Layer by layer - Combining Monads

We develop a method to incrementally construct programming languages. Our approach is categorical: each layer of the language is described as a monad. Our method either (i) concretely builds a distributive law between two monads, i.e. layers of the language, which then provides a monad structure to the composition of layers, or (ii) identifies precisely the algebraic obstacles to the existence of a distributive law and gives a best approximant language. The running example will involve three layers: a basic imperative language enriched first by adding non-determinism and then probabilistic choice. The first extension works seamlessly, but the second encounters an obstacle, which results in a best approximant language structurally very similar to the probabilistic network specification language ProbNetKAT

Quantifiers on languages and codensity monads

This paper contributes to the techniques of topo-algebraic recognition for languages beyond the regular setting as they relate to logic on words. In particular, we provide a general construction on recognisers corresponding to adding one layer of various kinds of quantifiers and prove a corresponding Reutenauer-type theorem. Our main tools are codensity monads and duality theory. Our construction hinges on a measure-theoretic characterisation of the profinite monad of the free S-semimodule monad for finite and commutative semirings S, which generalises our earlier insight that the Vietoris monad on Boolean spaces is the codensity monad of the finite powerset functor.Comment: 30 pages. Presentation improved and details of several proofs added. The main results are unchange

Taming aspects with monads and membranes

International audienceWhen a software system is developed using several aspects, special care must be taken to ensure that the resulting behavior is correct. This is known as the aspect interference problem, and existing approaches essentially aim to detect whether a system exhibits problematic interferences of aspects. In this paper we describe how to control aspect interference by construction by relying on the type system. More precisely, we combine a monadic embedding of the pointcut/advice model in Haskell with the notion of membranes for aspect-oriented programming. Aspects must explicitly declare the side effectsa nd the context they can act upon. Allowed patterns of control flow interference are declared at the membrane level and statically enforced. Finally, computational interference between aspects is controlled by the membrane topology. To combine independent and reusable aspects and monadic components into a program specification we use monad views, a recent technique for conveniently handling the monadic stack

The modern landscape of managing effects for the working programmer

The management of side effects is a crucial aspect of modern programming, especially in concurrent and distributed systems. This thesis analyses different approaches for managing side effects in programming languages, specifically focusing on unrestricted side effects, monads, and algebraic effects and handlers. Unrestricted side effects, used in mainstream imperative programming languages, can make programs difficult to reason about. Monads offer a solution to this problem by describing side effects in a composable and referentially transparent way but many find them cumbersome to use. Algebraic effects and handlers can address some of the shortcomings of monads by providing a way to model effects in more modular and flexible way. The thesis discusses the advantages and disadvantages of each of these approaches and compares them based on factors such as expressiveness, safety, and constraints they place on how programs must be implemented. The thesis focuses on ZIO, a Scala library for concurrent and asynchronous programming, which revolves around a ZIO monad with three type parameters. With those three parameters ZIO can encode the majority of practically useful effects in a single monad. ZIO takes inspiration from algebraic effects, combining them with monadic effects. The library provides a range of features, such as declarative concurrency, error handling, and resource management. The thesis presents examples of using ZIO to manage side effects in practical scenarios, highlighting its strengths over other approaches. The applicability of ZIO is evaluated by implementing a server side application using ZIO, and analyzing observations from the development process

Tracing monadic computations and representing effects

In functional programming, monads are supposed to encapsulate computations, effectfully producing the final result, but keeping to themselves the means of acquiring it. For various reasons, we sometimes want to reveal the internals of a computation. To make that possible, in this paper we introduce monad transformers that add the ability to automatically accumulate observations about the course of execution as an effect. We discover that if we treat the resulting trace as the actual result of the computation, we can find new functionality in existing monads, notably when working with non-terminating computations.Comment: In Proceedings MSFP 2012, arXiv:1202.240

Effective Aspects: A Typed Monadic Embedding of Pointcuts and Advice

International audienceAspect-oriented programming(AOP) aims to enhance modularity and reusability in software systems by offering an abstraction mechanism to deal with crosscutting concerns. However, in most general-purpose aspect languages aspects have almost unrestricted power, eventually conflicting with these goals. In this work we present Effective Aspects: a novel approach to embed the point- cut/advice model of AOP in a statically-typed functional programming language like Haskell. Our work extends EffectiveAdvice, by Oliveira, Schrijvers and Cook; which lacks quantification, and explores how to exploit the monadic setting in the full pointcut/advice model. Type soundness is guaranteed by exploiting the underlying type system, in particular phantom types and a new anti-unification type class. Aspects are first-class, can be deployed dynamically, and the pointcut language is extensible, therefore combining the flexibility of dynamically-typed aspect languages with the guarantees of a static type system. Monads enables us to directly reason about computational effects both in aspects and base programs using traditional monadic techniques. Using this we extend Aldrich's notion of Open Modules with effects, and also with protected pointcut interfaces to external advising. These restrictions are enforced statically using the type system. Also, we adapt the techniques of EffectiveAdvice to reason about and enforce control flow properties. Moreover, we show how to control effect interference us- ing the parametricity-based approach of EffectiveAdvice. However this approach falls short when dealing with interference between multiple aspects. We propose a different approach using monad views, a recently developed technique for han- dling the monad stack. Finally, we exploit the properties of our monadic weaver to enable the modular construction of new semantics for aspect scoping and weaving. These semantics also benefit fully from the monadic reasoning mechanisms present in the language. This work brings type-based reasoning about effects for the first time in the pointcut/advice model, in a framework that is both expressive and extensible; thus allowing development of robust aspect-oriented systems as well as being a useful research tool for experimenting with new aspect semantics

Preservation of Equations by Monoidal Monads

If a monad T is monoidal, then operations on a set X can be lifted canonically to operations on TX. In this paper we study structural properties under which T preserves equations between those operations. It has already been shown that any monoidal monad preserves linear equations; affine monads preserve drop equations (where some variable appears only on one side, such as x? y = y) and relevant monads preserve dup equations (where some variable is duplicated, such as x ? x = x). We start the paper by showing a converse: if the monad at hand preserves a drop equation, then it must be affine. From this, we show that the problem whether a given (drop) equation is preserved is undecidable. A converse for relevance turns out to be more subtle: preservation of certain dup equations implies a weaker notion which we call n-relevance. Finally, we identify a subclass of equations such that their preservation is equivalent to relevance