Cyclic Datatypes modulo Bisimulation based on Second-Order Algebraic Theories

Cyclic data structures, such as cyclic lists, in functional programming are tricky to handle because of their cyclicity. This paper presents an investigation of categorical, algebraic, and computational foundations of cyclic datatypes. Our framework of cyclic datatypes is based on second-order algebraic theories of Fiore et al., which give a uniform setting for syntax, types, and computation rules for describing and reasoning about cyclic datatypes. We extract the "fold" computation rules from the categorical semantics based on iteration categories of Bloom and Esik. Thereby, the rules are correct by construction. We prove strong normalisation using the General Schema criterion for second-order computation rules. Rather than the fixed point law, we particularly choose Bekic law for computation, which is a key to obtaining strong normalisation. We also prove the property of "Church-Rosser modulo bisimulation" for the computation rules. Combining these results, we have a remarkable decidability result of the equational theory of cyclic data and fold.Comment: 38 page

What Does Aspect-Oriented Programming Mean for Functional Programmers?

Aspect-Oriented Programming (AOP) aims at modularising crosscutting concerns that show up in software. The success of AOP has been almost viral and nearly all areas in Software Engineering and Programming Languages have become "infected" by the AOP bug in one way or another. Interestingly the functional programming community (and, in particular, the pure functional programming community) seems to be resistant to the pandemic. The goal of this paper is to debate the possible causes of the functional programming community's resistance and to raise awareness and interest by showcasing the benefits that could be gained from having a functional AOP language. At the same time, we identify the main challenges and explore the possible design-space

Towards a Convenient Category of Topological Domains

We propose a category of topological spaces that promises to be convenient for the purposes of domain theory as a mathematical theory for modelling computation. Our notion of convenience presupposes the usual properties of domain theory, e.g. modelling the basic type constructors, fixed points, recursive types, etc. In addition, we seek to model parametric polymorphism, and also to provide a flexible toolkit for modelling computational effects as free algebras for algebraic theories. Our convenient category is obtained as an application of recent work on the remarkable closure conditions of the category of quotients of countably-based topological spaces. Its convenience is a consequence of a connection with realizability models

A Convenient Category of Domains

We motivate and define a category of "topological domains", whose objects are certain topological spaces, generalising the usual $omega$-continuous dcppos of domain theory. Our category supports all the standard constructions of domain theory, including the solution of recursive domain equations. It also supports the construction of free algebras for (in)equational theories, provides a model of parametric polymorphism, and can be used as the basis for a theory of computability. This answers a question of Gordon Plotkin, who asked whether it was possible to construct a category of domains combining such properties

Automatic categorization of diverse experimental information in the bioscience literature

Background: Curation of information from bioscience literature into biological knowledge databases is a crucial way of capturing experimental information in a computable form. During the biocuration process, a critical first step is to identify from all published literature the papers that contain results for a specific data type the curator is interested in annotating. This step normally requires curators to manually examine many papers to ascertain which few contain information of interest and thus, is usually time consuming. We developed an automatic method for identifying papers containing these curation data types among a large pool of published scientific papers based on the machine learning method Support Vector Machine (SVM). This classification system is completely automatic and can be readily applied to diverse experimental data types. It has been in use in production for automatic categorization of 10 different experimental datatypes in the biocuration process at WormBase for the past two years and it is in the process of being adopted in the biocuration process at FlyBase and the Saccharomyces Genome Database (SGD). We anticipate that this method can be readily adopted by various databases in the biocuration community and thereby greatly reducing time spent on an otherwise laborious and demanding task. We also developed a simple, readily automated procedure to utilize training papers of similar data types from different bodies of literature such as C. elegans and D. melanogaster to identify papers with any of these data types for a single database. This approach has great significance because for some data types, especially those of low occurrence, a single corpus often does not have enough training papers to achieve satisfactory performance. Results: We successfully tested the method on ten data types from WormBase, fifteen data types from FlyBase and three data types from Mouse Genomics Informatics (MGI). It is being used in the curation work flow at WormBase for automatic association of newly published papers with ten data types including RNAi, antibody, phenotype, gene regulation, mutant allele sequence, gene expression, gene product interaction, overexpression phenotype, gene interaction, and gene structure correction. Conclusions: Our methods are applicable to a variety of data types with training set containing several hundreds to a few thousand documents. It is completely automatic and, thus can be readily incorporated to different workflow at different literature-based databases. We believe that the work presented here can contribute greatly to the tremendous task of automating the important yet labor-intensive biocuration effort

Applied Type System: An Approach to Practical Programming with Theorem-Proving

The framework Pure Type System (PTS) offers a simple and general approach to designing and formalizing type systems. However, in the presence of dependent types, there often exist certain acute problems that make it difficult for PTS to directly accommodate many common realistic programming features such as general recursion, recursive types, effects (e.g., exceptions, references, input/output), etc. In this paper, Applied Type System (ATS) is presented as a framework for designing and formalizing type systems in support of practical programming with advanced types (including dependent types). In particular, it is demonstrated that ATS can readily accommodate a paradigm referred to as programming with theorem-proving (PwTP) in which programs and proofs are constructed in a syntactically intertwined manner, yielding a practical approach to internalizing constraint-solving needed during type-checking. The key salient feature of ATS lies in a complete separation between statics, where types are formed and reasoned about, and dynamics, where programs are constructed and evaluated. With this separation, it is no longer possible for a program to occur in a type as is otherwise allowed in PTS. The paper contains not only a formal development of ATS but also some examples taken from ats-lang.org, a programming language with a type system rooted in ATS, in support of employing ATS as a framework to formulate advanced type systems for practical programming