Reaching for the Star: Tale of a Monad in Coq

Monadic programming is an essential component in the toolbox of functional programmers. For the pure and total programmers, who sometimes navigate the waters of certified programming in type theory, it is the only means to concisely implement the imperative traits of certain algorithms. Monads open up a portal to the imperative world, all that from the comfort of the functional world. The trend towards certified programming within type theory begs the question of reasoning about such programs. Effectful programs being encoded as pure programs in the host type theory, we can readily manipulate these objects through their encoding. In this article, we pursue the idea, popularized by Maillard [Kenji Maillard, 2019], that every monad deserves a dedicated program logic and that, consequently, a proof over a monadic program ought to take place within a Floyd-Hoare logic built for the occasion. We illustrate this vision through a case study on the SimplExpr module of CompCert [Xavier Leroy, 2009], using a separation logic tailored to reason about the freshness of a monadic gensym

A Direct-Style Effect Notation for Sequential and Parallel Programs

Modeling sequential and parallel composition of effectful computations has been investigated in a variety of languages for a long time. In particular, the popular do-notation provides a lightweight effect embedding for any instance of a monad. Idiom bracket notation, on the other hand, provides an embedding for applicatives. First, while monads force effects to be executed sequentially, ignoring potential for parallelism, applicatives do not support sequential effects. Composing sequential with parallel effects remains an open problem. This is even more of an issue as real programs consist of a combination of both sequential and parallel segments. Second, common notations do not support invoking effects in direct-style, instead forcing a rigid structure upon the code. In this paper, we propose a mixed applicative/monadic notation that retains parallelism where possible, but allows sequentiality where necessary. We leverage a direct-style notation where sequentiality or parallelism is derived from the structure of the code. We provide a mechanisation of our effectful language in Coq and prove that our compilation approach retains the parallelism of the source program

Idris 2 : Quantitative Type Theory in practice

Funding: This work was funded by EPSRC grant EP/T007265/1.Dependent types allow us to express precisely what a function is intended to do. Recent work on Quantitative Type Theory (QTT) extends dependent type systems with linearity, also allowing precision in expressing when a function can run. This is promising, because it suggests the ability to design and reason about resource usage protocols, such as we might find in distributed and concurrent programming, where the state of a communication channel changes throughout program execution. As yet, however, there has not been a full-scale programming language with which to experiment with these ideas. Idris 2 is a new version of the dependently typed language Idris, with a new core language based on QTT, supporting linear and dependent types. In this paper, we introduce Idris 2, and describe how QTT has influenced its design. We give examples of the benefits of QTT in practice including: expressing which data is erased at run time, at the type level; and, resource tracking in the type system leading to type-safe concurrent programming with session types.Publisher PD

A Typing Discipline for Hardware Interfaces

Modern Systems-on-a-Chip (SoC) are constructed by composition of IP (Intellectual Property) Cores with the communication between these IP Cores being governed by well described interaction protocols. However, there is a disconnect between the machine readable specification of these protocols and the verification of their implementation in known hardware description languages. Although tools can be written to address such separation of concerns, the tooling is often hand written and used to check hardware designs a posteriori. We have developed a dependent type-system and proof-of-concept modelling language to reason about the physical structure of hardware interfaces using user provided descriptions. Our type-system provides correct-by-construction guarantees that the interfaces on an IP Core will be well-typed if they adhere to a specified standard

A Framework for Resource Dependent EDSLs in a Dependently Typed Language (Pearl)

Idris' Effects library demonstrates how to embed resource dependent algebraic effect handlers into a dependently typed host language, providing run-time and compile-time based reasoning on type-level resources. Building upon this work, Resources is a framework for realising Embedded Domain Specific Languages (EDSLs) with type systems that contain domain specific substructural properties. Differing from Effects, Resources allows a language’s substructural properties to be encoded within type-level resources that are associated with language variables. Such an association allows for multiple effect instances to be reasoned about autonomically and without explicit type-level declaration. Type-level predicates are used as proof that the language’s substructural properties hold. Several exemplar EDSLs are presented that illustrates our framework’s operation and how dependent types provide correctness-by-construction guarantees that substructural properties of written programs hold