Proving Type Class Laws for Haskell

Arvidsson, Andreas; Johansson, Moa; Touche, Robin

doi:10.1007/978-3-030-14805-8_4

Cited by 4 publications

(2 citation statements)

References 18 publications

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“…On the topic of interfaces (type classes) and their laws there is related work in specifying (Jansson & Jeuring, 2002), rewriting (Peyton Jones et al, 2001), testing (Jeuring et al, 2012), and proving (Arvidsson et al, 2019) type class laws in Haskell. The equality challenges here are often related to the semantics of nontermination as described in the Fast and Loose Reasoning paper (Danielsson et al, 2006).…”

Section: Related Workmentioning

confidence: 99%

Extensional equality preservation and verified generic programming

Botta¹,

Brede²,

Jansson³

et al. 2021

J. Funct. Prog.

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In verified generic programming, one cannot exploit the structure of concrete data types but has to rely on well chosen sets of specifications or abstract data types (ADTs). Functors and monads are at the core of many applications of functional programming. This raises the question of what useful ADTs for verified functors and monads could look like. The functorial map of many important monads preserves extensional equality. For instance, if $$f,g \, : \, A \, \to \, B$$ are extensionally equal, that is, $$\forall x \in A$$ , $$f \, x = g \, x$$ , then $$map \, f \, : \, List \, A \to List \, B$$ and $$map \, g$$ are also extensionally equal. This suggests that preservation of extensional equality could be a useful principle in verified generic programming. We explore this possibility with a minimalist approach: we deal with (the lack of) extensional equality in Martin-Löf’s intensional type theories without extending the theories or using full-fledged setoids. Perhaps surprisingly, this minimal approach turns out to be extremely useful. It allows one to derive simple generic proofs of monadic laws but also verified, generic results in dynamical systems and control theory. In turn, these results avoid tedious code duplication and ad-hoc proofs. Thus, our work is a contribution toward pragmatic, verified generic programming.

show abstract

Section: Related Workmentioning

confidence: 99%

Extensional equality preservation and verified generic programming

Botta¹,

Brede²,

Jansson³

et al. 2021

J. Funct. Prog.

View full text Add to dashboard Cite

show abstract

“…On the topic of interfaces (type classes) and their laws there is related work in specifying (Jansson & Jeuring, 2002), rewriting (Peyton Jones et al, 2001), testing (Jeuring et al, 2012) and proving (Arvidsson et al, 2018) type class laws in Haskell. The equality challenges here are often related to the semantics of non-termination as described in the Fast and Loose Reasoning paper (Danielsson et al, 2006).…”

Section: Related Workmentioning

confidence: 99%

Extensional equality preservation and verified generic programming

Botta¹,

Brede²,

Jansson³

et al. 2020

Preprint

View full text Add to dashboard Cite

In verified generic programming, one cannot exploit the structure of concrete data types but has to rely on well chosen sets of specifications or abstract data types (ADTs). Functors and monads are at the core of many applications of functional programming. This raises the question of what useful ADTs for verified functors and monads could look like. The functorial map of many important monads preserves extensional equality. For instance, if f , g : A → B are extensionally equal, that is, ∀x ∈ A, f x = g x, then map f : List A → List B and map g are also extensionally equal. This suggests that preservation of extensional equality could be a useful principle in verified generic programming. We explore this possibility with a minimalist approach: we deal with (the lack of) extensional equality in Martin-Löf's intensional type theories without extending the theories or using full-fledged setoids. Perhaps surprisingly, this minimal approach turns out to be extremely useful. It allows one to derive simple generic proofs of monadic laws but also verified, generic results in dynamical systems and control theory. In turn, these results avoid tedious code duplication and adhoc proofs. Thus, our work is a contribution towards pragmatic, verified generic programming.

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Type-Checking CRDT Convergence

Zakhour,

Weisenburger,

Salvaneschi

2023

Proc. ACM Program. Lang.

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Conflict-Free Replicated Data Types (CRDTs) are a recent approach for keeping replicated data consistent while guaranteeing the absence of conflicts among replicas. For correct operation, CRDTs rely on a merge function that is commutative, associative and idempotent. Ensuring that such algebraic properties are satisfied by implementations, however, is left to the programmer, resulting in a process that is complex and error-prone. While techniques based on testing, automatic verification of a model, and mechanized or handwritten proofs are available, we lack an approach that is able to verify such properties on concrete CRDT implementations. In this paper, we present Propel, a programming language with a type system that captures the algebraic properties required by a correct CRDT implementation. The Propel type system deduces such properties by case analysis and induction: sum types guide the case analysis and algebraic properties in function types enable induction for free. Propel’s key feature is its capacity to reason about algebraic properties (a) in terms of rewrite rules and (b) to derive the equality or inequality of expressions from the properties. We provide an implementation of Propel as a Scala embedding, we implement several CRDTs, verify them with Propel and compare the verification process with four state-of-the-art verification tools. Our evaluation shows that Propel is able to automatically deduce the properties that are relevant for common CRDT implementations found in open-source libraries even in cases in which competitors timeout.

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Proving Type Class Laws for Haskell

Cited by 4 publications

References 18 publications

Extensional equality preservation and verified generic programming

Extensional equality preservation and verified generic programming

Extensional equality preservation and verified generic programming

Type-Checking CRDT Convergence

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