Subtyping constrained types

Trifonov, Valery; Smith, Scott F.

doi:10.1007/3-540-61739-6_52

Cited by 57 publications

(68 citation statements)

References 18 publications

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“…One may cite works by Aiken et al [1,2,5], the present author [16,15], Trifonov and Smith [22], as well as an abstract framework by Odersky, Sulzmann and Wehr [12]. Related systems include set-based analysis [8,6] and type inference systems based on feature constraints [9,10].…”

Section: Constraint-based Type Inferencementioning

confidence: 99%

A 3-Part Type Inference Engine

Pottier¹

2000

Programming Languages and Systems

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Abstract. Extending a subtyping-constraint-based type inference framework with conditional constraints and rows yields a powerful type inference engine. We illustrate this claim by proposing solutions to three delicate type inference problems: "accurate" pattern matchings, record concatenation, and "dynamic" messages. Until now, known solutions required significantly different techniques; our theoretical contribution is in using only a single (and simple) set of tools. On the practical side, this allows all three problems to benefit from a common set of constraint simplification techniques, leading to efficient solutions.

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Section: Constraint-based Type Inferencementioning

confidence: 99%

A 3-Part Type Inference Engine

Pottier¹

2000

Programming Languages and Systems

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“…Recent work in subtyping systems and in set constraints using notions of constraint entailment in the sense of the present paper includes [1,5,15,22,6,2,8,13]. In subtyping systems, a program is typed under a set of suptyping constraints consisting of inequalities of the form T < T ~, where T and T ~ are type expressions; the constraints express hypotheses about subtype relations which must hold between the types for the program to be well-typed.…”

Section: Constraint Entailmentmentioning

confidence: 99%

“…Works using entailment based simplification of set constraints include [1,6,2,8]. In subtyping systems, quite similar problems are currently attacked using entailment for subtyping constraints; recent work includes [15,22,13], see also [17] for further references to previous work in subtype simplification.…”

Section: Constraint Entailmentmentioning

confidence: 99%

Constraint automata and the complexity of recursive subtype entailment

Henglein¹,

Rehof²

1998

Automata, Languages and Programming

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Abstract. We study entailment of structural and nonstructural recursive subtyping constraints. Constraints are formal inequalities between type expressions, interpreted over an ordered set of possibly infinite labeled trees. The nonstructural ordering on trees is the one introduced by Amadio and Cardelli for subtyping with recursive types. The structural ordering compares only trees with common shape. A constraint set entails an inequality if every assignment of meanings (trees) to type expressions that satisfies all the constraints also satisfies the inequality. In this paper we prove that nonstructural subtype entailment is PSPACEhard, both for finite trees (simple types) and infinite trees (recursive types). For the structural ordering we prove that subtype entailment over infinite trees is PSPACE-complete, when the order on trees is generated from a lattice of type constants. Since structural subtype entailment over finite trees has been shown to be coNP-complete these are the first complexity-theoretic separation results that show that, informally, nonstructural subtype entailment is harder than structural entailment, and recursive entailment is harder than nonrecursive entailment.

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“…Despite extensive effort over many years, the exact complexity and even the decidability of entailment is open for non-structural subtype constraints [Rehof 1998;Henglein and Rehof 1997;1998;Flanagan and Felleisen 1997;Niehren and Priesnitz 1999;Trifonov and Smith 1996;Aiken et al 1997;Fähndrich and Aiken 1996;Pottier 1996;Marlow and Wadler 1997;Pottier 2001]. As we show in Section 2, the natural versions of entailment · 3 and subtyping constrained types can be encoded easily in the first-order theory of subtyping, so to gain insight into and take a step towards resolving these difficult problems, we study the full first-order theory in this paper.…”

Section: Introductionmentioning

confidence: 99%

The first-order theory of subtyping constraints

Aiken

Niehren

et al. 2002

Proceedings of the 29th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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We investigate the first-order theory of subtype constraints. We show that the first-order theory of non-structural subtyping is undecidable, and we show that in the case where all constructors are either unary or nullary, the first-order theory is decidable for both structural and non-structural subtyping. Our results hold for both simple and recursive types. The undecidability result is shown by a reduction from the Post's Correspondence Problem, and the decidability result is shown by a reduction to a decision problem on tree automata. In addition, we introduce the notion of a constrained tree automaton to express non-structural subtype entailment. This work is a step towards resolving long-standing open problems of the decidability of entailment for non-structural subtyping.

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Subtyping constrained types

Cited by 57 publications

References 18 publications

A 3-Part Type Inference Engine

A 3-Part Type Inference Engine

Constraint automata and the complexity of recursive subtype entailment

The first-order theory of subtyping constraints

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