GADTs, short for Generalized Algebraic DataTypes, extend usual algebraic datatypes with a form of dependent typing that has many useful applications, but raises serious issues for type inference. Pattern matching on GADTs introduces type equalities with limited scopes, which are a source of ambiguities that may destroy principal types—and must be resolved by type annotations. By tracing ambigui...

Today, we will use an algebraic approach to solve the matching problem. Our goal is to derive an algebraic test for deciding if a graph G = (V, E) has a perfect matching. We may assume that the number of vertices is even since this is a necessary condition for having a perfect matching. First, we will define a few basic needed notations.

This paper introduces the Egison programming language whose feature is strong pattern-matching facility against not only algebraic data types but also non-free data types whose data have multiple ways of representation such as sets and graphs. Our language supports multiple occurrences of the same variables in a pattern, multiple results of pattern-matching, polymorphism of pattern-constructors...

It is well known that a formal framework for the schema matching problem (SMP) is important because it facilitates the building of algorithm model and the evaluation of algorithms. An algebraic framework for schema matching is developed in this paper. First, based on universal algebra, we propose a meta-meta structure for schema, which is named multi-labeled schema. This definition has a distin...

Approximate string matching has a long history and employs a wide variety of methods (see e.g. the survey [2]). We consider a variant of approximate matching that compares a fixed pattern string to every substring in the text string by a rational-weighted edit distance (e.g. the indel distance, defined as the number of character insertions and deletions, or the indelsub/Levenshtein distance, wh...

This paper describes the use of powerful a lgebra ic matching techniques f o r apply ing rewr i t e ru les In equat ion s o l v i n g . A matcher Is presented tha t knows about the commutat iv l ty and a s s o c i a t i v i t y o f a d d i t i o n and m u l t i p l i c a t i o n , w i l l provide de fau l t s f o r missing summands and f a c t o r s , and i f necessary w i l l solve a l g e b r...

We present new algebraic approaches for several well-known combinatorial problems, including non-bipartite matching, matroid intersection, and some of their generalizations. Our work yields new randomized algorithms that are the most efficient known. For non-bipartite matching, we obtain a simple, purely algebraic algorithm with running time O(n) where n is the number of vertices and ω is the m...

We propose an extension of the join calculus with pattern matching on algebraic data types. Our initial motivation is twofold: to provide an intuitive semantics of the interaction between concurrency and pattern matching; to define a practical compilation scheme from extended join definitions into ordinary ones plus ML pattern matching. To assess the correctness of our compilation scheme, we de...

The purpose of this note is to present a proof of Hall's matching theorem (also called marriage theorem) which I have not encountered elsewhere in literature-what yet does not mean that it is necessarily new. We refer to Hall's theorem in the following form: Theorem 1 (Hall). Let n be a positive integer. Let be a bipartite graph whose set of vertices consists of n blue vertices B 1 ; B 2 Some n...