A sound and relatively complete Hoare-logic for a language with higher type procedures

Damm, Werner; Josko, Bernhard

doi:10.1007/bf00264295

Cited by 40 publications

(14 citation statements)

References 17 publications

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“…Theorem 6.25). As expected, the completeness result is relative to the assumption that the background theory for refinement predicates is sufficiently expressible to encode arbitrary functions definable in the target programming language [Damm and Josko 1983;German et al 1983German et al , 1989Goerdt 1985;Honda et al 2006;Olderog 1984;Reus and Streicher 2011;Unno et al 2013]. Additionally, we need to assume that the background theory is sufficiently expressible to handle termination of non-deterministic programs.…”

Section: :2mentioning

confidence: 90%

“…Relative completeness for higher-order programs requires a means of precisely expressing properties of function values (i.e., partial applications). Following the previous work [Damm and Josko 1983;German et al 1983German et al , 1989Goerdt 1985;Honda et al 2006;Olderog 1984;Reus and Streicher 2011;Unno et al 2013], we accomplish this by Gödel encoding. We remark that, as shown in [Unno et al 2013], it is often possible to avoid explicit encoding in practice and that the encoding is unnecessary for soundness.…”

Section: Encodingmentioning

confidence: 99%

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Relatively complete refinement type system for verification of higher-order non-deterministic programs

Unno

Satake

Terauchi

2017

Proc. ACM Program. Lang.

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This paper considers verification of non-deterministic higher-order functional programs. Our contribution is a novel type system in which the types are used to express and verify (conditional) safety, termination, non-safety, and non-termination properties in the presence of ∀-∃ branching behavior due to non-determinism. For instance, the judgement ⊢ e : {u :int | ϕ(u)} ∀∀ says that every evaluation of e either diverges or reduces to some integer u satisfying ϕ(u), whereas ⊢ e : {u :int | ψ (u)} ∃∀ says that there exists an evaluation of e that either diverges or reduces to some integer u satisfying ψ (u). Note that the former is a safety property whereas the latter is a counterexample to a (conditional) termination property. Following the recent work on type-based verification methods for deterministic higher-order functional programs, we formalize the idea on the foundation of dependent refinement types, thereby allowing the type system to express and verify rich properties involving program values, branching behaviors, and the combination thereof.Our type system is able to seamlessly combine deductions of both universal and existential facts within a unified framework, paving the way for an exciting opportunity for new type-based verification methods that combine both universal and existential reasoning. For example, our system can prove the existence of a path violating some safety property from a proof of termination that uses a well-foundedness termination argument. We prove that our type system is sound and relatively complete, and further, thanks to having both modes of non-determinism, we show that our types are closed under complement.

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Section: :2mentioning

confidence: 90%

Section: Encodingmentioning

confidence: 99%

Relatively complete refinement type system for verification of higher-order non-deterministic programs

Unno

Satake

Terauchi

2017

Proc. ACM Program. Lang.

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“…The paper [DJ83] handled the more general case of Algol-like programs with arbitrary finite modes by using higher-order predicate variables and unevaluated substitutions to such variables. Common to both papers is that they deviated from the standard notion of relative completeness in that they used a higher-oder assertion language and an appropriate notion of expressiveness.…”

Section: Clarke's Language Lmentioning

confidence: 99%

Fifty years of Hoare’s logic

Apt

Olderog

2019

Form. Asp. Comput.

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“…For this reason most of Hoare logics studied for these programming languages do not directly describe higher-order behaviour in assertions. One of the exceptions is work by Damm and Josco [56], where they use predicate variables (which represent e.g. postconditions) by instantiating them with a concrete predicate using a fixed correspondence in variables.…”

Section: Program Logics For Sublanguages Of Algol (2): Damm and Joscomentioning

confidence: 99%

An observationally complete program logic for imperative higher-order functions

Honda

Yoshida

Berger

2014

Theoretical Computer Science

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We establish a strong completeness property called observational completeness of the program logic for imperative, higher-order functions introduced in [1]. Observational completeness states that valid assertions characterise program behaviour up to observational congruence, giving a precise correspondence between operational and axiomatic semantics. The proof layout for the observational completeness which uses a restricted syntactic structure called finite canonical forms originally introduced in game-based semantics, and characteristic formulae originally introduced in the process calculi, is generally applicable for a precise axiomatic characterisation of more complex program behaviour, such as aliasing and local state.

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A sound and relatively complete Hoare-logic for a language with higher type procedures

Cited by 40 publications

References 17 publications

Relatively complete refinement type system for verification of higher-order non-deterministic programs

Relatively complete refinement type system for verification of higher-order non-deterministic programs

Fifty years of Hoare’s logic

An observationally complete program logic for imperative higher-order functions

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