scholarly journals Quantitative program reasoning with graded modal types

2019 ◽  
Vol 3 (ICFP) ◽  
pp. 1-30 ◽  
Author(s):  
Dominic Orchard ◽  
Vilem-Benjamin Liepelt ◽  
Harley Eades III
Keyword(s):  
Modal Types

Language implementation for Quantitative Program Reasoning with Graded Modal Types

2019 ◽  
Author(s):  
Dominic Orchard ◽  
Vilem-Benjamin Liepelt ◽  
Harley Eades III
Keyword(s):  
Language Implementation ◽  
Modal Types

Judgmental subtyping systems with intersection types and modal types

2013 ◽  
Vol 50 (7-8) ◽  
pp. 359-380
Author(s):  
Jeongbong Seo ◽  
Sungwoo Park
Keyword(s):  
Intersection Types ◽  
Modal Types

scholarly journals Contextual modal types for algebraic effects and handlers

2021 ◽  
Vol 5 (ICFP) ◽  
pp. 1-29
Author(s):  
Nikita Zyuzin ◽  
Aleksandar Nanevski
Keyword(s):  
Programming Languages ◽  
Type Theory ◽  
Operational Semantics ◽  
Algebraic Theory ◽  
Type System ◽  
Effect Theory ◽  
Explicit Substitutions ◽  
Type And Effect Systems ◽  
Modal Type ◽  
Modal Types

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.

An investigation of the verbal abilities of children with imaginary companions

2002 ◽  
Vol 22 (3) ◽  
pp. 249-264 ◽  
Author(s):  
Paula Bouldin ◽  
Edith L. Bavin ◽  
Chris Pratt
Keyword(s):  
Cognitive Skills ◽  
Relative Clauses ◽  
Language Use ◽  
Social Cognitive ◽  
Imaginary Companions ◽  
Verbal Abilities ◽  
Complement Clauses ◽  
Adverbial Clauses ◽  
Modal Types

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.

scholarly journals Resourceful Program Synthesis from Graded Linear Types

2021 ◽  
pp. 151-170
Author(s):  
Jack Hughes ◽  
Dominic Orchard
Keyword(s):  
Resource Constraints ◽  
Program Synthesis ◽  
Search Space ◽  
Linear Type ◽  
Synthesis Algorithm ◽  
Implementation Challenges ◽  
Fine Grained ◽  
Linear Types ◽  
Additional Constraints ◽  
Modal Types

AbstractLinear 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.

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

2012 ◽  
Vol 23 (1) ◽  
pp. 1-37 ◽  
Author(s):  
BRIGITTE PIENTKA
Keyword(s):  
Reconstruction Algorithm ◽  
Logical Framework ◽  
Reconstruction Process ◽  
Correctness Proofs ◽  
Free Variables ◽  
Type Reconstruction ◽  
Typed Languages ◽  
Modal Types

AbstractAlthough 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.

Modal types as staging specifications for run-time code generation

1998 ◽  
Vol 30 (3es) ◽  
pp. 8 ◽  
Author(s):  
Philip Wickline ◽  
Peter Lee ◽  
Frank Pfenning ◽  
Rowan Davies
Keyword(s):  
Code Generation ◽  
Time Code ◽  
Run Time ◽  
Modal Types

Modal Types and Ut, Re, Mi Tonalities: Tonal Coherence in Sacred Vocal Polyphony from about 1500

1992 ◽  
Vol 45 (3) ◽  
pp. 428-467 ◽  
Author(s):  
Cristle Collins Judd
Keyword(s):  
Modal Theory ◽  
Musical Tradition ◽  
Technical Vocabulary ◽  
Tonal Coherence ◽  
Analytical Approaches ◽  
Modal Types

An evaluation of Pietro Aron's understanding of "mode in polyphony" (Trattato della Natura et Cognitione di tutti gli tuoni [1525]) coupled with an analytical examination of Josquin's motet oeuvre leads to a new theory of tonal coherence in sacred vocal polyphony from about 1500. This theory provides a designation for, and identifies the markers of, the tonalities represented in the motets of Josquin; it is based on a nomenclature derived from the technical vocabulary of modal theory and the exigencies of a musical tradition rooted in plainchant, hexachordal manipulation of the gamut, and counterpoint. Three main tonal categories are defined and identified by hexachordal function of final as Ut, Re, and Mi tonalities. Comments by Glarean (Dodecachordon [1547]) support the essentially practical basis of these tonal designations. Each of these tonalities consists of, and is defined by, a distinct collection of "modal types," melodic-contrapuntal paradigms of tonal coherence that are identifiable in a variety of structural guises, from simple contrapuntal contexts to more abstract frameworks. Analytical examples from Josquin's motets illustrate procedural similarities in works belonging to different modal categories and structural distinctions within the same category, as well as demonstrating why diverse analytical approaches have seemed successful with certain works but inappropriate to others.

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