Related papers: Algebraic Pattern Matching in Join Calculus
We define the pattern fragment for higher-order unification problems in linear and affine type theory and give a deterministic unification algorithm that computes most general unifiers.
Connection calculi allow for very compact implementations of goal-directed proof search. We give an overview of our work related to connection tableaux calculi: First, we show optimised functional implementations of clausal and nonclausal…
Sound exhaustiveness checking of pattern-matching is an essential feature of functional programming languages, and OCaml supports it for GADTs. However this check is incomplete, in that it may fail to detect that a pattern can match no…
With today's public data sets containing billions of data items, more and more companies are looking to integrate external data with their traditional enterprise data to improve business intelligence analysis. These distributed data sources…
Haskell functions are defined as a series of clauses consisting of patterns that are matched against the arguments in the order of definition. In case an input is not matched by any of the clauses, an error occurs. Therefore it is desirable…
In recent years, the problem of association rule mining in transactional data has been well studied. We propose to extend the discovery of classical association rules to the discovery of association rules of conjunctive queries in arbitrary…
We propose a couple of oracle construction methods for quantum pattern matching. We in turn show that one of the construct can be used with the Grover's search algorithm for exact and partial pattern matching, deterministically. The other…
We study strategies of approximate pattern matching that exploit bidirectional text indexes, extending and generalizing ideas of Lam et al. We introduce a formalism, called search schemes, to specify search strategies of this type, then…
Recent technological advancements have led to the rapid generation of high-throughput biological data, which can be used to address novel scientific questions in broad areas of research. These data can be thought of as a large matrix with…
In this paper we develop an algebraic approach to data integration by combining techniques from functional programming, category theory, and database theory. In our formalism, database schemas and instances are algebraic (multi-sorted…
Analytical queries often require a mixture of relational and linear algebra operations applied to the same data. This poses a challenge to analytic systems that must bridge the gap between relations and matrices. Previous work has mainly…
Model merging acquires general capabilities without extra data or training by combining multiple models' parameters. Previous approaches achieve linear mode connectivity by aligning parameters into the same loss basin using permutation…
Despite the somewhat different techniques used in developing search engines and recommender systems, they both follow the same goal: helping people to get the information they need at the right time. Due to this common goal, search and…
As a promising step, the performance of data analysis and feature learning are able to be improved if certain pattern matching mechanism is available. One of the feasible solutions can refer to the importance estimation of instances, and…
Multi-AI collaboration, such as ensembling or debating large language models (LLMs), is a promising paradigm for aggregating information and boosting performance. A foundational step in these pipelines is to feed the responses of several…
We discuss a selection of recent developments in arithmetic combinatorics having to do with ``approximate algebraic structure'' together with some of their applications.
We introduce parallelism into the basic algebra of games to model concurrent game algebraically. Parallelism is treated as a new kind of game operation. The resulted algebra of concurrent games can be used widely to reason the parallel…
Worst-case optimal join algorithms are the class of join algorithms whose runtime match the worst-case output size of a given join query. While the first provably worst-case optimal join algorithm was discovered relatively recently, the…
Join patterns are an underexplored approach for the programming of concurrent and distributed systems. When applied to the actor model, join patterns offer the novel capability of matching combinations of messages in the mailbox of an…
Matrix congruence can be used to mimic linear maps between homogeneous quadratic polynomials in $n$ variables. We introduce a generalization, called standard-form congruence, which mimics affine maps between non-homogeneous quadratic…