Distributive Disjoint Polymorphism for Compositional Programming

Bi, Xuan; Xie, Ningning; Oliveira, Bruno C. d. S.; Schrijvers, Tom

doi:10.1007/978-3-030-17184-1_14

Cited by 9 publications

(24 citation statements)

References 47 publications

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“…The details of the elaboration of SEDEL's source language constructs into F i are outside of the scope of this paper, and are given in work by . A more recent version of SEDEL, employing the same encoding, but targeting the F + i calculus instead and enabling distributive subtyping and nested composition, was used by Bi et al (2019). We have used such a version to present the examples in Section 2.2.…”

Section: The Expression Problemmentioning

confidence: 99%

“…However, in coercive subtyping (Luo, 1999), subtyping triggers coercions, and such coercions can have an operational effect and change the underlying value. Previous work on intersection types with the merge operator (Dunfield, 2014;Oliveira et al, 2016;Alpuim et al, 2017;Bi et al, , 2019 employ an elaboration semantics with coercive subtyping: the elaboration introduces coercions that transform values. For example, a merge is translated into a pair, and the coercion from Int & Char to Int is a projection on the pair which takes the first component.…”

Section: A Type-driven Semantics For Type Preservationmentioning

confidence: 99%

“…Allowing unrestricted intersections adds extra expressive power. For instance, in calculi with polymorphism, unrestricted intersections can be used to encode bounded quantification (Cardelli & Wegner, 1985), whereas with disjoint intersections only such an encoding does not work (Bi et al, 2019;Xie et al, 2020). Various authors, including Pierce and Castagna, have (informally) observed that some form of bounded quantification can be encoded via (unrestricted) intersection types (Pierce, 1991;Castagna & Xu, 2011).…”

Section: Consistencymentioning

confidence: 99%

“…Determinism in TDOS offers the same guarantee that coherence offers in an elaboration semantics (both properties ensure that the semantics is unambiguous), but it is much simpler to prove. Additionally, the TDOS approach deals with recursion in a straightforward way, unlike λ i and subsequent calculi (Bi et al, , 2019 where recursion is very problematic for proving coherence.…”

Section: Introductionmentioning

confidence: 99%

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Taming the Merge Operator

Huang¹,

Zhao²,

Oliveira³

2021

J. Funct. Prog.

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Calculi with disjoint intersection types support a symmetric merge operator with subtyping. The merge operator generalizes record concatenation to any type, enabling expressive forms of object composition, and simple solutions to hard modularity problems. Unfortunately, recent calculi with disjoint intersection types and the merge operator lack a (direct) operational semantics with expected properties such as determinism and subject reduction, and only account for terminating programs. This paper proposes a type-directed operational semantics (TDOS) for calculi with intersection types and a merge operator. We study two variants of calculi in the literature. The first calculus, called λ i , is a variant of a calculus presented by Oliveira et al. (2016) and closely related to another calculus by Dunfield (2014). Although Dunfield proposes a direct small-step semantics for her calculus, her semantics lacks both determinism and subject reduction. Using our TDOS, we obtain a direct semantics for λ i that has both properties. The second calculus, called λ i + , employs the well-known subtyping relation of Barendregt, Coppo and Dezani-Ciancaglini (BCD). Therefore, λ i + extends the more basic subtyping relation of λ i , and also adds support for record types and nested composition (which enables recursive composition of merged components). To fully obtain determinism, both λ i and λ i + employ a disjointness restriction proposed in the original λ i calculus. As an added benefit the TDOS approach deals with recursion in a straightforward way, unlike previous calculi with disjoint intersection types where recursion is problematic. We relate the static and dynamic semantics of λ i to the original version of the calculus and the calculus by Dunfield. Furthermore, for λ i + , we show a novel formulation of BCD subtyping, which is algorithmic, has a very simple proof of transitivity and allows for the modular addition of distributivity rules (i.e. without affecting other rules of subtyping). All results have been fully formalized in the Coq theorem prover.

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Section: The Expression Problemmentioning

confidence: 99%

Section: A Type-driven Semantics For Type Preservationmentioning

confidence: 99%

Section: Consistencymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Taming the Merge Operator

Huang¹,

Zhao²,

Oliveira³

2021

J. Funct. Prog.

Self Cite

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“…Implicits. Cochis [Schrijvers et al 2019] is a calculus with highly expressive implicit resolution, including local instances. It achieves coherence by imposing restrictions on the implicit context and enforcing a deterministic resolution process.…”

Section: Related Workmentioning

confidence: 99%

Coherence of type class resolution

Bottu

Xie

Marntirosian

et al. 2019

Proc. ACM Program. Lang.

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Elaboration-based type class resolution, as found in languages like Haskell, Mercury and PureScript, is generally nondeterministic: there can be multiple ways to satisfy a wanted constraint in terms of global instances and locally given constraints. Coherence is the key property that keeps this sane; it guarantees that, despite the nondeterminism, programs still behave predictably. Even though elaboration-based resolution is generally assumed coherent, as far as we know, there is no formal proof of this property in the presence of sources of nondeterminism, like superclasses and flexible contexts.This paper provides a formal proof to remedy the situation. The proof is non-trivial because the semantics elaborates resolution into a target language where different elaborations can be distinguished by contexts that do not have a source language counterpart. Inspired by the notion of full abstraction, we present a two-step strategy that first elaborates nondeterministically into an intermediate language that preserves contextual equivalence, and then deterministically elaborates from there into the target language. We use an approach based on logical relations to establish contextual equivalence and thus coherence for the first step of elaboration, while the second step's determinism straightforwardly preserves this coherence property.

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