arXiv subjects

Nicolas Ratier

Publications and source records attributed to Nicolas Ratier.

2 recordsLinked to original sources

arXiv2021

Unification and combination of a class of traversal strategies made with pattern matching and fixed-points

Motivated by an ongoing project on computer aided derivation of asymptotic models governed by partial differential equations, we introduce a class of term transformations that consists of traversal strategies and insertion of contexts. We define unification and combination operations on this class which amount to merging transformations in order to obtain more complex ones. We show that the unification and combination operations enjoy nice algebraic properties like associativity, congruence and the existence of neutral elements. The main part of this paper is devoted to proving that the unification and combination operations are correct.

cs.LO↗

arXiv2019

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

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.

cs.LO↗