Unifying Theories of Programming with Monads

Gibbons, Jeremy

doi:10.1007/978-3-642-35705-3_2

Cited by 12 publications

(19 citation statements)

References 52 publications

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“…Traditionally, reasoning about pure functional programs is done through equational reasoning. There are several attempts to extend these techniques to the kinds of effectful programs we have presented in this paper [Gibbons 2013;Gibbons and Hinze 2011;Hutton and Fulger 2008].…”

Section: Related Workmentioning

confidence: 99%

A predicate transformer semantics for effects (functional pearl)

Swierstra

Baanen

2019

Proc. ACM Program. Lang.

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Reasoning about programs that use effects can be much harder than reasoning about their pure counterparts. This paper presents a predicate transformer semantics for a variety of effects, including exceptions, state, non-determinism, and general recursion. The predicate transformer semantics gives rise to a refinement relation that can be used to relate a program to its specification, or even calculate effectful programs that are correct by construction.

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Section: Related Workmentioning

confidence: 99%

A predicate transformer semantics for effects (functional pearl)

Swierstra

Baanen

2019

Proc. ACM Program. Lang.

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“…The starting point is the hierarchy of [13]. It needed to be adjusted to fit other papers [1,12,30,31]:…”

Section: Other Monads In the Hierarchy Of Effectsmentioning

confidence: 99%

“…-The proof scripts we obtain are faithful to the original proofs. We benchmark our library against numerous examples of the literature (most examples from [12,13,30,31]) and observe that formal proofs closely match their penciland-paper counterparts and that they can actually be shorter thanks to the terseness of SSReflect's tactic language. We also apply our framework to new examples such as the formalization of the semantics of an imperative language.…”

Section: Introductionmentioning

confidence: 99%

A Hierarchy of Monadic Effects for Program Verification Using Equational Reasoning

Affeldt

Nowak

Saikawa

2019

Lecture Notes in Computer Science

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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 because it is difficult to maintain pencil-and-paper proofs of large examples. We propose a formalization of a hierarchy of effects using monads in the Coq proof assistant that makes equational reasoning practical. Our main idea is to formalize the hierarchy of effects and algebraic laws like it is done when formalizing hierarchy of traditional algebras. We can then take advantage of the sophisticated rewriting capabilities of Coq to achieve concise proofs of programs. We also show how to ensure the consistency of our hierarchy by providing rigorous models. We explain the various techniques we use to formalize a rich hierarchy of effects (with nondeterminism, state, probability, and more), to mechanize numerous examples from the literature, and we furthermore discuss extensions and new applications.

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“…For probabilistic programming, several variants of probability monads have been proposed [16,5,3,16]. What is common to all of them is that the monad makes probabilistic choice points explicit, and sequences probabilistic computations using the monadic bind operator.…”

Section: Embeddings Against All Oddsmentioning

confidence: 99%

“…We briefly describe a "classical" probability monad [16,5,3]. Conceptually, Rand[A] represents a random process yielding an independent random variable at each monadic bind.…”

Section: A Classical Probability Monadmentioning

confidence: 99%

What are the Odds?

Stucki¹,

Amin²,

Jonnalagedda³

et al. 2013

Proceedings of the 4th Workshop on Scala

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Probabilistic programming is a powerful high-level paradigm for probabilistic modeling and inference. We present Odds, a small domain-specific language (DSL) for probabilistic programming, embedded in Scala. Odds provides first-class support for random variables and probabilistic choice, while reusing Scala's abstraction and modularity facilities for composing probabilistic computations and for executing deterministic program parts. Odds accurately represents possibly dependent random variables using a probability monad that models committed choice. This monadic representation of probabilistic models can be combined with a range of inference procedures. We present engines for exact inference, rejection sampling and importance sampling with look-ahead, but other types of solvers are conceivable as well. We evaluate Odds on several non-trivial probabilistic programs from the literature and we demonstrate how the basic probabilistic primitives can be used to build higher-level abstractions, such as rule-based logic programming facilities, using advanced Scala features.

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Unifying Theories of Programming with Monads

Cited by 12 publications

References 52 publications

A predicate transformer semantics for effects (functional pearl)

A predicate transformer semantics for effects (functional pearl)

A Hierarchy of Monadic Effects for Program Verification Using Equational Reasoning

What are the Odds?

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