Related papers: ACD Term Rewriting
Rewriting is a formalism widely used in computer science and mathematical logic. The classical formalism has been extended, in the context of functional languages, with an order over the rules and, in the context of rewrite based languages,…
We report on an inversion tool for a class of oriented conditional constructor term rewriting systems. Four well-behaved rule inverters ranging from trivial to full, partial and semi-inverters are included. Conditional term rewriting…
We introduce a coinductive definition of infinitary term rewriting. The setup is surprisingly simple, and has in contrast to the usual definitions of infinitary rewriting, neither need for ordinals nor for metric convergence. While the idea…
Complex reasoning problems are most clearly and easily specified using logical rules, but require recursive rules with aggregation such as count and sum for practical applications. Unfortunately, the meaning of such rules has been a…
This paper addresses the problem of creating simplifiers for logic formulas based on conditional term rewriting. In particular, the paper focuses on a program synthesis application where formula simplifications have been shown to have a…
Automatic Differentiation (AD) has become a dominant technique in ML. AD frameworks have first been implemented for imperative languages using tapes. Meanwhile, functional implementations of AD have been developed, often based on dual…
We propose a generalized version of context-sensitivity in term rewriting based on the notion of "forbidden patterns". The basic idea is that a rewrite step should be forbidden if the redex to be contracted has a certain shape and appears…
We study the termination of rewriting modulo a set of equations in the Calculus of Algebraic Constructions, an extension of the Calculus of Constructions with functions and predicates defined by higher-order rewrite rules. In a previous…
Considering patterns as sets of their instances, a difference operator over patterns computes a finite set of two given patterns, which represents the difference between the dividend pattern and the divisor pattern. A complement of a…
In Automatic Speech Recognition (ASR) systems, a recurring obstacle is the generation of narrowly focused output distributions. This phenomenon emerges as a side effect of Connectionist Temporal Classification (CTC), a robust sequence…
Modern large reasoning models demonstrate impressive problem-solving capabilities by employing sophisticated reasoning strategies. However, they often struggle to balance efficiency and effectiveness, frequently generating unnecessarily…
Ordered logics and type systems have been used in a variety of applications including computational linguistics, memory allocation, stream processing, logical frameworks, parametricity, and enforcing security protocols. In most…
A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. The term calculus is proved complete for a semantics in linearly distributive…
Large language models often struggle with complex long-horizon analytical tasks over unstructured tables, which typically feature hierarchical and bidirectional headers and non-canonical layouts. We formalize this challenge as Deep Tabular…
We present a constructive formalization of Abstract Rewriting Systems (ARS) in the Agda proof assistant, focusing on standard results in term rewriting. We define a taxonomy of concepts related to termination and confluence and investigate…
Large Language Models (LLMs) have shown remarkable performance in multi-turn dialogue. However, in multi-turn dialogue, models still struggle to stay aligned with what has been established earlier, follow dependencies across many turns, and…
We propose a notion of complexity for oriented conditional term rewrite systems satisfying certain restrictions. This notion is realistic in the sense that it measures not only successful computations, but also partial computations that…
This paper is an extended abstract of an analysis of term rewriting where the terms in the rewrite rules as well as the term to be rewritten are compressed by a singleton tree grammar (STG). This form of compression is more general than…
The authors' ATR programming formalism is a version of call-by-value PCF under a complexity-theoretically motivated type system. ATR programs run in type-2 polynomial-time and all standard type-2 basic feasible functionals are ATR-definable…
We give a method to prove confluence of term rewriting systems that contain non-terminating rewrite rules such as commutativity and associativity. Usually, confluence of term rewriting systems containing such rules is proved by treating…