Dependent types from counterexamples

TerauchiTachio,

doi:10.1145/1707801.1706315

Cited by 23 publications

(37 citation statements)

References 47 publications

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“…The transformation (−) in the previous section allowed us to reduce the refinement type checking |= t : τ to the firstorder refinement type checking |= (t) : (τ ) , but it does not necessarily enable us to prove the latter by using the existing automated verification tools [12,17,16,9,19,13]. This is due to the incompleteness of the tools for proving |= (t) : (τ ) .…”

Section: Transformations For Enabling First-order Refinement Type Chementioning

confidence: 99%

“…We obtain also first-order refinement type system by restricting the type system so that function variables are disallowed to occur in predicates in all the refinement types. Various automatic verification methods [12,17,16,9,19,13] are available for the first-order refinement types.…”

Section: Appendix B a Refinement Type Systemmentioning

confidence: 99%

“…. , x n )]Also, the equation below follows from the commuting conversion axiom:cclet y = t in t = o let y = t in t ,(D 16). which can be shown by a straightforward induction on t.…”

mentioning

confidence: 99%

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Verifying relational properties of functional programs by first-order refinement

Asada

Satô

Kobayashi

2017

Science of Computer Programming

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Much progress has been made recently on fully automated verification of higher-order functional programs, based on refinement types and higher-order model checking. Most of those verification techniques are, however, based on first-order refinement types, hence unable to verify certain properties of functions (such as the equality of two recursive functions and the monotonicity of a function, which we call relational properties). To relax this limitation, we introduce a restricted form of higher-order refinement types where refinement predicates can refer to functions, and formalize a systematic program transformation to reduce type checking/inference for higher-order refinement types to that for first-order refinement types, so that the latter can be automatically solved by using an existing software model checker. We also prove the soundness of the transformation, and report on implementation and experiments.

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Section: Transformations For Enabling First-order Refinement Type Chementioning

confidence: 99%

Section: Appendix B a Refinement Type Systemmentioning

confidence: 99%

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Verifying relational properties of functional programs by first-order refinement

Asada

Satô

Kobayashi

2017

Science of Computer Programming

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“…An algorithm to solve recursion-free systems of Horn constraints by repeated computation of binary interpolants was given in [43], for the purpose of type inference. Further techniques for solving Horn clauses were developed in [26].…”

Section: Related Workmentioning

confidence: 99%

On recursion-free Horn clauses and Craig interpolation

Rümmer

Hojjat

Kunčak

2014

Form Methods Syst Des

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One of the main challenges in software verification is efficient and precise analysis of programs with procedures and loops. Interpolation methods remain among the most promising techniques for such verification. To accommodate the demands of various programming language features, over the past years several extended forms of interpolation have been introduced. We give a precise ontology of such extended interpolation methods, and investigate the relationship between interpolation and fragments of constrained recursionfree Horn clauses. We also introduce a new notion of interpolation, disjunctive interpolation, which solves a more general class of problems in one step compared to previous notions of interpolants, such as tree interpolants or inductive sequences of interpolants. We present algorithms and complexity for construction of interpolants, as well as the corresponding decision problems for recursion-free Horn fragments. Finally, we give an extensive empirical evaluation using a solver for (recursive) Horn problems, in particular comparing the performance of tree interpolation and disjunctive interpolation for constraints modelling software verification tasks.

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“…There has been considerable recent progress in inference algorithms for refinement types (Rondon et al, 2008;Kawaguchi et al, 2009;Unno & Kobayashi, 2009;Terauchi, 2010;Jhala et al, 2011), some of which may be applicable to inferring type signatures for Dminor functions.…”

Section: Related Workmentioning

confidence: 99%

Semantic subtyping with an SMT solver

Bierman¹,

Gordon²,

Hriţcu³

et al. 2012

J. Funct. Prog.

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We study a first-order functional language with the novel combination of the ideas of refinement type (the subset of a type to satisfy a Boolean expression) and type-test (a Boolean expression testing whether a value belongs to a type). Our core calculus can express a rich variety of typing idioms; for example, intersection, union, negation, singleton, nullable, variant, and algebraic types are all derivable. We formulate a semantics in which expressions denote terms, and types are interpreted as first-order logic formulas. Subtyping is defined as valid implication between the semantics of types. The formulas are interpreted in a specific model that we axiomatize using standard first-order theories. On this basis, we present a novel type-checking algorithm able to eliminate many dynamic tests and to detect many errors statically. The key idea is to rely on a Satisfiability Modulo Theories solver to compute subtyping efficiently. Moreover, using a satisfiability modulo theories solver allows us to show the uniqueness of normal forms for non-deterministic expressions, provide precise counterexamples when type-checking fails, detect empty types, and compute instances of types statically and at run-time.

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Dependent types from counterexamples

Cited by 23 publications

References 47 publications

Verifying relational properties of functional programs by first-order refinement

Verifying relational properties of functional programs by first-order refinement

On recursion-free Horn clauses and Craig interpolation

Semantic subtyping with an SMT solver

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