Search for: All records

It follows from standard results that if A and C are locally λ-presentable categories and F : A → C is a λ-accessible functor, then the comma category 𝖨𝖽↓𝐹 is locally λ-presentable. We show that, under the same hypotheses, 𝐹↓𝖨𝖽 is also locally λ-presentable. 

We present a grammar for a robust class of data types that includes algebraic data types (ADTs), (truly) nested types, generalized algebraic data types (GADTs), and their higher-kinded analogues. All of the data types our grammar defines, as well as their associated type constructors, are shown to have fully functorial initial algebra semantics in locally presentable categories. Since local presentability is a modest hypothesis, needed for such semantics for even the simplest ADTs, our semantic framework is actually quite conservative. Our results thus provide evidence that if a category supports fully functorial initial algebra semantics for standard ADTs, then it does so for advanced higher-kinded data types as well. To give our semantics we introduce a new type former called Lan that captures on the syntactic level the categorical notion of a left Kan extension. We show how left Kan extensions capture propagation of a data type’s syntactic generators across the entire universe of types, via a certain completion procedure, so that the type constructor associated with a data type becomes a bona fide functor with a canonical action on morphisms. A by-product of our semantics is a precise measure of the semantic complexity of data types, given by the least cardinal λ for which the functor underlying a data type is λ-accessible. The proof of our main result allows this cardinal to be read off from a data type definition without much effort. It also gives a sufficient condition for a data type to have semantic complexity ω, thus characterizing those data types whose data elements are effectively enumerable. 

Abstract Accelerating the design and development of new advanced materials is one of the priorities in modern materials science. These efforts are critically dependent on the development of comprehensive materials cyberinfrastructures which enable efficient data storage, management, sharing, and collaboration as well as integration of computational tools that help establish processing–structure–property relationships. In this contribution, we present implementation of such computational tools into a cloud-based platform called BisQue (Kvilekval et al., Bioinformatics 26(4):554, 2010). We first describe the current state of BisQue as an open-source platform for multidisciplinary research in the cloud and its potential for 3D materials science. We then demonstrate how new computational tools, primarily aimed at processing–structure–property relationships, can be implemented into the system. Specifically, in this work, we develop a module for BisQue that enables microstructure-sensitive predictions of effective yield strength of two-phase materials. Towards this end, we present an implementation of a computationally efficient data-driven model into the BisQue platform. The new module is made available online (web address:https://bisque.ece.ucsb.edu/module_service/Composite_Strength/) and can be used from a web browser without any special software and with minimal computational requirements on the user end. The capabilities of the module for rapid property screening are demonstrated in case studies with two different methodologies based on datasets containing 3D microstructure information from (i) synthetic generation and (ii) sampling large 3D volumes obtained in experiments.