Promoting functions to type families in Haskell

Eisenberg, Richard A.; Stolarek, Jan

doi:10.1145/2775050.2633361

Cited by 6 publications

(2 citation statements)

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“…Dependent Types in Programming Integration of dependent types into Haskell has been a long standing goal [21] that dates back to Cayenne [4], a Haskell-like, fully dependent type language with undecidable type checking. Our approach differs significantly in that reflection and PLE use SMT-solvers to drastically simplify proofs over decidable theories.…”

Section: Related Workmentioning

confidence: 99%

Refinement reflection: complete verification with SMT

Vazou

Tondwalkar

Choudhury

et al. 2017

Proc. ACM Program. Lang.

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We introduce Refinement Reflection, a new framework for building SMT-based deductive verifiers. The key idea is to reflect the code implementing a user-defined function into the function's (output) refinement type. As a consequence, at uses of the function, the function definition is instantiated in the SMT logic in a precise fashion that permits decidable verification. Reflection allows the user to write equational proofs of programs just by writing other programs e.g. using pattern-matching and recursion to perform case-splitting and induction. Thus, via the propositions-as-types principle, we show that reflection permits the specification of arbitrary functional correctness properties. Finally, we introduce a proof-search algorithm called Proof by Logical Evaluation that uses techniques from model checking and abstract interpretation, to completely automate equational reasoning. We have implemented reflection in Liqid Haskell and used it to verify that the widely used instances of the Monoid, Applicative, Functor, and Monad typeclasses actually satisfy key algebraic laws required to make the clients safe, and have used reflection to build the first library that actually verifies assumptions about associativity and ordering that are crucial for safe deterministic parallelism.

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Section: Related Workmentioning

confidence: 99%

Refinement reflection: complete verification with SMT

Vazou

Tondwalkar

Choudhury

et al. 2017

Proc. ACM Program. Lang.

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“…Recently, Eisenberg and Stolarek (2014) introduced a library that promotes function definitions to closed type family definitions. This function promotion mechanism allows the programmer to use the familiar syntax of Haskell function definitions to define closed type families.…”

Section: Promoting Functionsmentioning

confidence: 99%

Composing and decomposing data types

Bahr

2014

Proceedings of the 10th ACM SIGPLAN Workshop on Generic Programming

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Wouter Swierstra's data typesà la carte is a technique to modularise data type definitions in Haskell. We give an alternative implementation of data typesà la carte that offers more flexibility in composing and decomposing data types. To achieve this, we refine the subtyping constraint, which is at the centre of data types a la carte. On the one hand this refinement is more general, allowing subtypings that intuitively should hold but were not derivable beforehand. This aspect of our implementation removes previous restrictions on how data types can be combined. On the other hand our refinement is more restrictive, disallowing subtypings that lead to more than one possible injection and should therefore be considered programming errors. Furthermore, from this refined subtyping constraint we derive a new constraint to express type isomorphism. We show how this isomorphism constraint allows us to decompose data types and to define extensible functions on data types in an ad hoc manner. The implementation makes essential use of closed type families in Haskell. The use of closed type families instead of type classes comes with a set of trade-offs, which we review in detail. Finally, we show that our technique can be used for other similar problem domains.

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