Quadratic Functionals of Second Order

Principal Quadratic Functionals and Self-Adjoint Second-Order Differential Equations.

On Monadic Parametricity of Second-Order Functionals

How can one rigorously specify that a given ML functional f : (int → int) → int is pure, i.e., f produces no computational effects except those produced by evaluation of its functional argument? In this paper, we introduce a semantic notion of monadic parametricity for second-order functionals which is a form of purity. We show that every monadically parametric f admits a question-answer strate...

Monadic Parametricity of Second-Order Functionals

A Representation Theorem for Second-Order Functionals

Representation theorems relate seemingly complex objects to concrete, more tractable ones. In this paper, we take advantage of the abstraction power of category theory and provide a datatypegeneric representation theorem. More precisely, we prove a representation theorem for a wide class of second-order functionals which are polymorphic over a class of functors. Types polymorphic over a class o...

Second order expansion of action functionals of noncommutative gauge theories

Field theory and gauge theory on noncommutative spaces have been established as their own areas of research in recent years. The hope prevails that a noncommutative gauge theory will deliver testable experimental predictions and will thus be a serious candidate for an extension of the Standard Model. This note contains the results for expanded gauge theory actions on a noncommutative space with...