Rule Oriented Programming

In REDUCE, global algebraic relations can be formulated with rules. A rule links an algebraic search pattern to a replacement pattern, sometimes controlled by additional conditions. Rules can be activated (and deactivated) globally, or they can be invoked with a limited scope for single evaluations. So the user has an arbitrary precise control over the algebraic simplification.

Example: Expanding trigonometric functions for combined arguments; the symbol represents an implicit .

Sin_Cos_rules:=
{sin(~x+~y)=>sin(x)*cos(y) + cos(x)*sin(y),
 cos(~x+~y)=>cos(x)*cos(y) - sin(x)*sin(y)};

Global activation is achieved by

let Sin_Cos_rules;

Note: REDUCE has no predefined ``knowledge'' about these relations for trigonometric functions, as they can be used as production rules in either form depending on whether expansion or collection is required; only the user can define which mode is adequate for his problem.

Using rules, a complete calculus can be implemented; the rule syntax here is very close to the mathematical notation for multistep cases.

Example: Definition of Hermite polynomials:

operator Hermite;
Hermite_rules:=
{Hermite(0,~x) => 1,
 Hermite(1,~x) => 2*x,
 Hermite(~n,~x) => 2*x*Hermite(n-1,x)
          -2*(n-1)*Hermite(n-2,x)
              when n>1};

let Hermite_rules;

Generation of a Hermite polynomial:

Hermite(4,z);

    4       2
16*Z  - 48*Z  + 12

see also: REDUCE Home Page