Graded modal type granule
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 ... WebDec 30, 2024 · The recent notion of graded modal types provides a framework for extending type theories with fine-grained data-flow reasoning. The Granule language …
Graded modal type granule
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WebMeeting 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. Webgraded 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 …
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WebMar 23, 2024 · Graded type theories are an emerging paradigm for augmenting the reasoning power of types with parameterizable, fine-grained analyses of program … WebDec 7, 2024 · Basic concepts. By default, the teacher selects numerical grades in Moodle from a range like 0–100. When advanced grading methods are enabled, the grade …
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.
WebMar 24, 2024 · This paper shows how graded modal types can be leveraged alongside session types to enable various non-linear concurrency behaviours to be re-introduced in a precise manner in a type system with a linear basis. The ideas here are demonstrated using Granule, a functional programming language with linear, indexed, and graded modal … incitec mackayWebWe develop a type-directed synthesis tool for Granule, a functional language which combines indexed, linear, and graded modal types [32]. Granule supports various … incitec pasture boosterWebWe would like to show you a description here but the site won’t allow us. incorporate non profit ontarioWebGraded Modal Dependent Type Theory (Grtt for short), which equips a dependent type theory with a general, parameterizable analysis of the flow of data, both in and between … incitec newsWebvarious 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 incorporate non profit in pennsylvaniaWebGraded 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} . incorporate now incWebHere, 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 ... incorporate number