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One can perform equational reasoning about computational effects with a purely functional programming language thanks to monads. Even though equational reasoning for effectful programs is desirable, it is not yet mainstream. This is partly…

Logic in Computer Science · Computer Science 2025-01-15 Reynald Affeldt , Jacques Garrigue , Takafumi Saikawa

Monads provide a simple and concise interface to user-defined computational effects in functional programming languages. This enables equational reasoning about effects, abstraction over monadic interfaces and the development of monad…

Programming Languages · Computer Science 2025-05-05 Yuchen Jiang , Runze Xue , Max S. New

This paper describes a categorical interpretation of the Wolfram Language and introduces a simple implementation of monadic types and the "do" notation. The monadic style of programming combined with the many built in functions of the…

Programming Languages · Computer Science 2020-05-20 Kacper Topolnicki

We describe a denotational semantics for an abstract effect system for a higher-order, shared-variable concurrent programming language. We prove the soundness of a number of general effect-based program equivalences, including a…

Programming Languages · Computer Science 2015-10-12 Nick Benton , Martin Hofmann , Vivek Nigam

Sequential effect systems are a class of effect system that exploits information about program order, rather than discarding it as traditional commutative effect systems do. This extra expressive power allows effect systems to reason about…

Programming Languages · Computer Science 2020-05-18 Colin S. Gordon

In this paper, a monad-based denotational model is introduced and shown adequate for the Proto-Quipper family of calculi, themselves being idealized versions of the Quipper programming language. The use of a monadic approach allows us to…

Programming Languages · Computer Science 2025-12-01 Ken Sakayori , Andrea Colledan , Ugo Dal Lago

Free monads (and their variants) have become a popular general-purpose tool for representing the semantics of effectful programs in proof assistants. These data structures support the compositional definition of semantics parameterized by…

Programming Languages · Computer Science 2022-07-28 Yao Li , Stephanie Weirich

Side effects are a core part of practical programming. However, they are often hard to reason about, particularly in a concurrent setting. We propose a foundation for reasoning about concurrent side effects using sessions. Primarily, we…

Programming Languages · Computer Science 2016-02-12 Dominic Orchard , Nobuko Yoshida

We present a novel programming language design that attempts to combine the clarity and safety of high-level functional languages with the efficiency and parallelism of low-level numerical languages. We treat arrays as eagerly-memoized…

Monads are a popular tool for the working functional programmer to structure effectful computations. This paper presents polymonads, a generalization of monads. Polymonads give the familiar monadic bind the more general type forall a,b. L a…

Programming Languages · Computer Science 2014-06-10 Michael Hicks , Gavin Bierman , Nataliya Guts , Daan Leijen , Nikhil Swamy

Pressed by the difficulty of writing asynchronous, event-driven code, mainstream languages have recently been building in support for a variety of advanced control-flow features. Meanwhile, experimental language designs have suggested…

Programming Languages · Computer Science 2020-10-20 Yizhou Zhang , Guido Salvaneschi , Andrew C. Myers

Algebraic effects & handlers are a modular approach for modeling side-effects in functional programming. Their syntax is defined in terms of a signature of effectful operations, encoded as a functor, that are plugged into the free monad;…

Programming Languages · Computer Science 2023-02-06 Birthe van den Berg , Tom Schrijvers

Type systems designed for information-flow control commonly use a program-counter label to track the sensitivity of the context and rule out data leakage arising from effectful computation in a sensitive context. Currently, type-system…

Programming Languages · Computer Science 2021-01-14 Andrew K. Hirsch , Ethan Cecchetti

Combining local exceptions and first class continuations leads to programs with complex control flow, as well as the possibility of expressing powerful constructs such as resumable exceptions. We describe and compare games models for a…

Logic in Computer Science · Computer Science 2013-09-06 James Laird

The original purpose of component-based development was to provide techniques to master complex software, through composition, reuse and parametrisation. However, such systems are rapidly moving towards a level in which software becomes…

Logic in Computer Science · Computer Science 2016-08-02 Renato Neves , Luis S. Barbosa , Dirk Hofmann , Manuel A. Martins

This thesis revolves around an area of computer science called "semantics". We work with operational semantics, equational theories, and denotational semantics. The first contribution of this thesis is a study of the commutativity of…

Logic in Computer Science · Computer Science 2024-06-12 Louis Lemonnier

We show how to smoothly incorporate in the object-oriented paradigm constructs to raise, compose, and handle effects in an arbitrary monad. The underlying pure calculus is meant to be a representative of the last generation of OO languages,…

Programming Languages · Computer Science 2025-04-23 Francesco Dagnino , Paola Giannini , Elena Zucca

Monads govern computational side-effects in programming semantics. They can be combined in a ''bottom-up'' way to handle several instances of such effects. Indexed monads and graded monads do this in a modular way. Here, instead, we equip…

Logic in Computer Science · Computer Science 2021-08-05 Carmen Constantin , Nuiok Dicaire , Chris Heunen

Effect handlers allow programmers to model and compose computational effects modularly. Effect systems statically guarantee that all effects are handled. Several recent practical effect systems are based on either row polymorphism or…

Programming Languages · Computer Science 2025-12-16 Wenhao Tang , Sam Lindley

Graded monads refine traditional monads using effect annotations in order to describe quantitatively the computational effects that a program can generate. They have been successfully applied to a variety of formal systems for reasoning…

Logic in Computer Science · Computer Science 2026-01-22 Satoshi Kura , Marco Gaboardi , Taro Sekiyama , Hiroshi Unno
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