Preordered forests, packed words and contraction algebras

Cotransforming Grammars with Shared Packed Parse Forests

SPPF (shared packed parse forest) is the best known graph representation of a parse forest (family of related parse trees) used in parsing with ambiguous/conjunctive grammars. Systematic general purpose transformations of SPPFs have never been investigated and are considered to be an open problem in software language engineering. In this paper, we motivate the necessity of having a transformati...

Coupled Transformations of Shared Packed Parse Forests

SPPF (shared packed parse forest) is the best known graph representation of a parse forest (family of related parse trees) used in parsing with ambiguous/conjunctive grammars. Systematic general purpose transformations of SPPFs have never been investigated and are considered to be an open problem in software language engineering. In this paper, we motivate the necessity of having a transformati...

Factorisation Forests for Infinite Words

Contraction Algebras and Unification of (Infinite) Terms

We introduce the class of contraction algebras in which the algebra of infinite and finite terms is free over the set of variables. We develop a general theory of systems of equations at the level of categories in close connection with the Banach Principle of Contraction. Two applications of this theory are given. The first is the case of regular systems of equations with arbitrary terms. The s...

Lyndon Words, Free Algebras and Shuffles

1. Introduction. A Lyndon word is a primitive word which is minimum in its conjugation class, for the lexicographical ordering. These words have been introduced by Lyndon in order to find bases of the quotients of the lower central series of a free group or, equivalently, bases of the free Lie algebra [2], [7]. They have also many combinatorial properties, with applications to semigroups, pi-ri...