On Canonical Forms and Simplification

On Equivalence and Canonical Forms

Decidability of de nitional equality and conversion of terms into canonical form play a central role in the meta-theory of a type-theoretic logical framework. Most studies of de nitional equality are based on a con uent, strongly-normalizing notion of reduction. Coquand has considered a di erent approach, directly proving the correctness of a practical equivalance algorithm based on the shape o...

On Canonical Binary Trilinear Forms

On Apolarity and Generic Canonical Forms

The theory of apolarity was first developed by Clebsch, Lasker, Richw x mond, Sylvester, and Wakeford 10, 17, 20 . They were first interested in studying homogeneous polynomials of degree p and in q variables, and in expressing them as sums of pth powers of linear terms. The problem is to minimize the number of pth powers which are required in such a sum. For instance, a result due to Sylvester...

Canonical Forms and Unification

Fay has described in 12,3] a complete T-unilication for equational theories T which possess a complete set of reductions as defined by Knuth & Bendix [12]. This algorithm relies essentially on using the narrowing process defined by Lankford I13]. In this paper, we first study the relations between narrowing and unification and we give a new version of Fay's algorithm. We then show bow to elimin...

Canonical Forms and Conservation

In this paper, we shall review earlier work on canonical forms in linear elasticity, and applications to the classi cation of conservation laws (path-independent integrals).