Contextual modal types for algebraic effects and handlers

Programming languages with algebraic effects often track the computations’ effects using type-and-effect systems. In this paper, we propose to view an algebraic effect theory of a computation as a variable context; consequently, we propose to track algebraic effects of a computation with contextual modal types . We develop ECMTT, a novel calculus which tracks algebraic effects by a contextualized variant of the modal □ (necessity) operator, that it inherits from Contextual Modal Type Theory (CMTT). Whereas type-and-effect systems add effect annotations on top of a prior programming language, the effect annotations in ECMTT are inherent to the language, as they are managed by programming constructs corresponding to the logical introduction and elimination forms for the □ modality. Thus, the type-and-effect system of ECMTT is actually just a type system. Our design obtains the properties of local soundness and completeness, and determines the operational semantics solely by β-reduction, as customary in other logic-based calculi. In this view, effect handlers arise naturally as a witness that one context (i.e., algebraic theory) can be reached from another, generalizing explicit substitutions from CMTT. To the best of our knowledge, ECMTT is the first system to relate algebraic effects to modal types. We also see it as a step towards providing a correspondence in the style of Curry and Howard that may transfer a number of results from the fields of modal logic and modal type theory to that of algebraic effects.

Resourceful Program Synthesis from Graded Linear Types

Linear types provide a way to constrain programs by specifying that some values must be used exactly once. Recent work on graded modal types augments and refines this notion, enabling fine-grained, quantitative specification of data use in programs. The information provided by graded modal types appears to be useful for type-directed program synthesis, where these additional constraints can be used to prune the search space of candidate programs. We explore one of the major implementation challenges of a synthesis algorithm in this setting: how does the synthesis algorithm efficiently ensure that resource constraints are satisfied throughout program generation? We provide two solutions to this resource management problem, adapting Hodas and Miller’s input-output model of linear context management to a graded modal linear type theory. We evaluate the performance of both approaches via their implementation as a program synthesis tool for the programming language Granule, which provides linear and graded modal typing.

The Informativity of Publicistic Texts of the XVIII Century in N. I. Novikov's Journals

The article deals with the stylistic specificity of journal text of the second half of the XVIII century, published by N. I. Novikov. The author identifies linguistic and compositional features in the comparison with the modern style model of publicism. The author analysed the dominant features of the texts: dialogicality, educational function, and the synthesis of pedagogical and publicistic discourse. The study focuses on the stylistic uniqueness of the titles and emphasizes that the specificity of N. I. Novikov’s journalistic language was determined by his linguistic personality, as well as by the target settings of informing the reader. The research method included analyses of thematic, compositional, factual, and modal types of information content of the media text. A semantic and stylistic analysis of headlines made it possible to define the following types: plot, nominative-ascertaining, genre, spatial, precedent, and address headlines, which had an informative function and penetrating boundaries. Analysing the expressive resources of the texts, the author observed the specifics and typical use of Novikov’s idiostyle. The strengthening compositional element of the analysed texts is the image of a real individual author, implemented in various textual images and actualised in the context of the stylistic effect of dialogicality. The field of application of the research results includes stylistics and rhetoric.

An insider's look at LF type reconstruction: everything you (n)ever wanted to know

Although type reconstruction for dependently typed languages is common in practical systems, it is still ill-understood. Detailed descriptions of the issues around it are hard to find and formal descriptions together with correctness proofs are non-existing. In this paper, we discuss a one-pass type reconstruction for objects in the logical framework LF, describe formally the type reconstruction process using the framework of contextual modal types, and prove correctness of type reconstruction. Since type reconstruction will find most general types and may leave free variables, we in addition describe abstraction which will return a closed object where all free variables are bound at the outside. We also implemented our algorithms as part of the Beluga language, and the performance of our type reconstruction algorithm is comparable to type reconstruction in existing systems such as the logical framework Twelf.

An investigation of the verbal abilities of children with imaginary companions

The purpose of this study was to investigate the language use of 40 children with imaginary companions (IC) and 40 children without imaginary companions (NIC) across two age levels: a younger group aged 4;0–5;11 and an older group aged 6;0–7;11. The study investigated the language of these children by examining their use of adverbial and relative clauses, complement clauses, co-ordinating conjunctions and modal types. The findings indicated that, compared with NICs, ICs used a significantly greater number of adverbial clauses, relative clauses, and and, with their use of but approaching significance. Overall, the results were interpreted as indicating that ICs use more mature language, and this demonstrates enhanced social-cognitive skills. It was concluded that the presence of imaginary companions is positively associated with language use and discourse competency of children.