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

Pattern tree-based XOLAP rollup operator for XML complex hierarchies

With the rise of XML as a standard for representing business data, XML data warehousing appears as a suitable solution for decision-support applications. In this context, it is necessary to allow OLAP analyses on XML data cubes. Thus, XQuery extensions are needed. To define a formal framework and allow much-needed performance optimizations on analytical queries expressed in XQuery, defining an algebra is desirable. However, XML-OLAP (XOLAP) algebras from the literature still largely rely on the relational model. Hence, we propose in this paper a rollup operator based on a pattern tree in order to handle multidimensional XML data expressed within complex hierarchies

Maude: specification and programming in rewriting logic

Maude is a high-level language and a high-performance system supporting executable specification and declarative programming in rewriting logic. Since rewriting logic contains equational logic, Maude also supports equational specification and programming in its sublanguage of functional modules and theories. The underlying equational logic chosen for Maude is membership equational logic, that has sorts, subsorts, operator overloading, and partiality definable by membership and equality conditions. Rewriting logic is reflective, in the sense of being able to express its own metalevel at the object level. Reflection is systematically exploited in Maude endowing the language with powerful metaprogramming capabilities, including both user-definable module operations and declarative strategies to guide the deduction process. This paper explains and illustrates with examples the main concepts of Maude's language design, including its underlying logic, functional, system and object-oriented modules, as well as parameterized modules, theories, and views. We also explain how Maude supports reflection, metaprogramming and internal strategies. The paper outlines the principles underlying the Maude system implementation, including its semicompilation techniques. We conclude with some remarks about applications, work on a formal environment for Maude, and a mobile language extension of Maude

Efficient Pattern Matching in Python

Pattern matching is a powerful tool for symbolic computations. Applications include term rewriting systems, as well as the manipulation of symbolic expressions, abstract syntax trees, and XML and JSON data. It also allows for an intuitive description of algorithms in the form of rewrite rules. We present the open source Python module MatchPy, which offers functionality and expressiveness similar to the pattern matching in Mathematica. In particular, it includes syntactic pattern matching, as well as matching for commutative and/or associative functions, sequence variables, and matching with constraints. MatchPy uses new and improved algorithms to efficiently find matches for large pattern sets by exploiting similarities between patterns. The performance of MatchPy is investigated on several real-world problems

Regular Expression Matching and Operational Semantics

Many programming languages and tools, ranging from grep to the Java String library, contain regular expression matchers. Rather than first translating a regular expression into a deterministic finite automaton, such implementations typically match the regular expression on the fly. Thus they can be seen as virtual machines interpreting the regular expression much as if it were a program with some non-deterministic constructs such as the Kleene star. We formalize this implementation technique for regular expression matching using operational semantics. Specifically, we derive a series of abstract machines, moving from the abstract definition of matching to increasingly realistic machines. First a continuation is added to the operational semantics to describe what remains to be matched after the current expression. Next, we represent the expression as a data structure using pointers, which enables redundant searches to be eliminated via testing for pointer equality. From there, we arrive both at Thompson's lockstep construction and a machine that performs some operations in parallel, suitable for implementation on a large number of cores, such as a GPU. We formalize the parallel machine using process algebra and report some preliminary experiments with an implementation on a graphics processor using CUDA.Comment: In Proceedings SOS 2011, arXiv:1108.279

On Region Algebras, XML Databases, and Information Retrieval

This paper describes some new ideas on developing a logical algebra for databases that manage textual data and support information retrieval functionality. We describe a first prototype of such a system