Introduction to higher order categorical logic
Introduction to higher order categorical logic
Axiomatic domain theory in categories of partial maps
Axiomatic domain theory in categories of partial maps
Models of Sharing Graphs: A Categorical Semantics of Let and Letrec
Models of Sharing Graphs: A Categorical Semantics of Let and Letrec
Uncertain Programming
Axioms for Recursion in Call-by-Value
Higher-Order and Symbolic Computation
Polarized proof-nets and λµ-calculus
Theoretical Computer Science
Lambda-My-Calculus: An Algorithmic Interpretation of Classical Natural Deduction
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
FoSSaCS '02 Proceedings of the 5th International Conference on Foundations of Software Science and Computation Structures
Duality between Call-by-Name Recursion and Call-by-Value Iteration
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
Complete Axioms for Categorical Fixed-Point Operators
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
Control categories and duality: on the categorical semantics of the lambda-mu calculus
Mathematical Structures in Computer Science
Premonoidal categories and notions of computation
Mathematical Structures in Computer Science
Polarized proof nets with cycles and fixpoints semantics
TLCA'03 Proceedings of the 6th international conference on Typed lambda calculi and applications
Parameters And Parametrization In Specification, Using Distributive Categories
Fundamenta Informaticae
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The λμ-calculus features both variables and names together with their binding mechanisms. This means that constructions on open terms are necessarily parameterized in two different 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 λμ-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 application of such consideration, we study the parameterizations of uniform fixed-point operators on control categories. We show a bijective correspondence between biparameterized fixed-point operators and nonparameterized ones under the uniformity conditions.