Results 1 
6 of
6
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 secon ..."
Abstract

Cited by 136 (15 self)
 Add to MetaCart
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”) ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
(“homme à demi tourné à droite”, “vase de cristal”, “montagne”)
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 ..."
Abstract
 Add to MetaCart
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 ..."
Abstract
 Add to MetaCart
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.
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 secon ..."
Abstract
 Add to MetaCart
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
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 ..."
Abstract
 Add to MetaCart
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