/* ** Noun forms of the arithmatic functions ** */

/* This file attempts to define arithmetic functions which do
   not perform their actual mathematical functions. That is to say
   noun forms of the standard arithmetic functions. This is to
   give much finer control over the simplification of very elementary
   expressions.
   
   Chris Sangwin 25 Oct 2005.
*/

/* Create noun forms of the functions of +, -, *, / and ^ 
   as follows.
   + n+ 
   - n- 
   * n* 
   / n/
   ^ n^
*/

/* (1) */
nary("n+",100);
prefix("n-",100);
nary("n*",120);
infix("n/",122,123);
infix("n^",140,139);

/* (2) */
load("noun_arith.lisp"); 

/* (3) */
verb_arith(ex) := block(
 ex:subst("+","N+",ex), 
 ex:subst("*","N*",ex), 
 ex:subst("-","N-",ex), 
 ex:subst("//","N/",ex), 
 ex:subst("^","N^",ex), 
 ev(ex));

/* (4) */
noun_arith(ex) := block(
 ex:subst("N+","+",ex), 
 ex:subst("N*","*",ex), 
 ex:subst("N-","-",ex), 
 ex:subst("N/","//",ex), 
 ex:subst("N^","^",ex), 
 ev(ex));

/* (4) */
gather_reduce(ex) := block(
 ex:subst("+","N+",ex), 
 ex:subst("*","N*",ex), 
 ex:subst("-","N-",ex), 
 ex:ev(ex),
 ex:subst("N+","+",ex), 
 ex:subst("N*","*",ex), 
 ex:subst("N-","-",ex), 
 ex);