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Term rewriting has a significant presence in various areas, not least in automated theorem proving where it is used as a proof technique. Many theorem provers employ specialised proof tactics for rewriting. This results in an interleaving…
We extend the notion of compositional associative rewriting as recently studied in the rule algebra framework literature to the setting of rewriting rules with conditions. Our methodology is category-theoretical in nature, where the…
We tackle the problem of data-structure rewriting including pointer redirections. We propose two basic rewrite steps: (i) Local Redirection and Replacement steps the aim of which is redirecting specific pointers determined by means of a…
Copatterns give functional programs a flexible mechanism for responding to their context, and composition can greatly enhance their expressiveness. However, that same expressive power makes it harder to precisely specify the behavior of…
We introduce the concept of structured synthesis for Markov decision processes where the structure is induced from finitely many pre-specified options for a system configuration. The resulting synthesis problem is in general a nonlinear…
Probabilistic programming is becoming increasingly popular thanks to its ability to specify problems with a certain degree of uncertainty. In this work, we focus on term rewriting, a well-known computational formalism. In particular, we…
We model collapsible and ordered pushdown systems with term rewriting, by encoding higher-order stacks and multiple stacks into trees. We show a uniform inverse preservation of recognizability result for the resulting class of term…
Despite the rising prevalence of neural sequence models, recent empirical evidences suggest their deficiency in compositional generalization. One of the current de-facto solutions to this problem is compositional data augmentation, aiming…
The main novelty of this paper is to consider an extension of the Calculus of Constructions where predicates can be defined with a general form of rewrite rules. We prove the strong normalization of the reduction relation generated by the…
Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the…
We demonstrate how category theory provides specifications that can efficiently be implemented via imperative algorithms and apply this to the field of graph rewriting. By examples, we show how this paradigm of software development makes it…
A rapidly growing body of research on compositional generalization investigates the ability of a semantic parser to dynamically recombine linguistic elements seen in training into unseen sequences. We present a systematic comparison of…
We present an online deliberation system using mutual evaluation in order to collaboratively develop solutions. Participants submit their proposals and evaluate each other's proposals; some of them may then be invited by the system to…
We present an approach for recursively splitting and rephrasing complex English sentences into a novel semantic hierarchy of simplified sentences, with each of them presenting a more regular structure that may facilitate a wide variety of…
Seq2seq learning has produced promising results on summarization. However, in many cases, system summaries still struggle to keep the meaning of the original intact. They may miss out important words or relations that play critical roles in…
We study the combination of the following already known ideas for showing confluence of unconditional or conditional term rewriting systems into practically more useful confluence criteria for conditional systems: Our syntactical separation…
Kan extensions provide a natural general framework for a variety of combinatorial problems. We have developed rewriting procedures for Kan extensions (over the category of sets) and this enables one program to address a wide range of…
In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…
We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…
This paper introduces a novel recurrent model for music composition that is tailored to the structure of polyphonic music. We propose an efficient new conditional probabilistic factorization of musical scores, viewing a score as a…