Cops and CoCoWeb: Infrastructure for Confluence Tools

In this paper we describe the infrastructure supporting confluence tools and competitions: Cops, the confluence problems database, and CoCoWeb, a convenient web interface for tools that participate in the annual confluence competition

Rewriting Transfinite Terms

We define rewriting over terms with positions of transfinite length

A Reduction-Preserving Completion for Proving Confluence of Non-Terminating Term Rewriting Systems

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 them as equational term rewriting systems and considering E-critical pairs and/or termination modulo E. In contrast, our method is based solely on usual critical pairs and it also (partially) works even if the system is not terminating modulo E. We first present confluence criteria for term rewriting systems whose rewrite rules can be partitioned into a terminating part and a possibly non-terminating part. We then give a reduction-preserving completion procedure so that the applicability of the criteria is enhanced. In contrast to the well-known Knuth-Bendix completion procedure which preserves the equivalence relation of the system, our completion procedure preserves the reduction relation of the system, by which confluence of the original system is inferred from that of the completed system

Confluence Competition 2018

We report on the 2018 edition of the Confluence Competition, a competition of software tools that aim to (dis)prove confluence and related properties of rewrite systems automatically

Proving Ground Confluence of Equational Specifications Modulo Axioms

Terminating functional programs should be deterministic, i.e., should evaluate to a unique result, regardless of the evaluation order. For equational functional programs such determinism is exactly captured by the ground confluence property. For terminating equations this is equivalent to ground local confluence, which follows from local confluence. Checking local confluence by computing critical pairs is the standard way to check ground confluence. The problem is that some perfectly reasonable equational programs are not locally confluent and it can be very hard or even impossible to make them so by adding more equations. We propose a three-step strategy to prove that an equational program as is is ground confluent: First: apply the strategy proposed in [8] to use non-joinable critical pairs as completion hints to either achieve local confluence or reduce the number of critical pairs. Second: use the inductive inference system proposed in this paper to prove the remaining critical pairs ground joinable. Third: to show ground confluence of the original specification, prove also ground joinable the equations added. These methods apply to order-sorted and possibly conditional equational programs modulo axioms such as, e.g., Maude functional modules.This work has been partially supported by NRL under contract number N00173-17-1-G002.Ope

Expression of the retinoic acid catabolic enzyme CYP26B1 in the human brain to maintain signaling homeostasis

Date of Acceptance: 27/08/2015 Funding was provided by the Wellcome Trust grant WT081633MA-NCE and Biological Sciences Research Council Grant BB/K001043/1. Prof Fragoso is the recipient of a Post Doctoral Science without Borders grant from the Brazilian National Council for Scientific and Technological Development (CNPq, 237450/2012-7).Peer reviewedPublisher PD

Gli3 Controls Corpus Callosum Formation by Positioning Midline Guideposts During Telencephalic Patterning

The corpus callosum (CC) represents the major forebrain commissure connecting the 2 cerebral hemispheres. Midline crossing of callosal axons is controlled by several glial and neuronal guideposts specifically located along the callosal path, but it remains unknown how these cells acquire their position. Here, we show that the Gli3 hypomorphic mouse mutant Polydactyly Nagoya (Pdn) displays agenesis of the CC and mislocation of the glial and neuronal guidepost cells. Using transplantation experiments, we demonstrate that agenesis of the CC is primarily caused by midline defects. These defects originate during telencephalic patterning and involve an up-regulation of Slit2 expression and altered Fgf and Wnt/β-catenin signaling. Mutations in sprouty1/2 which mimic the changes in these signaling pathways cause a disorganization of midline guideposts and CC agenesis. Moreover, a partial recovery of midline abnormalities in Pdn/Pdn;Slit2(-/-) embryos mutants confirms the functional importance of correct Slit2 expression levels for callosal development. Hence, Gli3 controlled restriction of Fgf and Wnt/β-catenin signaling and of Slit2 expression is crucial for positioning midline guideposts and callosal development

Biphasic Synaptic Ca Influx Arising from Compartmentalized Electrical Signals in Dendritic Spines

Dendritic spines compartmentalize synaptically-evoked biochemical signals. The authors show that electrical compartmentalization provided by a spine endows the associated synapse with additional modes of calcium signaling by shaping the kinetics of synaptic calcium currents