Fast Verified BCD Subtyping

Bessai, Jan; Rehof, Jakob; Düdder, Boris

doi:10.1007/978-3-030-22348-9_21

Cited by 3 publications

(4 citation statements)

References 14 publications

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“…However, such a rule introduces complications, and designing sound and complete algorithms is tricky. In particular, in previous work Pierce, 1989;Bessai et al, 2016Bessai et al, , 2019Siek, 2019), the distributivity rule leads to non-modular algorithmic formulations where many standard subtyping rules have to be changed due to distributivity. Furthermore, the metatheory of BCD subtyping is challenging.…”

Section: A Modular and Algorithmic Formulation Of Bcd Subtypingmentioning

confidence: 99%

“…It is also worth mentioning that our algorithmic relation keeps the simple judgment form A <: B, thus the system is easier to extend with orthogonal features, which have been presented with a subtyping relation of that form. Some BCD subtyping formulations require a different form to the subtyping relation Pierce, 1989;Bessai et al, 2016Bessai et al, , 2019.…”

Section: Lemma 65 (S-bcd-top In Declarative Bcd) If B Then a Bmentioning

confidence: 99%

“…The decidability of BCD subtyping is shown in several other works (Kurata & Takahashi, 1995;Rehof & Urzyczyn, 2011;Statman, 2015) through manual proofs, and there are also proofs formalized in Coq (Laurent, 2012;Bessai et al, 2016). Bessai et al (2019) developed a fast algorithm verified in Coq. Their algorithm is presented as a relational abstract machine specification, with a long proof due to the mismatch between the styles of the declarative system and algorithmic system.…”

Section: Bcd Subtyping Algorithmsmentioning

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: A Modular and Algorithmic Formulation Of Bcd Subtypingmentioning

confidence: 99%

Section: Lemma 65 (S-bcd-top In Declarative Bcd) If B Then a Bmentioning

confidence: 99%

Section: Bcd Subtyping Algorithmsmentioning

confidence: 99%

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Taming the Merge Operator

Huang¹,

Zhao²,

Oliveira³

2021

J. Funct. Prog.

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“…More recently, Jan Bessai kindly wrote us to explain how the Braga method, as outlined in the two pages TYPES 2018 abstract 2 and the accompanying code, helped him to implement his correct by construction algorithm for fast BCD subtyping. 30 On this example, he also extended the method to be able to capture some properties related to a measure of complexity of his algorithm. This gives us even more conviction that simple/short examples help at the understanding of the Braga method.…”

Section: Related Workmentioning

confidence: 99%

The Braga Method: Extracting Certified Algorithms from Complex Recursive Schemes in Coq

Larchey-Wendling

Monin

2021

Proof and Computation II

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CLS-SMT: Bringing Together Combinatory Logic Synthesis and Satisfiability Modulo Theories

Kallat

Schäfer

Vasileva

2019

Electron. Proc. Theor. Comput. Sci.

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We introduce an approach that aims to combine the usage of satisfiability modulo theories (SMT) solvers with the Combinatory Logic Synthesizer (CL)S framework. (CL)S is a tool for the automatic composition of software components from a user-specified repository. The framework yields a tree grammar that contains all composed terms that comply with a target type. Type specifications for (CL)S are based on combinatory logic with intersection types. Our approach translates the tree grammar into SMT functions, which allows the consideration of additional domain-specific constraints. We demonstrate the usefulness of our approach in several experiments.

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Fast Verified BCD Subtyping

Cited by 3 publications

References 14 publications

Taming the Merge Operator

Taming the Merge Operator

The Braga Method: Extracting Certified Algorithms from Complex Recursive Schemes in Coq

CLS-SMT: Bringing Together Combinatory Logic Synthesis and Satisfiability Modulo Theories

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