Reasoning with the HERMIT: tool support for equational reasoning on GHC core programs

FarmerAndrew,; SculthorpeNeil,; GillAndy,

doi:10.1145/2887747.2804303

Cited by 9 publications

(5 citation statements)

References 33 publications

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“…However, it is possible that much of the process could be automated to derive compilers in a mechanical manner from specifications of their correctness. Mechanisation options could range from a special-purpose library to assist in the process of equational reasoning [Mu et al 2009], to providing support for the calculation process in a general-purpose equational reasoning system [Farmer et al 2015], to a system that is customdesigned for our particular calculational approach [Handley and Hutton 2018].…”

Section: Conclusion and Further Workmentioning

confidence: 99%

Calculating dependently-typed compilers (functional pearl)

Pickard

Hutton

2021

Proc. ACM Program. Lang.

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Compilers are difficult to write, and difficult to get right. Bahr and Hutton recently developed a new technique for calculating compilers directly from specifications of their correctness, which ensures that the resulting compilers are correct-by-construction. To date, however, this technique has only been applicable to source languages that are untyped. In this article, we show that moving to a dependently-typed setting allows us to naturally support typed source languages, ensure that all compilation components are type-safe, and make the resulting calculations easier to mechanically check using a proof assistant.

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Section: Conclusion and Further Workmentioning

confidence: 99%

Calculating dependently-typed compilers (functional pearl)

Pickard

Hutton

2021

Proc. ACM Program. Lang.

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“…HERMIT [7] is a system for mechanising equational reasoning about Haskell programs. Properties are written as GHC rewrite rules in the Haskell source code and proven either interactively in the HERMIT shell or by writing a script which automates the process.…”

Section: Related Workmentioning

confidence: 99%

Proving Type Class Laws for Haskell

Arvidsson

Johansson

Touche

2019

Lecture Notes in Computer Science

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Type classes in Haskell are used to implement ad-hoc polymorphism, i.e. a way to ensure both to the programmer and the compiler that a set of functions are defined for a specific data type. All instances of such type classes are expected to behave in a certain way and satisfy laws associated with the respective class. These are however typically just stated in comments and as such, there is no real way to enforce that they hold. In this paper we describe a system which allows the user to write down type class laws which are then automatically instantiated and sent to an inductive theorem prover when declaring a new instance of a type class.

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“…Both these tools are automatic, but unpredictable and not programmer-extensible, which has limited them to verifying much simpler properties than the ones checked here. Another tool, HERMIT [Farmer et al 2015], proves equalities by rewriting the GHC core language, guided by user specified scripts. Compared to these tools, in Liquid Haskell the proofs are Haskell programs while SMT solvers are used to automate reasoning.…”

Section: Verification In Haskellmentioning

confidence: 99%

Theorem proving for all: equational reasoning in liquid Haskell (functional pearl)

et al. 2018

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Equational reasoning is one of the key features of pure functional languages such as Haskell. To date, however, such reasoning always took place externally to Haskell, either manually on paper, or mechanised in a theorem prover. This article shows how equational reasoning can be performed directly and seamlessly within Haskell itself, and be checked using Liquid Haskell. In particular, language learners -to whom external theorem provers are out of reach -can benefit from having their proofs mechanically checked. Concretely, we show how the equational proofs and derivations from Hutton [2016]'s textbook can be recast as proofs in Haskell (spoiler: they look essentially the same).

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Reasoning with the HERMIT: tool support for equational reasoning on GHC core programs

Cited by 9 publications

References 33 publications

Calculating dependently-typed compilers (functional pearl)

Calculating dependently-typed compilers (functional pearl)

Proving Type Class Laws for Haskell

Theorem proving for all: equational reasoning in liquid Haskell (functional pearl)

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