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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 20 (8 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.
Head normal form bisimulation for pairs and the λμcalculus (extended abstract
 In Proc. 21th Annual IEEE Symposium on Logic in Computer Science
, 2006
"... 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 functi ..."
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Cited by 7 (3 self)
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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
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.
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
Two Values Passing CPS Transformation for CallbyName Calculus with Constants
"... Yu G, Liu XX. Two values passing CPS transformation for callbyname calculus with constants. Journal of Software, 2008,19(10):2508−2516. ..."
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Yu G, Liu XX. Two values passing CPS transformation for callbyname calculus with constants. Journal of Software, 2008,19(10):2508−2516.