Graded modal type granule

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August undefined, 2024

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. 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 …

Deriving Distributive Laws for Graded Linear Types

WebBy clicking download,a status dialog will open to start the export process. The process may takea few minutes but once it finishes a file will be downloadable from your browser. You may continue to browse the DL while the export process is in progress. Webgraded 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 demonstrate this approach via a type system embodied in a … fishermans hat women

(PDF) Quantitative program reasoning with graded modal types

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 ... 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 ... 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 … fishermans haven yzerfontein

Short Paper: Graded Modal Types for Integrity and …

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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 WebMar 23, 2024 · Graded type theories are an emerging paradigm for augmenting the reasoning power of types with parameterizable, fine-grained analyses of program … canadian vs us cabinet makersWeb2 A Brief Granule and Graded Modal Types Primer Granule’s type system is based on the linear λ-calculus augmented with graded modal types [16]. With linear typing as the basis, we cannot write functions that discard or duplicate their inputs as in a standard functional programming language. However, we can introduce non-linearity via graded ... fishermans haven yamba

"Webgraded 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 demonstrate this approach via a type system embodied in a fully-ledged functional language called Granule, exploring various examples. " - Graded modal type granule

Graded modal type granule

Quantitative Program Reasoning with Graded Modal …

WebThe popularity of graded types is growing and their practical implications are being explored in research languages (e.g. Granule), and popular functional languages (e.g. Haskell [3] … WebGerty has some similarity to Granule [46]: both are functional languages with graded types. However, Granule has a linearly typed core and no dependent types (only indexed types), thus has no need for resource tracking at the type level (type indices are not subject to tracking and their syntax is restricted). 2 GrTT: Graded Modal Dependent ...

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WebGraded 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} . 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 when programming: when composing programs, it is often necessary to 'distribute' data types over graded modalities, and vice versa.

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 · 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...

WebTL;DR: This work proposes the umbrella notion of graded modal types, encompassing coeffect types and dual notions of type-based effect reasoning via graded monads, and … 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.

WebTL;DR: This work proposes the umbrella notion of graded modal types, encompassing coeffect types and dual notions of type-based effect reasoning via graded monads, and demonstrates this approach via a type system embodied in a fully-fledged functional language called Granule.

WebThis video was recorded at Code Mesh LDN 19 - http://bit.ly/37xc3NrGet involved in Code Sync's next conference - http://bit.ly/2Mcm4aS---QUANTITATIVE PROGRAM... fishermans head lightWebWe develop a type-directed synthesis tool for Granule, a functional language which combines indexed, linear, and graded modal types [32]. Granule supports various … fisherman shawl collar sweaterWebMar 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 … fisherman shawl neck sweaterWebNov 8, 2024 · Granule combines linear types with lightweight dependent types and graded modal types, providing a rich type system for enforcing fine-grained resource constraints on top of a functional language in the style of Haskell/ML. ... Graded modal type theory; GADTs and indexed types and their interaction with linearity and grading; Examples uses ... canadian voice acting agenciesWebGerty. A minimal, dependently-typed programming language with graded types based on Graded Modal Dependent Type Theory (grtt). You can find more details about this type … canadian wallet companiesWebwith graded modal types. We brieﬂy discuss our implementation involving this new operation for the graded modal language Granule. 1 Introduction Linear logic separates … canadian vs us women datingWebGraded Modal Dependent Type Theory (ESOP 2024) Close. 13. Posted by. Pikelet, Fathom. 11 months ago. Archived. Graded Modal Dependent Type Theory (ESOP 2024) canadian wage inflation calculator