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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 19 (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.
A universal innocent game model for the Bohm tree lambda theory
 In Computer Science Logic: Proceedings of the 8th Annual Conference on the EACSL
, 1999
"... Abstract. We present a game model of the untyped λcalculus, with equational theory equal to the Böhm tree λtheory B, which is universal (i.e. every element of the model is definable by some term). This answers a question of Di Gianantonio, Franco and Honsell. We build on our earlier work, which us ..."
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Cited by 4 (3 self)
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Abstract. We present a game model of the untyped λcalculus, with equational theory equal to the Böhm tree λtheory B, which is universal (i.e. every element of the model is definable by some term). This answers a question of Di Gianantonio, Franco and Honsell. We build on our earlier work, which uses the methods of innocent game semantics to develop a universal model inducing the maximal consistent sensible theory H ∗. To our knowledge these are the first syntaxindependent universal models of the untyped λcalculus. 1
Processes and Games
, 2003
"... A general theory of computing is important, if we wish to have a common mathematical footing based on which diverse scienti c and engineering eorts in computing are uniformly understood and integrated. A quest for such a general theory may take dierent paths. As a case for one of the possible paths ..."
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Cited by 1 (0 self)
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A general theory of computing is important, if we wish to have a common mathematical footing based on which diverse scienti c and engineering eorts in computing are uniformly understood and integrated. A quest for such a general theory may take dierent paths. As a case for one of the possible paths towards a general theory, this paper establishes a precise connection between a gamebased model of sequential functions by Hyland and Ong on the one hand, and a typed version of the calculus on the other. This connection has been instrumental in our recent eorts to use the calculus as a basic mathematical tool for representing diverse classes of behaviours, even though the exact form of the correspondence has not been presented in a published form. By redeeming this correspondence we try to make explicit a convergence of ideas and structures between two distinct threads of Theoretical Computer Science. This convergence indicates a methodology for organising our understanding on computation and that methodology, we argue, suggests one of the promising paths to a general theory.
On the denotational semantics of the untyped lambdamu calculus
, 2004
"... Starting with the idea of reflexive objects in Selinger’s control categories, we define three different denotational models of Parigot’s untyped lambdamu calculus. The first one is built from an intersection types system for the lambdamu calculus leading to a generalization of Engeler’s model of t ..."
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Starting with the idea of reflexive objects in Selinger’s control categories, we define three different denotational models of Parigot’s untyped lambdamu calculus. The first one is built from an intersection types system for the lambdamu calculus leading to a generalization of Engeler’s model of the untyped lambda calculus. The second model introduces correlation spaces (coming from Girard’s model of classical logic) in the usual coherent model of the untyped lambda calculus. The third model is simply obtained by showing that KerNickauOng’s game model of the untyped lambda calculus is also a model of the untyped lambdamu calculus. 1