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Axioms for Recursion in CallbyValue
 HIGHERORDER AND SYMBOLIC COMPUT
, 2001
"... We propose an axiomatization of fixpoint operators in typed callbyvalue programming languages, and give its justifications in two ways. First, it is shown to be sound and complete for the notion of uniform Tfixpoint operators of Simpson and Plotkin. Second, the axioms precisely account for Filins ..."
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Cited by 11 (5 self)
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We propose an axiomatization of fixpoint operators in typed callbyvalue programming languages, and give its justifications in two ways. First, it is shown to be sound and complete for the notion of uniform Tfixpoint operators of Simpson and Plotkin. Second, the axioms precisely account for Filinski's fixpoint operator derived from an iterator (infinite loop constructor) in the presence of firstclass continuations, provided that we define the uniformity principle on such an iterator via a notion of effectfreeness (centrality). We then explain how these two results are related in terms of the underlying categorical structures.
Duality between CallbyName Recursion and CallbyValue Iteration
 In Proc. Computer Science Logic, Springer Lecture Notes in Comput. Sci
, 2001
"... We investigate the duality between callbyname recursion and callbyvalue iteration on the calculi. The duality between callbyname and callbyvalue was first studied by Filinski, and Selinger has studied the categorytheoretic duality on the models of the callbyname calculus and the callby ..."
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Cited by 9 (4 self)
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We investigate the duality between callbyname recursion and callbyvalue iteration on the calculi. The duality between callbyname and callbyvalue was first studied by Filinski, and Selinger has studied the categorytheoretic duality on the models of the callbyname calculus and the callbyvalue one. We extend the callbyname calculus and the callbyvalue one with a fixedpoint operator and an iteration operator, respectively. We show that the dual translations constructed by Selinger can be expanded into our extended calculi, and we also discuss their implications to practical applications.
On the Equational Definition of the Least Prefixed Point
, 2003
"... We propose a method to axiomatize by equations the least pre xed point of an order preserving function. We discuss its domain of application and show that the Boolean Modal Calculus has a complete equational axiomatization. The method relies on the existence of a \closed structure" and its rel ..."
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Cited by 2 (0 self)
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We propose a method to axiomatize by equations the least pre xed point of an order preserving function. We discuss its domain of application and show that the Boolean Modal Calculus has a complete equational axiomatization. The method relies on the existence of a \closed structure" and its relationship to the equational axiomatization of Action Logic is made explicit. The implication operation of a closed strucure is not monotonic in one of its variables; we show that the existence of such a term that does not preserve the order is an essential condition for de ning by equations the least pre xed point. We stress the interplay between closed structures and xed point operators by showing that the theory of Boolean modal algebras is not a conservative extension of the theory of modal algebras. The latter is shown to lack the nite model property.
Hyperfunctions
, 2001
"... this in [KLP01], where a general construction of coalgebra enriched categories is given, motivated mostly by applications in the semantics of processes. (Categories of resumptions and hyperfunctions are the simplest examples of the construction.) While the semantic relevance and programming potent ..."
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Cited by 1 (1 self)
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this in [KLP01], where a general construction of coalgebra enriched categories is given, motivated mostly by applications in the semantics of processes. (Categories of resumptions and hyperfunctions are the simplest examples of the construction.) While the semantic relevance and programming potential of hyperfunctions are still unclear, their conceptual simplicity and mathematical attraction call for a further investigation. In what follows we summarize what we have discovered so far. The rst thing to look at is the relationship between [A; B] ) A and [B; A]. One would expect an isomorphism, but it does not follow automatically. Instead, there is only a map in one direction AB : ([B; A] ) B) ! [A; B] the anamorphism corresponding to a simple H A;B coalgebra structure on [B; A] )<F9.93