 page

Non-linear Pattern Matching with Backtracking for Non-free Data Types

Non-free data types are data types whose data have no canonical forms. For example, multisets are non-free data types because the multiset $\{a,b,b\}$ has two other equivalent but literally different forms $\{b,a,b\}$ and $\{b,b,a\}$. Pattern matching is known to provide a handy tool set to treat such data types. Although many studies on pattern matching and implementations for practical programming languages have been proposed so far, we observe that none of these studies satisfy all the criteria of practical pattern matching, which are as follows: i) efficiency of the backtracking algorithm for non-linear patterns, ii) extensibility of matching process, and iii) polymorphism in patterns. This paper aims to design a new pattern-matching-oriented programming language that satisfies all the above three criteria. The proposed language features clean Scheme-like syntax and efficient and extensible pattern matching semantics. This programming language is especially useful for the processing of complex non-free data types that not only include multisets and sets but also graphs and symbolic mathematical expressions. We discuss the importance of our criteria of practical pattern matching and how our language design naturally arises from the criteria. The proposed language has been already implemented and open-sourced as the Egison programming language

A Survey of Languages for Specifying Dynamics: A Knowledge Engineering Perspective

A number of formal specification languages for knowledge-based systems has been developed. Characteristics for knowledge-based systems are a complex knowledge base and an inference engine which uses this knowledge to solve a given problem. Specification languages for knowledge-based systems have to cover both aspects. They have to provide the means to specify a complex and large amount of knowledge and they have to provide the means to specify the dynamic reasoning behavior of a knowledge-based system. We focus on the second aspect. For this purpose, we survey existing approaches for specifying dynamic behavior in related areas of research. In fact, we have taken approaches for the specification of information systems (Language for Conceptual Modeling and TROLL), approaches for the specification of database updates and logic programming (Transaction Logic and Dynamic Database Logic) and the generic specification framework of abstract state machine