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. Web2 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 ...
[2112.14966] Deriving Distributive Laws for Graded Linear Type…
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 … circular sawmill blades 56 inch dia
Deriving Distributive Laws for Graded Linear Types DeepAI
Webwith graded modal types. We briefly discuss our implementation involving this new operation for the graded modal language Granule. 1 Introduction Linear logic separates … 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. 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 … diamond grayscale lyrics