     Implementation in ACL2 of Well-Founded Polynomial Orderings

The code under this directory explains the ideas behind section 3 in
an abstract setting, hiding implementation details and properties
which are not detailed in the corresponding paper. It has been tested
under ACL2 2.6/GCL 2.4.

* *.acl2:

Package definitions (TER, MON, UPOL and NPOL) and certification commands.

* term.lisp:

Terms (TER package). An encapsulation of the term ordering, the
ordinal embedding and their properties (mainly the well-foundedness of
the term ordering). See [1] for implementation details.

* monomial.lisp:

Monomials (MON package). The monomial ordering, the ordinal embedding
and their properties (mainly the well-foundedness of the monomial
ordering.

* upol.lisp:

Unnormalized polynomials (UPOL package). It just implements the
recognizers for unnormalized polynomials and objects in normal
form. The remaining functions of the polynomial encapsulation
presented in section 2 are not needed to implement the polynomial
ordering.

* ordinal-ordering.lisp:

Some useful theorems about the ordinal ordering, e0-ord-<. It is
proved that e0-ord-< is a partial strict order.

* npol-ordering-1.lisp:

Normalized polynomials (NPOL package). It explains how the monomial
ordering is lifted to normalized polynomials. It is assumed that the
monomial ordinal embedding does not produce zero.

* npol-ordering-2.lisp:

Normalized polynomials (NPOL package). It explains how the monomial
ordering is lifted to normalized polynomials. In this case it is not
assumed that the monomial ordinal embedding is not zero. It is shown
that it is always possible to build a modified ordinal embedding
holding this property without imposing any additional constraint. This
approach has the advantage of separating two concerns: the development
of monomial orderings and the development of induced polynomial
orderings.

Encapsulated events are developed in (event names may have changed):

[1] Medina Bulo, I., Alonso Jiménez, J. A., Palomo Lozano, F.:
    Automatic Verification of Polynomial Rings Fundamental Properties in ACL2.  
    The University of Texas at Austin, Department of Computer Sciences.	
    Technical Report 0029 (2000)

Inmaculada Medina Bulo		Francisco Palomo Lozano
inmaculada.medina@uca.es	francisco.palomo@uca.es
