patterns.h

/***************************************************************************************
 *                   The Patterns of Resemblance Arithmetic Library                    *
 *                                                                                     *
 *                              (By Samuel Alexander)                                  *
 *                           (Department of Mathematics)                               *
 *                           (The Ohio State University)                               *
 ***************************************************************************************
 *         As seen in the Online Patterns of Resemblance Ordinal Calculator            *
 *            For documentation, see http://www.semitrivial.com/patterns               *
 ***************************************************************************************
 * This library implements basic arithmetic for Timothy J. Carlson's Patterns of       *
 * Resemblance ordinal notation system.  Patterns of resemblance are a combinatorial   *
 * way of notating very large ordinals (up to the ordinal of Pi^1_1-CA_0, to be        *
 * precise).  The PORAL (Patterns of Resemblance Arithmetic Library) is a patterns     *
 * implementation in C.                                                                *
 ***************************************************************************************
 * patterns.h                                                                          *
 ***************************************************************************************
 * Header file for the basic UI commands of the library.                               *
 * In order to use functions from patterns.c in your own .c file, this header file is  *
 * the only header file that needs to be #included there.  This arrangement minimizes  *
 * risk of library users running into naming conflicts between library functions and   *
 * functions in their own projects.                                                    *
 **************************************************************************************/

#ifndef PATTERNS_H_INCLUDED
#define PATTERNS_H_INCLUDED

/*
 * Typedefs
 */
typedef struct PATTERN pattern;
typedef struct NODE node;

/*
 * Structures
 */

/*
 * Pattern data structure --- the main data structure the library is concerned with
 * Contains a linked list of nodes and a counter for that list; an id (autogenerated);
 * and a designated node which is its "point".  (Thus this is really a "pointed pattern",
 * to be pedantic.)
 */
struct PATTERN
{
  pattern *next;
  pattern *prev;
  node *first_node;
  node *last_node;
  int nodes;
  int type;
  char *id;
  node *point;
};

/*
 * Data structure for a single node in a pattern.
 *
 * The fields in most need of explanation are as follows.
 *  p: the pattern in which the node lives
 *  position: the number N such that this node is the Nth node in p
 *  decomposition: a NULL-terminated string of node *'s.  The intended
 *    interpretation is that if the node has decomposition n_1 ... n_k,
 *    then it is a decomposable node, equal to the sum n_1 + ... + n_k.
 *  less1: the biggest node x such that this node is less1 x.
 *    (Cultural note: "less1" is how pattern theorists pronounce the
 *     symbol whose LaTeX code is \leq_1 or \preceq_1.  Not to be confused
 *     with the symbol whose LaTeX is <_1 or \prec_1, which would be
 *     pronounced as "strictly less1".)
 */
struct NODE
{
  node *next;
  node *prev;
  pattern *p;
  char *id;
  int position;
  node **decomposition;
  node *less1;
  unsigned long natural;
  int isnatural;
  int simplify_data;
};

/*
 * Simple error reporting.
 */
#define PATTERN_ERROR_BUFSIZE 8192
extern char global_pattern_error[PATTERN_ERROR_BUFSIZE+1];
extern pattern *pattern_too_large;

/*
 * Function prototypes from patterns.c,
 * not used anywhere else in the patterns library
 * (these are mainly just "UI" functions, to give
 *  the library the barest standalone usability,
 *  the actual Patterns of Resemblance Calculator
 *  uses much more sophisticated functions.)
 */

pattern *new_pattern( int nodes );
pattern *pattern_sum( pattern *p, pattern *q );
pattern *pattern_product( pattern *p, pattern *q );
pattern *pattern_exponential( pattern *p );
pattern *pattern_logarithm( pattern *p );
int pattern_compare( pattern *p, pattern *q );
pattern *pattern_simplify( pattern *p );
pattern *pattern_amalgamate( pattern *p, pattern *q );
void patterns_initialize( void );

/*
 * Function prototypes from patterns.c
 * that are used elsewhere in the patterns library.
 */
pattern *copy_pattern( pattern *p );

#endif //Ends "#ifndef PATTERNS_H_INCLUDED"