Quelle presentation.c Sprache: C

/****************************************************************************
**
**    presentation.c          Presentation                     Werner Nickel
**                                         nickel@mathematik.tu-darmstadt.de
*/

#include "config.h"

#include "presentation.h"
#include "pcarith.h"

static node *Word(void);

/*
**    ------------------------ GENERAL PURPOSE -------------------------
**    The first part of this file just contain some auxiliary functions.
*/

/*
**    FreeNode() recursively frees a given node.
*/
void    FreeNode(node *n) {
if (n->type != TGEN && n->type != TNUM) {
  FreeNode(n->cont.op.l);
  FreeNode(n->cont.op.r);
}
Free(n);
}

/*
**    GetNode() allocates space for a node of given type.
*/
static node    *GetNode(EvalType type) {
node    *n;

n = (node *)Allocate(sizeof(node));
n->type = type;

return n;
}

/*
**    GenNumber() maintains the array GenNames[] of generator names which
**    have been read so far. GenNumber() is called from the parser in order
**    to create a new generator or to look up an existing one. The generator
**    name is communicated to GenNumber() through the variable gname.
**
**    If GenNumber() is called with the flag CREATE it checks if the generator
**    name in gname has not occurred before and, if not, creates a new entry
**    and returns the new generator number. If the name had occurred before
**    the illegal generator number 0 is returned.
**
**    If GenNumber() is called with the flag NOCREATE it searches for the
**    generator name and returns the corresponding number if a matching entry
**    in GenNames[] is found. If no matching entry is found, the illegal
**    generator number 0 is returned.
*/
static char     **GenNames;
static unsigned NrGens = 0;

#define NOCREATE 0
#define CREATE   1

static gen GenNumber(char *gname, int status) {
unsigned        i;

if (status == CREATE && NrGens == 0)  /* Initialize GenNames[]. */
  GenNames = (char **)Allocate(128 * sizeof(char*));

for (i = 1; i <= NrGens; i++)  /* Find the generator name. */
  if (strcmp(gname, GenNames[i]) == 0) {
   if (status == CREATE) return (gen)0;
   return (gen)i;
  }

/* It's a new generator. */
if (status == NOCREATE) return (gen)0;
NrGens++;
if (NrGens % 128 == 0)
  GenNames = (char **)ReAllocate((void *)GenNames,
                                 (NrGens + 128) * sizeof(char *));

i = strlen(gname);
GenNames[ NrGens ] = (char *)Allocate((i + 1) * sizeof(char));
strcpy(GenNames[NrGens], gname);

return NrGens;
}

/*
**    GenName() is the inverse function for GenNumber(). It returns the
**    name of a generator given by its number.
*/
const char *GenName(gen g) {
if (g > (gen)NrGens)
  return 0;
return GenNames[g];
}

/*
**    ------------------------- SCANNER ---------------------------
**    The second part of this file contains the scanner. The parser
**    starts after the function Generator().
*/

/*
**    The following macros define tokens.
*/
typedef enum {
LPAREN,
RPAREN,
LBRACK,
RBRACK,
LBRACE,
RBRACE,

MULT,
POWER,
EQUAL,
DEQUALL,
DEQUALR,

PLUS,
MINUS,

LANGLE,
RANGLE,

PIPE,
COMMA,
SEMICOLON,
NUMBER,
GEN
} TokenType;

static int      Ch;             /* Contains the next char on the input. */
static TokenType Token;          /* Contains the current token. */
static int      Line;           /* Current line number. */
static int      TLine;          /* Line number where token starts. */
static int      Char;           /* Current character number. */
static int      TChar;          /* Character number where token starts. */
static const char     *InFileName;    /* Current input file name. */
static const char     *OutFileName;   /* Current output file name. */
static FILE     *InFp;          /* Current input file pointer. */
static FILE     *OutFp;         /* Current output file pointer. */
static int      N;              /* Contains the integer just read. */
static char     Gen[128];       /* Contains the generator name. */
/*
static const char     *TokenName[] = {
"", "LParen", "RParen", "LBrack", "RBrack", "LBrace",
"RBrace", "Mult",   "Power",  "Equal",  "DEqualL",
"DEqualR", "Plus",   "Minus",  "LAngle", "RAngle",
"Pipe",   "Comma",  "Number", "Gen"
};
*/

/*
**    SyntaxError() just prints a syntax error and the line and place
**    where is occurred and then exits.
**    No recovery from syntax errors :-)
*/
static void SyntaxError(const char *str) {
if (str == 0)
  fprintf(stderr, "%s, line %d, char %d.\n",
          InFileName, TLine, TChar);
else
  fprintf(stderr, "%s, line %d, char %d: %s.\n",
          InFileName, TLine, TChar, str);

exit(1);
}

/*
**    ReadCh() reads the next character from the current input file.
**    At the same time it checks for lines terminated with '\'. Such
**    a line is continued in the next line, therefore ReadCh() discards
**    '\' and the following '\n'.
*/
static void ReadCh(void) {

Ch = getc(InFp);
Char++;
if (Ch == '\\') {
  Ch = getc(InFp);
  if (Ch == '\n') { Line++; Char = 0; ReadCh(); }
  else             { ungetc(Ch, InFp); Ch = '\\'; }
}
}

/*
**    SkipBlanks() skips the characters ' ', '\t' and '\n' as well as
**    comments. A comment starts with '#' and finishes at the end of
**    the line.
*/
static void     SkipBlanks(void) {

/* If Ch is empty, the next character is fetched. */
if (Ch == '\0') ReadCh();

/* First blank characters and comments are skipped. */
while (Ch == ' ' || Ch == '\t' || Ch == '\n' || Ch == '#') {
  if (Ch == '#') {  /* Skip to the end of line. */
   while (Ch != '\n') ReadCh();
  }
  if (Ch == '\n') { Line++; Char = 0; }
  ReadCh();
}
}

/*
**    Number reads a number from the input.
*/
static void Number(void) {

unsigned int    m, n = 0, overflow = 0;

while (isdigit(Ch)) {
  m = n;
  n = 10 * n + (Ch - '0');
  if ((n - (Ch - '0')) / 10 != m) { overflow = 1; break; }
  ReadCh();
}

if (overflow) {
  fprintf(stderr, "Integer overflow reading %u%c", m, Ch);
  ReadCh();
  while (isdigit(Ch)) { fprintf(stderr, "%c", Ch); ReadCh(); }
  fprintf(stderr, " in\n");
  SyntaxError((char *)0);
} else if (n >= (1U << (8 * sizeof(unsigned int) - 1))) {
  fprintf(stderr, "Integer overflow reading %u in\n", n);
  SyntaxError((char *)0);
}

N = n;
}

/*
**    Generator() reads characters from the input stream until a non-
**    alphanumeric character is encountered. Only the first 127 characters
**    are significant as generator name and are copied into the global
**    array Gen[]. All other characters are discarded.
*/
static void     Generator(void) {

int     i;

for (i = 0; i < 127 && (isalnum(Ch) || Ch == '_' || Ch == '.'); i++) {
  Gen[i] = Ch;
  ReadCh();
}
Gen[i] = '\0';
/* Discard the rest. */
while (isalnum(Ch) || Ch == '_' || Ch == '.') ReadCh();
}

/*
**    NextToken reads the next token from the input stream. It first
**    skips all the blank characters and comments.
*/
static void NextToken(void) {
SkipBlanks();
TChar = Char;
TLine = Line;
switch (Ch) {
case '(':
{ Token = LPAREN; ReadCh(); break; }
case ')':
{ Token = RPAREN; ReadCh(); break; }
case '[':
{ Token = LBRACK; ReadCh(); break; }
case ']':
{ Token = RBRACK; ReadCh(); break; }
case '{':
{ Token = LBRACE; ReadCh(); break; }
case '}':
{ Token = RBRACE; ReadCh(); break; }

case '*':
{ Token = MULT;   ReadCh(); break; }
case '^':
{ Token = POWER;  ReadCh(); break; }
case ':': {
  ReadCh();
  if (Ch != '=') SyntaxError("illegal character");
  Token = DEQUALL;
  ReadCh();
  break;
}
case '=': {
  ReadCh();
  if (Ch != ':') Token = EQUAL;
  else { Token = DEQUALR; ReadCh(); }
  break;
}

case '+':
{ Token = PLUS;   ReadCh(); break; }
case '-':
{ Token = MINUS;  ReadCh(); break; }

case '<':
{ Token = LANGLE; ReadCh(); break; }
case '>':
{ Token = RANGLE; ReadCh(); break; }

case '|':
{ Token = PIPE;      ReadCh(); break; }
case ',':
{ Token = COMMA;     ReadCh(); break; }
case ';':
{ Token = SEMICOLON; ReadCh(); break; }

case '0':
case '1' :
case '2' :
case '3' :
case '4' :
case '5':
case '6' :
case '7' :
case '8' :
case '9' :
{ Token = NUMBER; Number(); break; }
default :
  if (isalnum(Ch) || Ch == '_' || Ch == '.')
  { Token = GEN; Generator(); break; }
  else SyntaxError("illegal character");
}
/*      printf( "# NextToken(): %s\n", TokenName[Token] );*/
}

/*
**    ------------------------- PARSER ----------------------------
**    Here the third part of this file starts containing the parser.
**
**    This is the grammar that defines the syntax of a finite presentation.
**    Quoted items (except 'empty') are recognized by the scanner and returned
**    as so called tokens. The unquoted symbol | indicates alternatives.
**
**    presentation: '<' genlist '|' rellist '>' |
**                  '<' genlist ; genlist '|' rellist '>'
**
**    genlist:         'empty' | genseq
**    genseq:          'generator' | 'generator' ',' genseq
**
**    rellist:         'empty' | relseq
**    relseq:          relation | relation ',' relseq
**
**    relation:        word | word '=' word | word '=:' word | word ':=' word
**
**    word:            power | power '*' word
**
**    power:           atom '^' atom | atom '^' snumber | atom
**
**    atom:            'generator' | '(' word ')' | commutator
**
**    commutator:      '[' word ',' wordseq ']'
**    wordseq          word | word ',' wordseq
**
**    snumber:         'sign' 'number' | 'number'
*/

/*
**    InitParser() does exactly what the name suggests.
*/
static void InitParser(FILE *fp, const char *filename) {
InFp = fp;
InFileName = filename;

Ch = '\0';
Char = 0;
Line = 1;

NextToken();
}

/*
**    Snumber() reads a signed number. The defining rule is:
**
**    snumber:         '+' 'number' | '-' 'number' | 'number'
*/
static node     *Snumber(void) {

node    *n = 0;

if (Token == NUMBER) {
  n = GetNode(TNUM);
  n->cont.n = N;
  NextToken();
} else if (Token == PLUS) {
  NextToken();
  if (Token != NUMBER) SyntaxError("Number expected");
  n = GetNode(TNUM);
  n->cont.n = N;
  NextToken();
} else if (Token == MINUS) {
  NextToken();
  if (Token != NUMBER) SyntaxError("Number expected");
  n = GetNode(TNUM);
  n->cont.n = -N;
  NextToken();
} else SyntaxError("Number expected");

return n;
}

/*
**    The defining rules for commutators are:
**
**    commutator:      '[' word ',' wordseq ']'
**                   | '[' word ',' 'number' word ]
**    wordseq          word | word ',' wordseq
**
**    A word starts either with 'generator', with '(' or with '['.
*/
static node     *Commutator(void) {

node            *n, *o;

if (Token != LBRACK)
  SyntaxError("Left square bracket expected");

NextToken();
if (Token != GEN && Token != LPAREN && Token != LBRACK)
  SyntaxError("Word expected");

o = Word();
if (Token != COMMA) SyntaxError("Comma expected");
while (Token == COMMA) {
  NextToken();
  if (Token != GEN && Token != NUMBER &&
          Token != LPAREN && Token != LBRACK)
   SyntaxError("Word expected");

  if (Token == NUMBER) {
   /* An Engel relation is on the input stream. */
   n = GetNode(TENGEL);
   n->cont.op.l = o;

   if (N <= 0) SyntaxError("Engel-n must be positive");

   n->cont.op.e = GetNode(TNUM);
   n->cont.op.e->cont.n = N;
   NextToken();

   n->cont.op.r = Word();
   break;
  } else {
   n = GetNode(TCOMM);
   n->cont.op.l = o;
   n->cont.op.r = Word();
   o = n;
  }
}
if (Token != RBRACK) SyntaxError("Right square bracket missing");
NextToken();
return n;
}

/*
**    Atom() reads an atom. Note that Atom() creates a generator by
**    calling GenNumber().
**
**    The defining rule for atoms is:
**
**    atom:            'generator' | '(' word ')' | commutator
*/
static node     *Atom(void) {

node            *n = 0;

if (Token == GEN) {
  n = GetNode(TGEN);
  n->cont.g = GenNumber(Gen, NOCREATE);
  if (n->cont.g == (gen)0) SyntaxError("Unknown generator");
  NextToken();
} else if (Token == LPAREN) {
  NextToken();
  n = Word();
  if (Token != RPAREN)
   SyntaxError("Closing parenthesis expected");
  NextToken();
} else if (Token == LBRACK) {
  n = Commutator();
} else {
  SyntaxError("Generator, left parenthesis or commutator expected");
}
return n;
}

/*
**    Power() reads a power. The defining rule is:
**
**    power:           atom | atom '^' atom | atom '^' snumber |
**
*/
static node     *Power_(void) {

node    *n, *o;

o = Atom();
if (Token == POWER) {
  NextToken();
  if (Token == PLUS || Token == MINUS || Token == NUMBER) {
   n = o;
   o = GetNode(TPOW);
   o->cont.op.l = n;
   o->cont.op.r = Snumber();
  } else {
   n = o;
   o = GetNode(TCONJ);
   o->cont.op.l = n;
   o->cont.op.r = Atom();
  }
}
return o;
}

/*
**    Word() reads a word. The defining rule is:
**
**    word:            power | power '*' word
**
**    A word starts either with 'generator', with '(' or with '['.
*/
static node *Word(void) {

node    *n, *o;

o = Power_();
if (Token == MULT) {
  NextToken();
  n = o;
  o = GetNode(TMULT);
  o->cont.op.l = n;
  o->cont.op.r = Word();
}

return o;
}

/*
**    Relation() reads a relation. The defining rule is:
**
**    relation:        word | word '=' word | word '=:' word | word ':=' word
**
**    A relation starts either with 'generator', with '(' or with '['.
*/
static node     *Relation(void) {

node    *n, *o;

if (Token != GEN && Token != LPAREN && Token != LBRACK)
  SyntaxError("relation expected");

o = Word();
if (Token == EQUAL) {
  NextToken();
  n = o;
  o = GetNode(TREL);
  o->cont.op.l = n;
  o->cont.op.r = Word();
} else if (Token == DEQUALL) {
  NextToken();
  n = o;
  o = GetNode(TDRELL);
  o->cont.op.l = n;
  o->cont.op.r = Word();
} else if (Token == DEQUALR) {
  NextToken();
  n = o;
  o = GetNode(TDRELR);
  o->cont.op.l = n;
  o->cont.op.r = Word();
}

return o;
}

/*
**    RelList() reads a list of relations. The defining rules are:
**
**    rellist:         'empty' | relseq
**    relseq:          relation | relation ',' relseq
**
**    A relation starts either with 'generator', with '(' or with '['.
*/
static node     **RelList(void) {

node     **rellist;
unsigned n = 0;

rellist = (node **)Allocate(sizeof(node *));
rellist[0] = (node *)0;
if (Token != GEN && Token != LPAREN && Token != LBRACK)
  return rellist;

rellist = (node**)ReAllocate((void *)rellist, 2 * sizeof(node *));
rellist[n++] = Relation();
while (Token == COMMA) {
  NextToken();
  rellist = (node**)ReAllocate((void *)rellist, (n + 2) * sizeof(node *));
  rellist[n++] = Relation();
}
rellist[n] = (node *)0;

return rellist;
}

/*
**    GenList() reads a list of generators.  The list of generators may
**    consist of abstract generators and identical generators.  Identical
**    generators are used to specify identical relations.
**
**    The defining rules are:
**
**    genlist:         'empty' | genseq | genseq ; genseq
**    genseq:          'generator' | 'generator' ',' genseq
*/
static int      GenList(void) {

int     nrgens = 0;

if (Token != GEN) return nrgens;

nrgens++;
if (GenNumber(Gen, CREATE) == (gen)0)
  SyntaxError("Duplicate generator");
NextToken();
while (Token == COMMA) {
  NextToken();
  if (Token != GEN) SyntaxError("Generator expected");
  nrgens++;
  if (GenNumber(Gen, CREATE) == (gen)0)
   SyntaxError("Duplicate generator");
  NextToken();
}

return nrgens;
}

/*
**    The following data structure holds a presentation.
*/
struct  pres {
unsigned nragens;      /* number of abstract generators  */
unsigned nrigens;      /* number of identical generators */
unsigned nrrels;       /* number of relations            */
node     **rels;       /* pointer to relations           */
};

static  struct pres Pres;

/*
**    NumberOfAbstractGens() returns the number of abstract generators.
*/
int     NumberOfAbstractGens(void) { return Pres.nragens; }

/*
**    NumberOfIdenticalGens() returns the number of identical generators.
*/
int     NumberOfIdenticalGens(void) { return Pres.nrigens; }

/*
**    NumberOfGens() returns the number of abstract and identical generators.
*/
int     NumberOfGens(void) { return Pres.nragens + Pres.nrigens; }

/*
**    NumberOfRels() returns the number of relations.
*/
int     NumberOfRels(void) { return Pres.nrrels; }

/*
**    NextRelation() returns the next relation, if it exists,
**    and returns the null pointer otherwise.
**    FirstRelation initializes the variable NextRel and calls
**    NextRelation().
**    NthRelation() returns the n-th relation, if n is in the
**    range [0..NumberOfRels()-1] and the null pointer otherwise.
**    CurrentRelation() returns the relation just being processed.
*/
static  int     NextRel;
node    *NextRelation(void) {

if (NextRel >= NumberOfRels()) return (node *)0;

return Pres.rels[NextRel++];
}

node    *FirstRelation(void) {

NextRel = 0;
return NextRelation();
}

node    *NthRelation(int n) {
if (n < 0 || n >= NumberOfRels()) return (node *)0;

return Pres.rels[n];
}

node    *CurrentRelation(void) { return Pres.rels[NextRel - 1]; }

/*
**    Presentation reads a finite presentation. The syntax of a presentation
**    is:
**        presentation: '<' genlist '|' rellist '>' |
**                      '<' genlist ; genlist '|' rellist '>'
*/
void    Presentation(FILE *fp, const char *filename) {
InitParser(fp, filename);

if (Token != LANGLE) SyntaxError("presentation expected");
NextToken();

if (Token != GEN && Token != PIPE)
  SyntaxError("generator or vertical bar expected");

Pres.nragens = GenList();

if (Token == SEMICOLON) {
  NextToken();
  Pres.nrigens = GenList();
} else
  Pres.nrigens = 0;

if (Token != PIPE) SyntaxError("vertical bar expected");
NextToken();

Pres.rels = RelList();
Pres.nrrels = 0;
while (Pres.rels[Pres.nrrels]) Pres.nrrels++;

if (Token != RANGLE)
  SyntaxError("presentation has to be closed by '>'");
}

node    *ReadWord(void) {

node    *n;

if (Token != SEMICOLON) n = Word();
else {
  NextToken();
  return ReadWord();
}

if (Token != SEMICOLON)
  SyntaxError("word has to be finished by ';'");

return  n;
}

/*
**    ----------------------- EVALUATOR ------------------------
**    The fourth part of this file contains the evaluator.
*/
static EvalFunc EvalFunctions[TLAST];

void    SetEvalFunc(EvalType type, EvalFunc function) {
if (type <= TNUM || type >= TLAST) {
  printf("Evaluation error: illegal type in SetEvalFunc()\n");
  exit(1);
}

EvalFunctions[type] = function;
}

void    *EvalNode(node *n) {
void          *e, *l, *r;

if (n->type == TNUM)
  return (void *) & (n->cont.n);

switch (n->type) {
case TGEN:                  /* TGEN is a unary node. */
  return WordGen(n->cont.g);

case TCOMM:                 /* Adjust the class.     */
  Class--;
  l = EvalNode(n->cont.op.l);
  if (l != (void *)0) r = EvalNode(n->cont.op.r);
  Class++;

  if (l == (void *)0) return l;
  if (r == (void *)0) { Free(l); return r; }

  return WordComm((word)l, (word)r);

case TENGEL:                /* TENGEL is a ternary node. */

  if ((e = EvalNode(n->cont.op.e)) == (void *)0) return e;

  Class -= *(int *)e;
  l = EvalNode(n->cont.op.l);
  if (l != (void *)0) r = EvalNode(n->cont.op.r);
  Class += *(int *)e;

  if (l == (void *)0) { Free(e); return l; }
  if (r == (void *)0) { Free(e); Free(l); return r; }

  return WordEngel((word)l, (word)r, (int *)e);

default:

  if (EvalFunctions[n->type] == 0) {
   fprintf(stderr, "No evaluation function for type %d.\n", n->type);
   exit(5);
  }

  if ((l = EvalNode(n->cont.op.l)) == (void *)0) return l;
  if ((r = EvalNode(n->cont.op.r)) == (void *)0) {
   Free(l);
   return r;
  }

  return (*EvalFunctions[n->type])((word)l, r);
}
}

static
void    TraverseNode(node *n, gen *igens) {
if (n->type == TNUM) return;

if (n->type == TGEN) {
  if (WordGen(n->cont.g) == (void *)0)

   igens[ n->cont.g - NumberOfAbstractGens() ] = 1;

  return;
}

TraverseNode(n->cont.op.l, igens);
TraverseNode(n->cont.op.r, igens);
}

int  NrIdenticalGensNode = 0;
gen  *IdenticalGenNumberNode = 0;

int  NumberOfIdenticalGensNode(node *n) {
gen  g,  nr;

if (IdenticalGenNumberNode != (gen *)0)
  Free(IdenticalGenNumberNode);

IdenticalGenNumberNode =
     (gen *)Allocate((NumberOfIdenticalGens() + 1) * sizeof(gen));

TraverseNode(n, IdenticalGenNumberNode);

for (nr = 0, g = 1; g <= NumberOfIdenticalGens(); g++)
  if (IdenticalGenNumberNode[ g ] == 1)
   IdenticalGenNumberNode[ g ] = ++nr;

NrIdenticalGensNode = nr;
return nr;
}

void    **EvalRelations(void) {

void     **results;
unsigned r;

results = (void **)Allocate((Pres.nrrels + 1) * sizeof(void *));
for (r = 0; r < Pres.nrrels; r++)
  results[r] = EvalNode(Pres.rels[r]);

results[r] = (void *)0;
return results;
}

/*
**    ----------------------- PRINTING ------------------------
**    And the last part contains the print functions.
*/

/*
**    PrintNum() prints an integer.
*/
static void     PrintNum(int n) {
fprintf(OutFp, "%d", n);
}

/*
**    PrintGen() prints a generator.
*/
void    PrintGen(gen g) {
fprintf(OutFp, "%s", GenName(g));
}

/*
**    PrintComm() prints a commutator using the following rule for
**    left normed commutators :
**                              [[a,b],c] = [a,b,c]
*/
static void     PrintComm(node *l, node *r, int bracket) {
if (bracket) fprintf(OutFp, "[");

/* If the left operand is a commutator, don't print its brackets. */
if (l->type == TCOMM)
  PrintComm(l->cont.op.l, l->cont.op.r, 0);
else
  PrintNode(l);

fprintf(OutFp, ",");
PrintNode(r);

if (bracket) fprintf(OutFp, "]");
}

/*
**    PrintEngel() prints a commutator using the following rule for
**    Engel relations:
**                              [u, n v]
*/
static void     PrintEngel(node *l, node *r, node *e) {
fprintf(OutFp, "[");
PrintNode(l);
fprintf(OutFp, ", ");
PrintNode(e);
fprintf(OutFp, " ");
PrintNode(r);
fprintf(OutFp, "]");
}

/*
**    PrintMult() prints a product. It is not necessary to check if
**    parentheses have to be printed since '*' has the lowest precedence
**    of all operators except '='. But '=' can only occur at the top of
**    an expression tree.
*/
static void     PrintMult(node *l, node *r) {
PrintNode(l);
fprintf(OutFp, "*");
PrintNode(r);
}

/*
**    PrintPow() prints an expression raised to an integer. If the expression
**    is a product, it has to be enclosed in parentheses because of the lower
**    precedence of '*'. If the expression is again a power or a conjugation,
**    it has to be enclosed in parenthesis because '^' is not an associative
**    operator.
*/
static void     PrintPow(node *l, node *r) {
if (l->type == TPOW || l->type == TCONJ || l->type == TMULT) {
  putc('(', OutFp);
  PrintNode(l);
  putc(')', OutFp);
} else
  PrintNode(l);

putc('^', OutFp);
if (r->type != TNUM) {
  fprintf(OutFp, "Fatal error in tree.\n");
  exit(5);
}
fprintf(OutFp, "%d", r->cont.n);
}

/*
**    PrintConj() prints an expression conjugated by another expression.
**    If one of the expressions is a product, a power or another conjugation,
**    it has to be enclosed in parentheses for the same reasons PrintPow()
**    has to enclose the basis in parentheses.
*/
static void     PrintConj(node *l, node *r) {
if (l->type == TPOW || l->type == TCONJ || l->type == TMULT) {
  putc('(', OutFp);
  PrintNode(l);
  putc(')', OutFp);
} else
  PrintNode(l);

putc('^', OutFp);

if (r->type == TPOW || r->type == TCONJ || r->type == TMULT) {
  putc('(', OutFp);
  PrintNode(r);
  putc(')', OutFp);
} else
  PrintNode(r);
}

/*
**    PrintRel() prints a relation. No parenthesis are necessary since
**    '=' has the lowest precedence of all binary operators.
*/
static void     PrintRel(node *l, node *r) {
PrintNode(l);
fprintf(OutFp, " = ");
PrintNode(r);
}

/*
**    PrintDRelL() prints a defining relation. No parenthesis are necessary
**    since '=:' has the lowest precedence of all binary operators.
*/
static void     PrintDRelL(node *l, node *r) {
PrintNode(l);
fprintf(OutFp, " := ");
PrintNode(r);
}

/*
**    PrintDRelR() prints a defining relation. No parenthesis are necessary
**    since '=:' has the lowest precedence of all binary operators.
*/
static void     PrintDRelR(node *l, node *r) {
PrintNode(l);
fprintf(OutFp, " =: ");
PrintNode(r);
}

/*
**    PrintNode() just looks at the type of a node and then calls the
**    appropriate print function.
*/
void    PrintNode(node *n) {
switch (n->type) {
case TNUM:
{ PrintNum(n->cont.n); break; }
case TGEN:
{ PrintGen(n->cont.g); break; }
case TMULT:
{ PrintMult(n->cont.op.l, n->cont.op.r); break; }
case TPOW:
{ PrintPow(n->cont.op.l, n->cont.op.r); break; }
case TCONJ:
{ PrintConj(n->cont.op.l, n->cont.op.r); break; }
case TCOMM:
{ PrintComm(n->cont.op.l, n->cont.op.r, 1); break; }
case TREL:
{ PrintRel(n->cont.op.l, n->cont.op.r); break; }
case TDRELL:
{ PrintDRelL(n->cont.op.l, n->cont.op.r); break; }
case TDRELR:
{ PrintDRelR(n->cont.op.l, n->cont.op.r); break; }
case TENGEL: {
  PrintEngel(n->cont.op.l, n->cont.op.r,
             n->cont.op.e);
  break;
}
default:
{ fprintf(OutFp, "\nunknown node type\n"); exit(5); }
}
}

/*
**    PrintPresentation() prints the presentation stored in the global
**    variable Pres.
*/
void    PrintPresentation(FILE *fp) {
gen     g;
int     r;

InitPrint(fp);

if (Pres.nragens == 0) return;

/* Open the presentation. */
fprintf(OutFp, "< ");

/* Print the generators first. */
PrintGen(1);
for (g = 2; g <= (gen)Pres.nragens; g++) {
  fprintf(OutFp, ", ");
  PrintGen(g);
}

if (Pres.nrigens > 0) {
  fprintf(OutFp, "; ");
  PrintGen(Pres.nragens + 1);
  for (g = Pres.nragens + 2; g <= (gen)(Pres.nragens + Pres.nrigens); g++) {
   fprintf(OutFp, ", ");
   PrintGen(g);
  }
}

/* Now the delimiter. */
fprintf(OutFp, " |\n");

/* Now the relations. */
if (Pres.rels[0] != (node *)0) {
  fprintf(OutFp, " ");
  PrintNode(Pres.rels[0]);
}
for (r = 1; Pres.rels[r] != (node *)0; r++) {
  fprintf(OutFp, ",\n ");
  PrintNode(Pres.rels[r]);
}

/* And close the presentation. */
fprintf(OutFp, " >\n");
}

void    InitPrint(FILE *fp) {
OutFp = fp;
OutFileName = "";
}

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Beweissystem der NASA

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NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

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