Quantified class constraints

Bottu, Gert-Jan; Karachalias, Georgios; Schrijvers, Tom; Oliveira, Bruno C. d. S.; Wadler, Philip

doi:10.1145/3156695.3122967

Cited by 8 publications

(16 citation statements)

References 29 publications

(22 reference statements)

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“…We cannot illustrate this with COCHIS as, to keep its definition small, it is not equipped with higher-kinded types. The interested reader can find examples in the work of Bottu et al (2017).…”

Section: An Overview Of Cochismentioning

confidence: 99%

“…Nevertheless, if retaining global uniqueness is desired, that can be modelled by the subset of COCHIS without local declarations. In fact, based on the resolution algorithm of an early version of COCHIS, the Glasgow Haskell compiler (GHC) has been recently extended with quantified class constraints (Bottu et al, 2017;GHC, 2017b). Quantified class constraints enable higher-order rules in a setting with global scoping.…”

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confidence: 99%

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COCHIS: Stable and coherent implicits

Schrijvers¹,

Oliveira

Wadler³

et al. 2019

J. Funct. Prog.

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Implicit programming (IP) mechanisms infer values by type-directed resolution, making programs more compact and easier to read. Examples of IP mechanisms include Haskell’s type classes, Scala’s implicits, Agda’s instance arguments, Coq’s type classes and Rust’s traits. The design of IP mechanisms has led to heated debate: proponents of one school argue for the desirability of strong reasoning properties, while proponents of another school argue for the power and flexibility of local scoping or overlapping instances. The current state of affairs seems to indicate that the two goals are at odds with one another and cannot easily be reconciled. This paper presents COCHIS, the Calculus Of CoHerent ImplicitS, an improved variant of the implicit calculus that offers flexibility while preserving two key properties: coherence and stability of type substitutions. COCHIS supports polymorphism, local scoping, overlapping instances, first-class instances and higher-order rules, while remaining type-safe, coherent and stable under type substitution. We introduce a logical formulation of how to resolve implicits, which is simple but ambiguous and incoherent, and a second formulation, which is less simple but unambiguous, coherent and stable. Every resolution of the second formulation is also a resolution of the first, but not conversely. Parts of the second formulation bear a close resemblance to a standard technique for proof search called focusing. Moreover, key for its coherence is a rigorous enforcement of determinism.

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Section: An Overview Of Cochismentioning

confidence: 99%

mentioning

confidence: 99%

COCHIS: Stable and coherent implicits

Schrijvers¹,

Oliveira

Wadler³

et al. 2019

J. Funct. Prog.

Self Cite

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“…composes partial functions (left-to-right), captured by Kleisli arrows of the Maybe monad. The constraint ForallF Functor p captures a universally quantified constraint [6]: for all types u then p u has an instance of the Functor class. 4 The requirement for comap to take partial functions is in response to the frequent need to restrict the domain of bidirectional transformations.…”

Section: Definitionmentioning

confidence: 99%

Composing Bidirectional Programs Monadically

Xia

Orchard

Wang

2019

Programming Languages and Systems

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Software frequently converts data from one representation to another and vice versa. Naïvely specifying both conversion directions separately is error prone and introduces conceptual duplication. Instead, bidirectional programming techniques allow programs to be written which can be interpreted in both directions. However, these techniques often employ unfamiliar programming idioms via restricted, specialised combinator libraries. Instead, we introduce a framework for composing bidirectional programs monadically, enabling bidirectional programming with familiar abstractions in functional languages such as Haskell. We demonstrate the generality of our approach applied to parsers/printers, lenses, and generators/predicates. We show how to leverage compositionality and equational reasoning for the verification of round-tripping properties for such monadic bidirectional programs.

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“…Not only is the size of the constraint bigger than the one we started with, but the axiom can also be applied infinitely many times (to capture that all nested list types are instances of Eq): the resolution tree now contains infinite paths. Thus, even a backtracking approach (such as the one used by Bottu et al [2017]) cannot handle bidirectional instances in an obvious way: bidirectional axioms need to be used selectively to ensure the termination of type inference.…”

Section: Challenge 2: Termination Of Type Inferencementioning

confidence: 99%

“…Elaboration of terms, types, and constraints for our core calculus is also standard and can be found in prior work (see for example the work of Bottu et al [2017]). The signatures of the corresponding judgments are the following:…”

Section: Elaboration Of Terms Types and Constraintsmentioning

confidence: 99%

Bidirectional type class instances

Pauwels

Karachalias

Derhaeg³

et al. 2019

Proceedings of the 12th ACM SIGPLAN International Symposium on Haskell

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GADTs were introduced in Haskell's eco-system more than a decade ago, but their interaction with several mainstream features such as type classes and functional dependencies has a lot of room for improvement. More specifically, for some GADTs it can be surprisingly difficult to provide an instance for even the simplest of type classes.In this paper we identify the source of this shortcoming and address it by introducing a conservative extension to Haskell's type classes: Bidirectional Type Class Instances. In essence, under our interpretation class instances correspond to logical bi-implications, in contrast to their traditional unidirectional interpretation.We present a fully-fledged design of bidirectional instances, covering the specification of typing and elaboration into System FC, as well as an algorithm for type inference and elaboration. We provide a proof-of-concept implementation of our algorithm, and revisit the meta-theory of type classes in the presence of our extension.CCS Concepts • Theory of computation → Type theory; • Software and its engineering → Functional languages.

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Quantified class constraints

Cited by 8 publications

References 29 publications

COCHIS: Stable and coherent implicits

COCHIS: Stable and coherent implicits

Composing Bidirectional Programs Monadically

Bidirectional type class instances

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