Introduction to higher order categorical logic
Introduction to higher order categorical logic
Axioms for Recursion in Call-by-Value
Higher-Order and Symbolic Computation
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
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 bi-parameterized family of operators. In this paper, we study these bi-parameterized 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 case, we study parameterizations of uniform fixed-point operators on control categories, and show bijective correspondences between parameterized fixed-point operators and non-parameterized ones under uniformity conditions.