Graded modal type granule
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Graded modal type granule
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Webproperties. Granule’s type system combines linear types, indexed types (lightweight dependent types), and graded modal types to enable novel quantitative reasoning. Linear types treat data like a physical resource which must be used once, and then never again [Girard1987;Wadler1990]. For example, the identity function is linearly typed as it ... WebGranule is a functional programming language with a linear type system and fine-grained effects and coeffects via graded modal types. An introduction to Granule can …
WebHere, we propose the umbrella notion of graded modal types, encompassing coeffect types and dual notions of type-based effect reasoning via graded monads. In combination with linear and indexed types, we show that graded modal types provide an expressive type theory for quantitative program reasoning, advancing the reach of type systems to ... Webvarious modal logics. Several research languages, such as Idris 2 [Brady2024] and Agda [Agda-Team 2024], are starting to adopt ideas from this domain, and new systems like Granule [Orchard et al. 2024] are being developed to explore its possibilities. Our concrete motivation for studying graded type systems is a desire to merge Haskell’s current
WebSection2 introduces our core type theory (a subset of Granule’s type sys-tem) based on the linear λ-calculus extended with graded modal types, pairs, and sums. Section3 describes the two core synthesis calculi (subtractive and additive) as augmented inversions of the typing rules, as well as a variant of additive synthesis. WebDec 30, 2024 · We use Granule since it is the main vehicle for the developments here, and introduce some of the key concepts of graded modal types (in a linear context) along the way. 1.1 Motivating Example Consider the situation of projecting the first element of a pair.
WebDec 30, 2024 · The Granule language explores this idea in the context of linear types. In this practical setting, we observe that the presence of graded modal types can introduce an additional impediment...
WebMar 23, 2024 · Graded type theories are an emerging paradigm for augmenting the reasoning power of types with parameterizable, fine-grained analyses of program … philip walderman snoopWebThe recent idea of graded modal types provides a framework for extending type theories with quanti-tative reasoning principles. The Granule language explores this idea in the context of linear types. In this practical setting, when composing programs it is often necessary to distribute algebraic data types over graded modalities, and vice versa. philip wakeham artistWebgraded type systems have been designed which enforce prop-erties based on coeffects, where the inputs that can be passed into a program are the focus. Such systems (with … philip wale wh irelandWebJul 26, 2024 · graded modal types provide an expressive type theory for quantitative program reasoning, advancing the reach of type systems to capture and verify a broader set of program properties. We... philip walker crickWebGraded Modal Types family of modalities where is drawn from a pre-ordered semiring rA r (ℛ,*,1,+,0, ⊑ ) generalises to… generalises to…? 2/13 Granule Linear Types (data as a resource) Graded Modal Types (quantitative reasoning) Indexed Types (precision) 3/13 Demonstration 4/13 The Problem push : forall {a b : Type, s : Semiring, r : s} . try ff14 for freeWebMeeting The Granule Project Meeting on Graded Types 17th June 2024 - School of Computing, University of Kent (+ online) Graded type systems can be understood broadly as imbuing type systems with additional information that follows the underlying structure of a program or proof. philip wakefield mdWebDec 30, 2024 · The Granule language explores this idea in the context of linear types. In this practical setting, we observe that the presence of graded modal types can introduce an additional impediment when programming: when composing programs, it is often necessary to 'distribute' data types over graded modalities, and vice versa. philip walker gloucester city council