by J. M. Boyle, T. J. Harmer and V. L. Winter
In E. Arge, A.M. Bruaset and H.P. Langtangen (eds.) Modern Software Tools in Scientific Computing pp 353-372, Birkhäuser, 1997
TAMPR stands for Transformation Assisted Multiple Program Realisation System. The TAMPR system, which has been in use since the seventies, is designed for the derivation of efficient implementations from a specification through transformations, in particular in the domain of numerical programming.
A TAMPR specification consists of a series of rewrite rules. The TAMPR rewrite engine applies rewrite rules exhaustively to reach a canonical form. The problem of non-termination caused by rules that are each others inverses is solved in TAMPR by organizing a large transformation into a sequence of consecutive canonicalizations under different sets of rewrite rules. Typically such a sequence starts with several preparatory steps that bring the program in the right form, followed by the pivotal step which achieves the actual transformation, followed by some post-processing.
In the paper this is illustrated with the transformation
from a polynomial in y:
(x^2 + 2x + 1)y^2 + (x^2 - 9)y - (20x^2 + 18x - 18)to the equivalent polynomial in
x
(y^2 + y - 20)x^2 + (2y^2 - 18)x + (y^2 - 9y + 18)This is achieved by means of the following pipeline of canonicalizations:
sum-of-monomonials; x-commuted-to-right; like-powers-collected; x-factored-out(Note that the paper uses a different notation for this.) The
sum-of-monomonials transforms the polynomial into
x^2y^2 + 2xy^2 + y^2 + x^2y -9y -20x^2 - 18x + 18By commuting the multiplications, the
x-commuted-to-right
canonical form is achieved:
y^2x^2 + 2y^2x + y^2 + yx^2 -9y -20x^2 - 18x + 18The
like-powers-collected canonical form commutes
the additions to bring monomonials with the same power of $x$
together:
y^2x^2 + yx^2 - 20x^2 + 2y^2x - 18x + y^2 -9y + 18Finally, by factoring out the powers of
x, the desired form is
reached.