# Unification and combination of iterative insertion strategies with rudimentary traversals and failure

## TL;DR

This paper presents a new, general framework for combining navigation strategies and context insertions in term extensions, with properties like associativity and idempotency, aimed at aiding multiscale PDE modeling.

## Contribution

It introduces a novel, algebraic combination operation for term extensions that is associative, neutral, and idempotent, independent of specific application semantics.

## Key findings

- The combination operation is associative and admits a neutral element.
- The class of extensions is closed under the combination operation.
- The framework is applicable to multiscale PDE model derivation.

## Abstract

We introduce a new class of extensions of terms that consists in navigation strategies and insertion of contexts. We introduce an operation of combination on this class which is associative, admits a neutral element and so that each extension is idempotent. The class of extension is also shown to be closed by combination, with a constructive proof. This new framework is general and independent of any application semantics. However it has been introduced for the kernel of a software tool which aims at aiding derivation of multiscale partial differential equation models.