Graded modal type granule
WebNov 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 ... 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} .
Graded modal type granule
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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. 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 …
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... 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 ...
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] … 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 …
WebGraded 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 …
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 … import .xyz files into houdiniWebGerty 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 ... import xyz from ol/source/xyzWebMeeting 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. import xtoolkitWebDec 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 … import yougetWeb2 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 ... importyingwenWebMar 23, 2024 · Graded type theories are an emerging paradigm for augmenting the reasoning power of types with parameterizable, fine-grained analyses of program … importyourcar.co.nz reviewWebSection2 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. import yeti for uk