Soundness and completeness proofs by coinductive methods

We show how codatatypes can be employed to produce compact, high-level proofs of key results in logic: the soundness and completeness of proof systems for variations of first-order logic. For the classical completeness result, we first establish an abstract property of possibly infinite derivation trees. The abstract proof can be instantiated for a wide range of Gentzen and tableau systems for various flavors of first-order logic. Soundness becomes interesting as soon as one allows infinite proofs of first-order formulas. This forms the subject of several cyclic proof systems for first-order logic augmented with inductive predicate definitions studied in the literature. All the discussed results are formalized using Isabelle/HOL’s recently introduced support for codatatypes and corecursion. The development illustrates some unique features of Isabelle/HOL’s new coinductive specification language such as nesting through non-free types and mixed recursion–corecursion

The Coral Trait Database, a curated database of trait information for coral species from the global oceans.

Trait-based approaches advance ecological and evolutionary research because traits provide a strong link to an organism's function and fitness. Trait-based research might lead to a deeper understanding of the functions of, and services provided by, ecosystems, thereby improving management, which is vital in the current era of rapid environmental change. Coral reef scientists have long collected trait data for corals; however, these are difficult to access and often under-utilized in addressing large-scale questions. We present the Coral Trait Database initiative that aims to bring together physiological, morphological, ecological, phylogenetic and biogeographic trait information into a single repository. The database houses species- and individual-level data from published field and experimental studies alongside contextual data that provide important framing for analyses. In this data descriptor, we release data for 56 traits for 1547 species, and present a collaborative platform on which other trait data are being actively federated. Our overall goal is for the Coral Trait Database to become an open-source, community-led data clearinghouse that accelerates coral reef research