A Formalized General Theory of Syntax with Bindings: Extended Version

Gheri, Lorenzo; Popescu, Andrei

doi:10.1007/s10817-019-09522-2

Cited by 12 publications

(24 citation statements)

References 98 publications

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“…We formalize a logic with bound variables, and there is a large body of related work that deals with this issue (e.g. [37,21,7]) and a range of logics and systems with special support for handling bound variables (e.g. [33,34,35]).…”

Section: Related Workmentioning

confidence: 99%

Isabelle’s Metalogic: Formalization and Proof Checker

Nipkow

Roßkopf

2021

Automated Deduction – CADE 28

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Isabelle is a generic theorem prover with a fragment of higher-order logic as a metalogic for defining object logics. Isabelle also provides proof terms. We formalize this metalogic and the language of proof terms in Isabelle/HOL, define an executable (but inefficient) proof term checker and prove its correctness w.r.t. the metalogic. We integrate the proof checker with Isabelle and run it on a range of logics and theories to check the correctness of all the proofs in those theories.

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Section: Related Workmentioning

confidence: 99%

Isabelle’s Metalogic: Formalization and Proof Checker

Nipkow

Roßkopf

2021

Automated Deduction – CADE 28

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show abstract

“…We formalize a logic with bound variables, and there is a large body of related work that deals with this issue (e.g. [36,21,7]) and a range of logics and systems with special support for handling bound variables (e.g. [32,33,34]).…”

Section: Related Workmentioning

confidence: 99%

Isabelle's Metalogic: Formalization and Proof Checker

Nipkow,

Roßkopf

2021

Preprint

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Isabelle is a generic theorem prover with a fragment of higherorder logic as a metalogic for defining object logics. Isabelle also provides proof terms. We formalize this metalogic and the language of proof terms in Isabelle/HOL, define an executable (but inefficient) proof term checker and prove its correctness w.r.t. the metalogic. We integrate the proof checker with Isabelle and run it on a range of logics and theories to check the correctness of all the proofs in those theories. ⋆ Supported by Wirtschaftsministerium Bayern under DIK-2002-0027//DIK0185/03 and DFG GRK 2428 ConVeY

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“…However, in the papers describing these applications we have emphasized neither (1) the general theory underlying our framework nor (2) the framework's deployment to support reasoning within these applications. The first gap has been filled in a recent paper [47]. The second gap is being filled by the current paper, which is intended as a companion to [47].…”

Section: Introductionmentioning

confidence: 98%

“…The first gap has been filled in a recent paper [47]. The second gap is being filled by the current paper, which is intended as a companion to [47].…”

Section: Introductionmentioning

confidence: 98%

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Case Studies in Formal Reasoning About Lambda-Calculus: Semantics, Church-Rosser, Standardization and HOAS

Gheri¹,

Popescu²

2021

Preprint

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We have previously published the Isabelle/HOL formalization of a general theory of syntax with bindings. In this companion paper, we instantiate the general theory to the syntax of lambda-calculus and formalize the development leading to several fundamental constructions and results: sound semantic interpretation, the Church-Rosser and standardization theorems, and higher-order abstract syntax encoding. For Church-Rosser and standardization, our work covers both the call-by-name and call-by-value versions of the calculus, following classic papers by Takahashi and Plotkin. During the formalization, we were able to stay focused on the high-level ideas of the development-thanks to the arsenal provided by our general theory: a wealth of basic facts about the substitution, swapping and freshness operators, as well as recursive-definition and reasoning principles, including a specialization to semantic interpretation of syntax.

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A Formalized General Theory of Syntax with Bindings: Extended Version

Abstract: including the URL of the record and the reason for the withdrawal request.Noname manuscript No.

Cited by 12 publications

References 98 publications

Isabelle’s Metalogic: Formalization and Proof Checker

Isabelle’s Metalogic: Formalization and Proof Checker

Isabelle's Metalogic: Formalization and Proof Checker

Case Studies in Formal Reasoning About Lambda-Calculus: Semantics, Church-Rosser, Standardization and HOAS

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