Bases for parametrized iterativity

Bases for parametrized iterativity

Parametrized iterativity of an algebra means the existence of unique solutions of all finitary recursive systems of equations where recursion is allowed to use only some variables (chosen as a parameter). We show how such algebras can be introduced in an arbitrary category A by employing a base, i.e., an operation interpreting objects of A as monads on A. For every base we prove that free base ...

Complete Iterativity for Algebras with Effects

Completely iterative algebras (cias) are those algebras in which recursive equations have unique solutions. In this paper we study complete iterativity for algebras with computational effects (described by a monad). First, we prove that for every analytic endofunctor on Set there exists a canonical distributive law over any commutative monad M , hence a lifting of that endofunctor to the Kleisl...

Symbolic Analysis for Boundary Problems: From Rewriting to Parametrized Gröbner Bases

We review our algebraic framework for linear boundary problems (concentrating on ordinary differential equations). Its starting point is an appropriate algebraization of the domain of functions, which we have named integro-differential algebras. The algebraic treatment of boundary problems brings up two new algebraic structures whose symbolic representation and computational realization is base...

The Nature of Iterativity: Evidence from Lango

Parametrized Types for C++

Type parameterization is the ability to defrne a type in terms of another, unspecifled, type. Versions of the parameterized type may then be created for several particular parameter types. A language supporting type parameterization allows specification ofgeneral container types such as list, vector, and associative array where the specific type of the elements is left as a parameter. Thus, a p...