Coinductive big-step operational semantics

Leroy, Xavier; Grall, Hervé

doi:10.1016/j.ic.2007.12.004

Cited by 125 publications

(115 citation statements)

References 31 publications

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“…For example, one can use co-induction to precisely define diverging computations [18,20], or the pretty-big-step approach to reduce duplication in the definition [10]. Notably, these techniques still define the semantics using inductive (and co-inductive) relations rather than recursive functions, and we are not aware of any relational approach with all of the advantages listed above.…”

Section: Introductionmentioning

confidence: 99%

Functional Big-Step Semantics

Owens

Myreen

Kumar

et al. 2016

Lecture Notes in Computer Science

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Abstract. When doing an interactive proof about a piece of software, it is important that the underlying programming language's semantics does not make the proof unnecessarily difficult or unwieldy. Both smallstep and big-step semantics are commonly used, and the latter is typically given by an inductively defined relation. In this paper, we consider an alternative: using a recursive function akin to an interpreter for the language. The advantages include a better induction theorem, less duplication, accessibility to ordinary functional programmers, and the ease of doing symbolic simulation in proofs via rewriting. We believe that this style of semantics is well suited for compiler verification, including proofs of divergence preservation. We do not claim the invention of this style of semantics: our contribution here is to clarify its value, and to explain how it supports several language features that might appear to require a relational or small-step approach. We illustrate the technique on a simple imperative language with C-like for-loops and a break statement, and compare it to a variety of other approaches. We also provide ML and lambda-calculus based examples to illustrate its generality.

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Section: Introductionmentioning

confidence: 99%

Functional Big-Step Semantics

Owens

Myreen

Kumar

et al. 2016

Lecture Notes in Computer Science

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“…We now state that if the VCs hold for all functions then any expression having a valid WP executes safely. It is proved by co-induction, using the axiom of excluded middle to distinguish whether the execution of an expression does or does not terminate, following the guidelines of Leroy and Grall [19]. Notice that it is enough to prove the verification conditions for each function separately, even if functions can be mutually recursive, there is no circular reasoning.…”

Section: Soundness Resultsmentioning

confidence: 99%

“…The operational semantics is defined in big-step style following the approach of Leroy and Grall [19]. A first set of inference rules inductively defines the semantics of terminating expressions (Fig.…”

Section: Operational Semanticsmentioning

confidence: 99%

A Certified Multi-prover Verification Condition Generator

Herms

Marché

Monate

2012

Verified Software: Theories, Tools, Experiments

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Deduction-based software verification tools have reached a maturity allowing them to be used in industrial context where a very high level of assurance is required. This raises the question of the level of confidence we can grant to the tools themselves. We present a certified implementation of a verification condition generator. An originality is its genericity with respect to the logical context, which allows us to produce proof obligations for a large class of theorem provers. This implementation is conducted within the Coq proof assistant, and is crafted so that it can be extracted into a standalone executable, independent of Coq, which is another originality.

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“…In our previous papers, [12] and [14], we defined a small-step semantics which ensures that well-typed programs do not "get stuck". Here, following [19], we give a coinductive characterization of the divergence judgment e | σ | ρ ⇑. The divergence judgment e | σ | ρ ⇑ is defined in Fig.…”

Section: Lemma 2 (Type Preservation For Exceptionsmentioning

confidence: 99%

A Provably Correct Compilation of Functional Languages into Scripting Languages

Giannini¹,

Shaqiri²

2017

SACS

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In this paper we consider the problem of translating core F#, a typed functional language including mutable variables and exception handling, into scripting languages such as JavaScript or Python. In previous work, we abstracted the most significant characteristics of scripting languages in an intermediate language (IL for short). IL is a block-structured imperative language in which a definition of a name does not have to statically precede its use. We define a bigstep operational semantics for core F# and for IL and formalise the translation of F# expressions into IL. The main contribution of the paper is the proof of correctness of the given translation, which is done by showing that the evaluation of a well-typed F# program converges to a primitive value if and only if the evaluation of its translation into IL converges to the same value.

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Coinductive big-step operational semantics

Cited by 125 publications

References 31 publications

Functional Big-Step Semantics

Functional Big-Step Semantics

A Certified Multi-prover Verification Condition Generator

A Provably Correct Compilation of Functional Languages into Scripting Languages

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