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Mechanized metatheory for the masses: The POPLmark challenge
 In Theorem Proving in Higher Order Logics: 18th International Conference, number 3603 in LNCS
, 2005
"... Abstract. How close are we to a world where every paper on programming languages is accompanied by an electronic appendix with machinechecked proofs? We propose an initial set of benchmarks for measuring progress in this area. Based on the metatheory of System F<:, a typed lambdacalculus with se ..."
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Cited by 145 (14 self)
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Abstract. How close are we to a world where every paper on programming languages is accompanied by an electronic appendix with machinechecked proofs? We propose an initial set of benchmarks for measuring progress in this area. Based on the metatheory of System F<:, a typed lambdacalculus with secondorder polymorphism, subtyping, and records, these benchmarks embody many aspects of programming languages that are challenging to formalize: variable binding at both the term and type levels, syntactic forms with variable numbers of components (including binders), and proofs demanding complex induction principles. We hope that these benchmarks will help clarify the current state of the art, provide a basis for comparing competing technologies, and motivate further research. 1
The Primitive Proof Theory of the λCalculus
, 2003
"... (“homme à demi tourné à droite”, “vase de cristal”, “montagne”) ..."
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Cited by 7 (2 self)
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(“homme à demi tourné à droite”, “vase de cristal”, “montagne”)
Formalizing proofs in Isabelle/HOL of equational properties for the lambdacalculus using onesorted variable names. Honours dissertation, University of Edinburgh; available from the author’s homepage, 2001. 29 Rod Burstall. Proving properties of programs
 The Computer Journal
, 1967
"... Abstract: We present the Isabelle/HOL formalisation of some key equational properties of the untyped λcalculus with onesorted variable names. Existing machine formalisations of λcalculus proofs typically rely on alternative representations and/or proof principles to facilitate mechanization and ..."
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Cited by 2 (2 self)
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Abstract: We present the Isabelle/HOL formalisation of some key equational properties of the untyped λcalculus with onesorted variable names. Existing machine formalisations of λcalculus proofs typically rely on alternative representations and/or proof principles to facilitate mechanization and we briefly account for these works. Our own development remains faithful to the standard textbook presentation and the usual penandpaper proof practices; we reason purely inductively over the standard firstorder syntax of the calculus, using only primitive proof principles of the syntax and the reduction relations under consideration. We prove the confluence property of the λcalculus at the raw syntactic level and derive confluence of the real λcalculus (the structural collapse onto equivalence classes of the raw calculus) via a general result about abstract rewrite systems which we also formalise. We then show a technical property of the residual theory of the calculus which suggests the general applicability of the method to other equational properties of the calculus. Finally, we make some prooftechnical observations pertaining to the extent to which
Structural Induction and the λCalculus
"... Abstract. We consider formal provability with structural induction and related proof principles in the λcalculus presented with firstorder abstract syntax over onesorted variable names. As well as summarising and elaborating on earlier, formally verified proofs (in Isabelle/HOL) of the relative re ..."
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Abstract. We consider formal provability with structural induction and related proof principles in the λcalculus presented with firstorder abstract syntax over onesorted variable names. As well as summarising and elaborating on earlier, formally verified proofs (in Isabelle/HOL) of the relative renamingfreeness of βresidual theory and βconfluence, we also present proofs of ηconfluence, βηconfluence, the strong weaklyfinite βdevelopment (aka residualcompletion) property, residual βconfluence, ηoverβpostponement, and notably βstandardisation. In the latter case, the known proofs fail in instructive ways. Interestingly, our uniform proof methodology, which has relevance beyond the λcalculus, properly contains penandpaper proof practices in a precise sense. The proof methodology also makes precise what is the full algebraic proof burden of the considered results, which we, moreover, appear to be the first to resolve. 1
This paper is posted at ScholarlyCommons. http://repository.upenn.edu/cis papers/235Mechanized Metatheory for the Masses: The PoplMark Challenge
"... Abstract. How close are we to a world where every paper on programming languages is accompanied by an electronic appendix with machinechecked proofs? We propose an initial set of benchmarks for measuring progress in this area. Based on the metatheory of System F<:, a typed lambdacalculus with se ..."
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Abstract. How close are we to a world where every paper on programming languages is accompanied by an electronic appendix with machinechecked proofs? We propose an initial set of benchmarks for measuring progress in this area. Based on the metatheory of System F<:, a typed lambdacalculus with secondorder polymorphism, subtyping, and records, these benchmarks embody many aspects of programming languages that are challenging to formalize: variable binding at both the term and type levels, syntactic forms with variable numbers of components (including binders), and proofs demanding complex induction principles. We hope that these benchmarks will help clarify the current state of the art, provide a basis for comparing competing technologies, and motivate further research. 1
Properties for the λCalculus using OneSorted Variable Names
, 2001
"... Abstract: We present the Isabelle/HOL formalisation of some key equational properties of the untyped λcalculus with onesorted variable names. Existing machine formalisations of λcalculus proofs typically rely on alternative representations and/or proof principles to facilitate mechanization and w ..."
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Abstract: We present the Isabelle/HOL formalisation of some key equational properties of the untyped λcalculus with onesorted variable names. Existing machine formalisations of λcalculus proofs typically rely on alternative representations and/or proof principles to facilitate mechanization and we briefly account for these works. Our own development remains faithful to the standard textbook presentation and the usual penandpaper proof practices; we reason purely inductively over the standard firstorder syntax of the calculus, using only primitive proof principles of the syntax and the reduction relations under consideration. We prove the confluence property of the λcalculus at the raw syntactic level and derive confluence of the real λcalculus (the structural collapse onto equivalence classes of the raw calculus) via a general result about abstract rewrite systems which we also formalise. We then show a technical property of the residual theory of the calculus which suggests the general applicability of the method to other equational properties of the calculus. Finally, we make some prooftechnical observations pertaining to the extent to which
A Formalised FirstOrder . . .
, 2002
"... We present the titular proof development that has been verified in Isabelle/HOL. As a first, the proof is conducted exclusively by the primitive proof principles of the standard syntax and of the considered reduction relations: the naive way, so to speak. Curiously, the Barendregt Variable Conventio ..."
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We present the titular proof development that has been verified in Isabelle/HOL. As a first, the proof is conducted exclusively by the primitive proof principles of the standard syntax and of the considered reduction relations: the naive way, so to speak. Curiously, the Barendregt Variable Convention takes on a central technical role in the proof. We also show (i) that our presentation of the λcalculus coincides with Curry’s and Hindley’s when terms are considered equal up to αequivalence and (ii) that the confluence properties of all considered systems are equivalent.
General
"... I describe the mechanisation in HOL of some basic λcalculus theory, using the axioms proposed by Gordon and Melham [4]. Using these as a foundation, I mechanised the proofs from Chapters 2 and 3 of Hankin [5] (equational theory and reduction theory), followed by most of Chapter 11 of Barendregt [2 ..."
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I describe the mechanisation in HOL of some basic λcalculus theory, using the axioms proposed by Gordon and Melham [4]. Using these as a foundation, I mechanised the proofs from Chapters 2 and 3 of Hankin [5] (equational theory and reduction theory), followed by most of Chapter 11 of Barendregt [2] (residuals, finiteness of developments, and the standardisation theorem). I discuss the ease of use of the GordonMelham axioms, as well as the mechanical support I implemented to make some basic tasks more straightforward.
Formalizing Proofs in Isabelle/HOL of Equational Properties for the *Calculus using OneSorted Variable Names
, 2001
"... Acknowledgements My sincerest thanks are due in the first instance to my supervisor, Ren'e Vestergaard, for innumerable pieces of advice (by turns both practical and cryptic), for technical and moral support, for important references, and not least for feeding me for a week during my visit to J ..."
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Acknowledgements My sincerest thanks are due in the first instance to my supervisor, Ren'e Vestergaard, for innumerable pieces of advice (by turns both practical and cryptic), for technical and moral support, for important references, and not least for feeding me for a week during my visit to JeanYves Girard's group in Marseilles in March this year (which he made possible).