Comprehending monads

Wadler, Philip

doi:10.1145/91556.91592

Cited by 468 publications

(316 citation statements)

References 14 publications

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“…Popularised by [28], monads became a kind of standard means to incorporate stateful computations into a purely functional world.…”

Section: Formal Presentations Of Automata: the Monadic Approachmentioning

confidence: 99%

Monadic Sequence Testing and Explicit Test-Refinements

Brucker

Wolff²

2016

Tests and Proofs

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We present an abstract framework for sequence testing that is implemented in Isabelle/HOL-TestGen. Our framework is based on the theory of state-exception monads, explicitly modelled in HOL, and can cope with typed input and output, interleaving executions including abort, and synchronisation. The framework is particularly geared towards symbolic execution and has proven effective in several large case-studies involving system models based on large (or infinite) state. On this basis, we rephrase the concept of test-refinements for inclusion, deadlock and IOCO-like tests, together with a formal theory of its relation to traditional, IO-automata based notions.

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“…Popularised by [28], monads became a kind of standard means to incorporate stateful computations into a purely functional world.…”

Section: Formal Presentations Of Automata: the Monadic Approachmentioning

confidence: 99%

Monadic Sequence Testing and Explicit Test-Refinements

Brucker

Wolff²

2016

Tests and Proofs

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“…In Isabelle/HOL, refinement is supported by the Refinement Framework [15,16] and the Isabelle Collection Framework [14,13]. The former framework implements a refinement calculus [3] based on a nondeterminism monad [24], and the latter one provides a large collection of verified efficient data structures. Both frameworks come with tool support to simplify their usage for algorithm development and to automate canonical tasks such as verification condition generation.…”

Section: Refinement Frameworkmentioning

confidence: 99%

A Fully Verified Executable LTL Model Checker

Esparza

Lammich

Neumann

et al. 2013

Computer Aided Verification

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Abstract. We present an LTL model checker whose code has been completely verified using the Isabelle theorem prover. The checker consists of over 4000 lines of ML code. The code is produced using recent Isabelle technology called the Refinement Framework, which allows us to split its correctness proof into (1) the proof of an abstract version of the checker, consisting of a few hundred lines of "formalized pseudocode", and (2) a verified refinement step in which mathematical sets and other abstract structures are replaced by implementations of efficient structures like red-black trees and functional arrays. This leads to a checker that, while still slower than unverified checkers, can already be used as a trusted reference implementation against which advanced implementations can be tested. We report on the structure of the checker, the development process, and some experiments on standard benchmarks.

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“…In the above code, we exploit the fact that Maybe is monadic [12,16,17]. In particular, we utilise the basic operations of the Maybe monad, namely return, which converts a pure value into an impure result, (>>=), used to sequence computations, mzero, corresponding to failure, and mplus, for sequential choice.…”

Section: Adding a New Effectmentioning

confidence: 99%

Towards Modular Compilers for Effects

Day

Hutton

2012

Lecture Notes in Computer Science

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Abstract. Compilers are traditionally factorised into a number of separate phases, such as parsing, type checking, code generation, etc. However, there is another potential factorisation that has received comparatively little attention: the treatment of separate language features, such as mutable state, input/output, exceptions, concurrency and so forth. In this article we focus on the problem of modular compilation, in which the aim is to develop compilers for separate language features independently, which can then be combined as required. We summarise our progress to date, issues that have arisen, and further work.

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Comprehending monads

Cited by 468 publications

References 14 publications

Monadic Sequence Testing and Explicit Test-Refinements

Monadic Sequence Testing and Explicit Test-Refinements

A Fully Verified Executable LTL Model Checker

Towards Modular Compilers for Effects

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