Automatically Proving Equivalence by Type-Safe Reflection

Slama, Franck; Brady, Edwin

doi:10.1007/978-3-319-62075-6_4

Cited by 5 publications

(7 citation statements)

References 14 publications

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“…In this example, the prelude function, isLTE, is used to provide a value that inhabits the type Dec (LTE p0' p4). Under the Curry-Howard correspondence and Intensional Type Theories [44] upon which Idris is based, the type Dec (LTE p0' p4) is a proposition and the result of (isLTE 32933 188784) is a proof of that proposition, and thus a proof of the assertion itself. Accordingly, we say that the result of the abstract evaluation of dijkstra is a mechanical proof of the assertions therein, where Idris is used as a proof assistant.…”

Section: Contract Definition and Derivationmentioning

confidence: 99%

Type-Driven Verification of Non-functional Properties

Brown

Barwell

Marquer

et al. 2019

Proceedings of the 21st International Symposium on Principles and Practice of Declarative Programming

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Energy, Time and Security (ETS) properties of programs are becoming increasingly prioritised by developers, especially where applications are running on ETS sensitive systems, such as embedded devices or the Internet of Things. Moreover, developers currently lack tools and language properties to allow them to reason about ETS. In this paper, we introduce a new contract specification framework, called Drive, which allows a developer to reason about ETS or other non-functional properties of their programs as first-class properties of the language. Furthermore, we introduce a contract specification language, allowing developers to reason about these first-class ETS properties by expressing contracts that are proved correct by an underlying formal type system. Finally, we show our contract framework over a number of representable examples, demonstrating provable worst-case ETS properties. CCS CONCEPTS• Software and its engineering → Formal software verification; Imperative languages; Software maintenance tools; • Security and privacy → Software security engineering.

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Section: Contract Definition and Derivationmentioning

confidence: 99%

Type-Driven Verification of Non-functional Properties

Brown

Barwell

Marquer

et al. 2019

Proceedings of the 21st International Symposium on Principles and Practice of Declarative Programming

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“…Dependently typed languages take advantage of the Curry-Howard correspondence, which states that, given a suitably rich type system, (certain kinds of) proofs can be represented as programs [30]. For languages with insufficiently rich type systems, such as C, dependently-typed languages can be used to produce an abstract interpretation [11] of a given program in those languages.…”

Section: Dependent Typesmentioning

confidence: 99%

“…Finally, we demonstrate our executable formalisation on a representative example, capturing a range of programmer-provided assertions and non-functional properties, and demonstrable proofs of these assertions. In line with the Curry-Howard correspondence [28,30], we formulate our definitions of…”

Section: Introductionmentioning

confidence: 99%

A trustworthy framework for resource-aware embedded programming

Barwell

Brown

2019

Proceedings of the 31st Symposium on Implementation and Application of Functional Languages

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Systems with non-functional requirements, such as Energy, Time and Security (ETS), are of increasing importance due to the proliferation of embedded devices with limited resources such as drones, wireless sensors, and tablet computers. Currently, however, there are little to no programmer supported methodologies or frameworks to allow them to reason about ETS properties in their source code. Drive is one such existing framework supporting the developer by lifting non-functional properties to the source-level through the Contract Specification Language (CSL), allowing non-functional properties to be first-class citizens, and supporting programmerwritten code-level contracts to guarantee the non-functional specifications of the program are met. In this paper, we extend the Drive system by providing rigorous implementations of the underlying proof-engine, modeling the specification of the annotations and assertions from CSL for a representative subset of C, called Imp. We define both an improved abstract interpretation that automatically derives proofs of assertions, and define inference algorithms for the derivation of both abstract interpretations and the context over which the interpretation is indexed. We use the dependentlytyped programming language, Idris, to give a formal definition, and implementation, of our abstract interpretation. Finally, we show our well-formed abstract interpretation over some representative exemplars demonstrating provable assertions of ETS.

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“…Pientka (2013)). Some use reflection (Slama and Brady 2017), some are based on algorithms that are similar to first-order resolution (Gonthier and Mahboubi 2010), and others (e.g. Liquid Haskell) incorporate third-party SMT solvers (Vazou et al 2018).…”

Section: B) ← Type(γ M a → B) ∧ Type(γ N A)mentioning

confidence: 99%

Proof-relevant Horn Clauses for Dependent Type Inference and Term Synthesis

Farka¹,

Ekaterina²,

Hammond³

2018

Theory and Practice of Logic Programming

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First-order resolution has been used for type inference for many years, including in Hindley-Milner type inference, type-classes, and constrained data types. Dependent types are a new trend in functional languages. In this paper, we show that proof-relevant first-order resolution can play an important role in automating type inference and term synthesis for dependently typed languages. We propose a calculus that translates type inference and term synthesis problems in a dependently typed language to a logic program and a goal in the proof-relevant first-order Horn clause logic. The computed answer substitution and proof term then provide a solution to the given type inference and term synthesis problem. We prove the decidability and soundness of our method.

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Automatically Proving Equivalence by Type-Safe Reflection

Cited by 5 publications

References 14 publications

Type-Driven Verification of Non-functional Properties

Type-Driven Verification of Non-functional Properties

A trustworthy framework for resource-aware embedded programming

Proof-relevant Horn Clauses for Dependent Type Inference and Term Synthesis

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