Observational equality: now for good

Building on the recent extension of dependent type theory with a universe of definitionally proof-irrelevant types, we introduce TTobs, a new type theory based on the setoidal interpretation of dependent type theory. TTobs equips every type with an identity relation that satisfies function extensionality, propositional extensionality, and definitional uniqueness of identity proofs (UIP). Compared to other existing proposals to enrich dependent type theory with these principles, our theory features a notion of reduction that is normalizing and provides an algorithmic canonicity result, which we formally prove in Agda using the logical relation framework of Abel et al. Our paper thoroughly develops the meta-theoretical properties of TTobs, such as the decidability of the conversion and of the type checking, as well as consistency. We also explain how to extend our theory with quotient types, and we introduce a setoidal version of Swan's Id types that turn it into a proper extension of MLTT with inductive equality.

Logical Relations as Types: Proof-Relevant Parametricity for Program Modules

The theory of program modules is of interest to language designers not only for its practical importance to programming, but also because it lies at the nexus of three fundamental concerns in language design: the phase distinction , computational effects , and type abstraction . We contribute a fresh “synthetic” take on program modules that treats modules as the fundamental constructs, in which the usual suspects of prior module calculi (kinds, constructors, dynamic programs) are rendered as derived notions in terms of a modal type-theoretic account of the phase distinction. We simplify the account of type abstraction (embodied in the generativity of module functors) through a lax modality that encapsulates computational effects, placing projectibility of module expressions on a type-theoretic basis. Our main result is a (significant) proof-relevant and phase-sensitive generalization of the Reynolds abstraction theorem for a calculus of program modules, based on a new kind of logical relation called a parametricity structure . Parametricity structures generalize the proof-irrelevant relations of classical parametricity to proof- relevant families, where there may be non-trivial evidence witnessing the relatedness of two programs—simplifying the metatheory of strong sums over the collection of types, for although there can be no “relation classifying relations,” one easily accommodates a “family classifying small families.” Using the insight that logical relations/parametricity is itself a form of phase distinction between the syntactic and the semantic, we contribute a new synthetic approach to phase separated parametricity based on the slogan logical relations as types , by iterating our modal account of the phase distinction. We axiomatize a dependent type theory of parametricity structures using two pairs of complementary modalities (syntactic, semantic) and (static, dynamic), substantiated using the topos theoretic Artin gluing construction. Then, to construct a simulation between two implementations of an abstract type, one simply programs a third implementation whose type component carries the representation invariant.

Prospects for the Role of Ferroptosis in Fluorosis

As a strong oxidant, fluorine can induce oxidative stress resulting in cellular damage. Ferroptosis is an iron-dependent type of cell death caused by unrestricted lipid peroxidation (LPO) and subsequent plasma membrane rupture. This article indicated a relationship between fluorosis and ferroptosis. Evidence of the depletion of glutathione (GSH) and increased oxidized GSH can be found in a variety of organisms in high fluorine environments. Studies have shown that high fluoride levels can reduce the antioxidant capacity of antioxidant enzymes, while increasing the contents of reactive oxygen species (ROS) and malondialdehyde (MDA), resulting in oxidative stress and fluoride-induced oxidative stress, which are related to iron metabolism disorders. Excessive fluorine causes insufficient GSH, glutathione peroxidase (GSH-Px) inhibition, and oxidative stress, resulting in ferroptosis, which may play an important role in the occurrence and development of fluorosis.

Deciphering the Biological Significance of ADAR1–Z-RNA Interactions

Adenosine deaminase acting on RNA 1 (ADAR1) is an enzyme responsible for double-stranded RNA (dsRNA)-specific adenosine-to-inosine RNA editing, which is estimated to occur at over 100 million sites in humans. ADAR1 is composed of two isoforms transcribed from different promoters: p150 and N-terminal truncated p110. Deletion of ADAR1 p150 in mice activates melanoma differentiation-associated protein 5 (MDA5)-sensing pathway, which recognizes endogenous unedited RNA as non-self. In contrast, we have recently demonstrated that ADAR1 p110-mediated RNA editing does not contribute to this function, implying that a unique Z-DNA/RNA-binding domain α (Zα) in the N terminus of ADAR1 p150 provides specific RNA editing, which is critical for preventing MDA5 activation. In addition, a mutation in the Zα domain is identified in patients with Aicardi–Goutières syndrome (AGS), an inherited encephalopathy characterized by overproduction of type I interferon. Accordingly, we and other groups have recently demonstrated that Adar1 Zα-mutated mice show MDA5-dependent type I interferon responses. Furthermore, one such mutant mouse carrying a W197A point mutation in the Zα domain, which inhibits Z-RNA binding, manifests AGS-like encephalopathy. These findings collectively suggest that Z-RNA binding by ADAR1 p150 is essential for proper RNA editing at certain sites, preventing aberrant MDA5 activation.