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A complete, coinductive syntactic theory of sequential control and state
 In POPL
, 2007
"... 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.
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 15 (5 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.
Themes in Final Semantics
 Dipartimento di Informatica, Università di
, 1998
"... C'era una volta un re seduto in canap`e, che disse alla regina raccontami una storia. La regina cominci`o: "C'era una volta un re seduto in canap`e ..."
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Cited by 6 (2 self)
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C'era una volta un re seduto in canap`e, che disse alla regina raccontami una storia. La regina cominci`o: &quot;C'era una volta un re seduto in canap`e
A Uniform Syntactical Method for Proving Coinduction Principles in lambdacalculi
 In: Proc. of TAPSOFT'97
, 1997
"... . Coinductive characterizations of various observational congruences which arise in the semantics of calculus, when terms are evaluated according to various reduction strategies, are discussed. We analyze and extend to nonlazy strategies, both deterministic and nondeterministic, Howe's cong ..."
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Cited by 4 (3 self)
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. Coinductive characterizations of various observational congruences which arise in the semantics of calculus, when terms are evaluated according to various reduction strategies, are discussed. We analyze and extend to nonlazy strategies, both deterministic and nondeterministic, Howe's congruence candidate method for proving the coincidence of the applicative (bisimulation) and the contextual equivalences. This purely syntactical method is based itself on a coinductive argument. Introduction This paper is part of a general project aiming at finding elementary proof principles for reasoning rigorously on infinite computational objects, see [4, 9] for the case of higher order functions, and [8] for the case of higher order processes. In this paper, as in [4, 9], we focus on the behaviour of terms when these are evaluated according to various reduction strategies. We address the problem of showing the coincidence of the applicative (bisimulation) equivalence with the observational ...
Relational Reasoning about Functions and Nondeterminism
, 1998
"... Reproduction of all or part of this workis permitted for educational or research use on condition that this copyright notice isincluded in any copy. See back inner page for a list of recent BRICS Dissertation Series publications. Copies may be obtained by contacting: ..."
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Reproduction of all or part of this workis permitted for educational or research use on condition that this copyright notice isincluded in any copy. See back inner page for a list of recent BRICS Dissertation Series publications. Copies may be obtained by contacting:
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]:
SN Combinators and Partial Combinatory Algebras
"... . We introduce an intersection typing system for combinatory logic, such that a term of combinatory logic is typeable iff it is sn. We then prove the soundness and completeness for the class of partial combinatory algebras. Let F be the class of nonempty filters which consist of types. Then F is an ..."
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. We introduce an intersection typing system for combinatory logic, such that a term of combinatory logic is typeable iff it is sn. We then prove the soundness and completeness for the class of partial combinatory algebras. Let F be the class of nonempty filters which consist of types. Then F is an extensional nontotal partial combinatory algebra. Furthermore, it validates the strongest consistent equality of the set of sn terms of combinatory logic. By F , we can solve BethkeKlop's question; "find a suitable representation of the finally collapsed partial combinatory algebra of P ". Here, P is a partial combinatory algebra, and is the set of closed sn terms of combinatory logic modulo the inherent equality. Our solution is the following: the finally collapsed partial combinatory algebra of P is representable in F . To be more precise, it is isomorphically embeddable into F . 1 Introduction Combinatory logic (cl, for short) is a simple rewriting system where the terms (clterms, fo...