A practical module system for LF

Rabe, Florian; Schürmann, Carsten

doi:10.1145/1577824.1577831

Cited by 23 publications

(27 citation statements)

References 17 publications

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“…The idea of development graphs turned out to be very fruitful in the past and various research groups adopted this approach. The proof semantics of CASL [17], the theory structuring mechanisms in OMDoc [10], the recent module system for Twelf [18] and also locales in Isabelle [4] were influenced by the notion of development graphs. The presented approach allows for an efficient support of specification and verification with the help of heterogeneous development graphs.…”

Section: Resultsmentioning

confidence: 99%

Change Management for Heterogeneous Development Graphs

Autexier

Hutter

Mossakowski

2010

Verification, Induction, Termination Analysis

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Abstract. The error-prone process of formal specification and verification of large systems requires an efficient, evolutionary formal development approach. Development graphs have been designed to support such an approach. They can formally represent the actual state of a software development comprising specification and verification work in a structured way and assist the user in her evolutionary development by the incorporated change management support. In this paper we extend this work with respect to heterogeneous development graphs allowing one to make use of different institutions, i.e. logics, for specifying and verifying large developments. We also push forward the idea of stringent locality of definitions by introducing pre-signatures and pre-signature morphisms, which allow us to build up signatures in an incremental and parametric way.

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Section: Resultsmentioning

confidence: 99%

Change Management for Heterogeneous Development Graphs

Autexier

Hutter

Mossakowski

2010

Verification, Induction, Termination Analysis

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“…This means that adding a single new syntactic construct to the object language may require a substantial amount of boilerplate to be written as well. A topic for future work would be to develop a streamlined way of generating assertion logics and representation logics from an LF signature, possibly by utilizing the experimental Twelf module system [9].…”

Section: Discussionmentioning

confidence: 99%

“…The Twelf module system has recently been extended with a notion of logical relations [9,10]. The module system allows the definition of isolated signatures and morphisms, which are transformations of types and terms in one signature to types and terms in another.…”

Section: Related Workmentioning

confidence: 99%

Structural logical relations with case analysis and equality reasoning

Rasmussen

Filinski

2013

Proceedings of the Eighth ACM SIGPLAN International Workshop on Logical Frameworks &Amp; Meta-Languages: Theory &Amp; Practice

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Formalizing proofs by logical relations in the Twelf proof assistant is known to be notoriously difficult. However, as demonstrated by Schürmann and Sarnat [In Proc. of 23rd Symp. on Logic in Computer Science, 2008] such proofs can be represented and verified in Twelf if done so using a Gentzen-style auxiliary assertion logic which is subsequently proved consistent via cut elimination.We demonstrate in this paper an application of the above methodology to proofs of observational equivalence between expressions in a simply typed lambda calculus with a call-by-name operational semantics. Our use case requires the assertion logic to be extended with reasoning principles not present in the original presentation of the formalization method. We address this by generalizing the assertion logic to include dependent sorts, and demonstrate that the original cut elimination proof continues to apply without modification.

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“…Here we mimic the concrete syntax of our Twelf implementation [Pfenning and Schürmann 1999;Rabe and Schürmann 2009] and use the keywords %sig to introduce signatures and %infix to introduce infix notations for certain binary symbols.…”

Section: General Ideasmentioning

confidence: 99%

Logical relations for a logical framework

Rabe

Sojakova

2013

ACM Trans. Comput. Logic

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Logical relations are a central concept used to study various higher-order type theories and occur frequently in the proofs of a wide variety of meta-theorems. Besides extending the logical relation principle to more general languages, an important research question has been how to represent and thus verify logical relation arguments in logical frameworks.We formulate a theory of logical relations for Dependent Type Theory (DTT) with β η-equality which guarantees that any valid logical relation satisfies the Basic Lemma. Our definition is syntactic and reflective in the sense that a relation at a type is represented as a DTT type family but also permits expressing certain semantic definitions. We use the Edinburgh Logical Framework (LF) incarnation of DTT and implement our notion of logical relations in the type-checker Twelf. This enables us to formalize and mechanically decide the validity of logical relation arguments. Furthermore, our implementation includes a module system so that logical relations can be built modularly. We validate our approach by formalizing and verifying several syntactic and semantic meta-theorems in Twelf. Moreover, we show how object languages encoded in DTT can inherit a notion of logical relation from the logical framework.

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A practical module system for LF

Cited by 23 publications

References 17 publications

Change Management for Heterogeneous Development Graphs

Change Management for Heterogeneous Development Graphs

Structural logical relations with case analysis and equality reasoning

Logical relations for a logical framework

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