A formalization of an Ordered Logical Framework in Hybrid with applications to continuation machines

Momigliano, Alberto; Polakow, Jeff

doi:10.1145/976571.976581

Cited by 3 publications

(4 citation statements)

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“…A significant case study using this infrastructure has being tackled by Alan Martin [62,63] and consists of an investigation of the meta-theory of a functional programming language with references using a variety of approaches, culminating with the usage of a linearly ordered SL. This study extends the work in Section 5 and [79], as well as offering a different encoding of Mini-ML with references than the one analyzed with a linear logical framework [18]. 29 Martin's forthcoming doctoral thesis [62] also illustrates that it is possible to use alternate techniques for induction at the SL level.…”

Section: Hybrid Variantsmentioning

confidence: 64%

“…We follow that up with an extensive review and comparison of related work in Section 6, and conclude in Section 7. This paper is an archival documentation of Hybrid 0.1 (see Section 6.5 for the terminology), extending previous joint work with Simon Ambler and Roy Crole [2,3,[75][76][77], Jeff Polakow [79] and Venanzio Capretta [17].…”

mentioning

confidence: 57%

“…We exemplify this approach by implementing a fragment of Polakow's ordered logic as an SL and test it with a proof of type preservation of a continuation machine for Mini-ML, as we sketched in [79]. For the sake of presentation we shall deal with a call-by-name operational semantics.…”

Section: Ordered Linear Logic As a Specification Logicmentioning

confidence: 99%

“…Acknowledgements Most of the material in this paper is based on previous joint work with Simon Ambler and Roy Crole [2,3,[75][76][77], Jeff Polakow [79] and Venanzio Capretta [17], whose contributions we gratefully acknowledge. The paper has also benefited from discussions with Andy Gordon, Alan Martin, Marino Miculan, Dale Miller, Brigitte Pientka, Randy Pollack, Frank Pfenning and Carsten Schürman.…”

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confidence: 99%

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Hybrid

Felty

Momigliano

2010

J Autom Reasoning

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Combining higher-order abstract syntax and (co)-induction in a logical framework is well known to be problematic. We describe the theory and the practice of a tool called Hybrid, within Isabelle/HOL and Coq, which aims to address many of these difficulties. It allows object logics to be represented using higher-order abstract syntax, and reasoned about using tactical theorem proving and principles of (co)induction. Moreover, it is definitional, which guarantees consistency within a classical type theory. The idea is to have a de Bruijn representation of λ-terms providing a definitional layer that allows the user to represent object languages using higher-order abstract syntax, while offering tools for reasoning about them at the higher level. In this paper we describe how to use Hybrid in a multi-level reasoning fashion, similar in spirit to other systems such as Twelf and Abella. By explicitly referencing provability in a middle layer called a specification logic, we solve the problem of reasoning by (co)induction in the presence of non-stratifiable hypothetical judgments, which allow very elegant and succinct specifications of object logic inference rules. We first demonstrate the method on a simple example, formally proving type soundness (subject reduction) for a fragment of a pure functional language, using a minimal intuitionistic logic as the specification logic. We then prove an analogous result for a continuation-machine presentation of the operational semantics of the same language, encoded this time in an ordered linear logic that serves as the specification layer. This example demonstrates the ease with which we can incorporate new specification logics, and also illustrates a significantly more complex object logic whose encoding is elegantly expressed using features of the new specification logic.

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Section: Hybrid Variantsmentioning

confidence: 64%