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From Settheoretic Coinduction to Coalgebraic Coinduction: some results, some problems
, 1999
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Eager normal form bisimulation
 In Proc. 20th Annual IEEE Symposium on Logic in Computer Science
, 2005
"... Abstract. Normal form bisimulation is a powerful theory of program equivalence, originally developed to characterize LévyLongo tree equivalence and Boehm tree equivalence. It has been adapted to a range of untyped, higherorder calculi, but types have presented a difficulty. In this paper, we prese ..."
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Cited by 14 (4 self)
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Abstract. Normal form bisimulation is a powerful theory of program equivalence, originally developed to characterize LévyLongo tree equivalence and Boehm tree equivalence. It has been adapted to a range of untyped, higherorder calculi, but types have presented a difficulty. In this paper, we present an account of normal form bisimulation for types, including recursive types. We develop our theory for a continuationpassing style calculus, JumpWithArgument (JWA), where normal form bisimilarity takes a very simple form. We give a novel congruence proof, based on insights from game semantics. A notable feature is the seamless treatment of etaexpansion. We demonstrate the normal form bisimulation proof principle by using it to establish a syntactic minimal invariance result and the uniqueness of the fixed point operator at each type.
A typed storepassing translation for general references
"... We present a storepassing translation of System F with general references into an extension of System Fω with certain wellbehaved recursive kinds. This provides a purely syntactic account of a possible worlds model. 1 ..."
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Cited by 4 (0 self)
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We present a storepassing translation of System F with general references into an extension of System Fω with certain wellbehaved recursive kinds. This provides a purely syntactic account of a possible worlds model. 1
On the observational theory of the CPScalculus
"... We study the observational theory of Thielecke’s CPScalculus, a distillation of the target language of ContinuationPassing Style transforms. We define a labelled transition system for the CPScalculus from which we derive a (weak) labelled bisimilarity that completely characterises Morris’ context ..."
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We study the observational theory of Thielecke’s CPScalculus, a distillation of the target language of ContinuationPassing Style transforms. We define a labelled transition system for the CPScalculus from which we derive a (weak) labelled bisimilarity that completely characterises Morris’ contextequivalence. We prove a context lemma showing that Morris’ contextequivalence coincides with a simpler contextequivalence closed under a smaller class of contexts. Then we profit of the determinism of the CPScalculus to give a simpler labelled characterisation of Morris’ equivalence, in the style of Abramsky’s applicative bisimilarity. We enhance our bisimulation proofmethods with upto bisimilarity and upto context proof techniques. We use our bisimulation proof techniques to investigate a few algebraic properties on diverging terms that cannot be proved using the original axiomatic semantics of the CPScalculus. Finally, we prove the full abstraction of Thielecke’s encoding of the CPScalculus into a fragment of Fournet and Gonthier’s Joincalculus with single pattern definitions.
Abstract A Complete, CoInductive Syntactic Theory of Sequential Control and State
"... We present a new coinductive syntactic theory, eager normal form bisimilarity, for the untyped callbyvalue lambda calculus extended with continuations and mutable references. We demonstrate that the associated bisimulation proof principle is easy to use and that it is a powerful tool for proving ..."
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We present a new coinductive syntactic theory, eager normal form bisimilarity, for the untyped callbyvalue lambda calculus extended with continuations and mutable references. We demonstrate that the associated bisimulation proof principle is easy to use and that it is a powerful tool for proving equivalences between recursive imperative higherorder programs. The theory is modular in the sense that eager normal form bisimilarity for each of the calculi extended with continuations and/or mutable references is a fully abstract extension of eager normal form bisimilarity for its subcalculi. For each calculus, we prove that eager normal form bisimilarity is a congruence and is sound with respect to contextual equivalence. Furthermore, for the calculus with both continuations and mutable references, we show that eager normal form bisimilarity is complete: it coincides with contextual equivalence. Categories and Subject Descriptors D.3.3 [Programming Languages]:
A lambda calculus for D∞
, 2002
"... We define an extension of lambda calculus which is fully abstract for Scott's D_infinitymodels. We do so by constructing an infinitary lambda calculus which not only has the confluence property, but also is normalising: every term has its infinity etaBöhm tree as unique normal form. The exten ..."
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We define an extension of lambda calculus which is fully abstract for Scott's D_infinitymodels. We do so by constructing an infinitary lambda calculus which not only has the confluence property, but also is normalising: every term has its infinity etaBöhm tree as unique normal form. The extension incorporates...
Bisimulations upto: beyond firstorder transition systems
"... Abstract. The bisimulation proof method can be enhanced by employing ‘bisimulations upto ’ techniques. A comprehensive theory of such enhancements has been developed for firstorder (i.e., CCSlike) labelled transition systems (LTSs) and bisimilarity, based on the notion of compatible function for ..."
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Abstract. The bisimulation proof method can be enhanced by employing ‘bisimulations upto ’ techniques. A comprehensive theory of such enhancements has been developed for firstorder (i.e., CCSlike) labelled transition systems (LTSs) and bisimilarity, based on the notion of compatible function for fixedpoint theory. We transport this theory onto languages whose bisimilarity and LTS go beyond those of firstorder models. The approach consists in exhibiting fully abstract translations of the more sophisticated LTSs and bisimilarities onto the firstorder ones. This allows us to reuse directly the large corpus of upto techniques that are available on firstorder LTSs. The only ingredient that has to be manually supplied is the compatibility of basic upto techniques that are specific to the new languages. We investigate the method on the picalculus, the λcalculus, and a (callbyvalue) λcalculus with references. 1
Head Normal Form Bisimulation for Pairs and the λµCalculus (Extended Abstract)
"... Böhm tree equivalence up to possibly infinite η expansion for the pure λcalculus can be characterized as a bisimulation equivalence. We call this coinductive syntactic theory extensional head normal form bisimilarity and in this paper we extend it to the λFPcalculus (the λcalculus with functiona ..."
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Böhm tree equivalence up to possibly infinite η expansion for the pure λcalculus can be characterized as a bisimulation equivalence. We call this coinductive syntactic theory extensional head normal form bisimilarity and in this paper we extend it to the λFPcalculus (the λcalculus with functional and surjective pairing) and to two untyped variants of Parigot’s λµcalculus. We relate the extensional head normal form bisimulation theories for the different calculi via Fujita’s extensional CPS transform into the λFPcalculus. We prove that extensional hnf bisimilarity is fully abstract for the pure λcalculus by a coinductive reformulation of Barendregt’s proof for Böhm tree equivalence up to possibly infinite η expansion. The proof uses the socalled Böhmout technique from Böhm’s proof of the Separation Property for the λcalculus. Moreover, we extend the full abstraction result to extensional hnf bisimilarity for the λFPcalculus. For the “standard ” λµcalculus, the Separation Property fails, as shown by David and Py, and for the same reason extensional hnf bisimilarity is not fully abstract. However, an “extended ” variant of the λµcalculus satisfies the Separation Property, as shown by Saurin, and for this extended λµcalculus. 1
A typed storepassing . . .
, 2011
"... We present a storepassing translation of System F with general references into an extension of System Fω with certain wellbehaved recursive kinds. This seems to be the first typepreserving storepassing translation for general references. It can be viewed as a purely syntactic account of a possib ..."
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We present a storepassing translation of System F with general references into an extension of System Fω with certain wellbehaved recursive kinds. This seems to be the first typepreserving storepassing translation for general references. It can be viewed as a purely syntactic account of a possible worlds model.