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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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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.
Relational parametricity and control
 Logical Methods in Computer Science
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Semantics of linear continuationpassing in callbyname
 In Proc. Functional and Logic Programming, Springer Lecture Notes in Comput. Sci
, 2004
"... Abstract. We propose a semantic framework for modelling the linear usage of continuations in typed callbyname programming languages. On the semantic side, we introduce a construction for categories of linear continuations, which gives rise to cartesian closed categories with “linear classical disj ..."
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Cited by 6 (4 self)
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Abstract. We propose a semantic framework for modelling the linear usage of continuations in typed callbyname programming languages. On the semantic side, we introduce a construction for categories of linear continuations, which gives rise to cartesian closed categories with “linear classical disjunctions ” from models of intuitionistic linear logic with sums. On the syntactic side, we give a simply typed callbyname λµcalculus in which the use of names (continuation variables) is restricted to be linear. Its semantic interpretation into a category of linear continuations then amounts to the callbyname continuationpassing style (CPS) transformation into a linear lambda calculus with sum types. We show that our calculus is sound for this CPS semantics, hence for models given by the categories of linear continuations.
Parameterizations and FixedPoint Operators on Control Categories
 Fundam. Inform
, 2005
"... The #calculus features both variables and names, together with their binding mechanisms. This means that constructions on open terms are necessarily parameterized in two di#erent ways for both variables and names. Semantically, such a construction must be modeled by a biparameterized family of ope ..."
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The #calculus features both variables and names, together with their binding mechanisms. This means that constructions on open terms are necessarily parameterized in two di#erent ways for both variables and names. Semantically, such a construction must be modeled by a biparameterized family of operators. In this paper, we study these biparameterized operators on Selinger's categorical models of the # calculus called control categories. The overall development is analogous to that of Lambek's functional completeness of cartesian closed categories via polynomial categories. As a particular and important case, we study parameterizations of uniform fixedpoint operators on control categories, and show bijective correspondences between parameterized fixedpoint operators and nonparameterized ones under uniformity conditions.
Callbyname and callbyvalue in normal modal logic
"... Abstract. This paper provides a callbyname and a callbyvalue calculus, both of which have a CurryHoward correspondence to the minimal normal logic K. The calculi are extensions of the λµcalculi, and their semantics are given by CPS transformations into a calculus corresponding to the intuition ..."
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Abstract. This paper provides a callbyname and a callbyvalue calculus, both of which have a CurryHoward correspondence to the minimal normal logic K. The calculi are extensions of the λµcalculi, and their semantics are given by CPS transformations into a calculus corresponding to the intuitionistic fragment of K. The duality between callbyname and callbyvalue with modalities is investigated in our calculi. 1
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"... We study the equational theory of Parigot’s secondorder λµcalculus in connection with a callbyname continuationpassing style (CPS) translation into a fragment of the secondorder λcalculus. It is observed that the relational parametricity on the target calculus induces a natural notion of equiv ..."
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We study the equational theory of Parigot’s secondorder λµcalculus in connection with a callbyname continuationpassing style (CPS) translation into a fragment of the secondorder λcalculus. It is observed that the relational parametricity on the target calculus induces a natural notion of equivalence on the λµterms. On the other hand, the unconstrained relational parametricity on the λµcalculus turns out to be inconsistent with this CPS semantics. Following these facts, we propose to formulate the relational parametricity on the λµcalculus in a constrained way, which might be called “focal parametricity”. 1.
Axioms for Recursion in CallbyValue (Extended Abstract)
, 2001
"... ) Masahito Hasegawa and Yoshihiko Kakutani Research Institute for Mathematical Sciences, Kyoto University {hassei,kakutani}@kurims.kyotou.ac.jp Abstract. We propose an axiomatization of fixpoint operators in typed callbyvalue programming languages, and give its justifications in two ways. First ..."
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) Masahito Hasegawa and Yoshihiko Kakutani Research Institute for Mathematical Sciences, Kyoto University {hassei,kakutani}@kurims.kyotou.ac.jp Abstract. 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 T fixpoint 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 controls, provided that we define the uniformity principle on such an iterator via a notion of e#ectfreeness (centrality). We also investigate how these two results are related in terms of the underlying categorical models. 1 Introduction While the equational theories of fixpoint operators in callbyname programming languages and in domain theory have been extensively studied and now there are some canonical axiomatizations (inc...