parser algorithm for postfix operators

2.1: adda/syntax/parser algorithm for postfix operators:
. when checking for existence,
the word (is) could be used in 2 ways:
(is x) checks for existence,
(x is t) checks for x's type = t .
. another idea is having support for
english-style postfix operators:
then you could write (x exists)
and you'd parse this like an infix
except you're not looking for a 2nd arg .
. its syntax for being declared
could be similar to that of other functions:
myInfix(arg1,arg2:t).ReturnType .
-- anything with 2 args is an infix operator .

the parser's algorithm:

. subexpressions are composed of atoms
that are the leaf in trees branched by
pre-, post- and infix operators;
in addition to the operators
branching is formed by enclosures;
eg, when we find any of:
( { [ <.
we call get-subexpression,
which considers its terminators to be:
, ; . : ) } ] .>
(depending on context and spacing);
and, anything in between these terminators
will be a subexpression .

find a term:

. a term is whatever results in a linear list,
as opposed to a branching tree .
. we might find a string of prefix operators,
we eventually find an atom,
and then we might find a string of postfixes .
. so to start,
we're expecting either an atom or a prefix:
. when we finally find an atom,
we can call [find end of term].

[find end of term]:

. after getting the next token (that is,
a symbol within the text we are parsing)
there are several cases:
# terminator:
. we found a complete subexpression .
# postfix:
. a postfix is treed just like an infix
because it's simpler for robots to read
(we invented the idea of a postfix
just for humans to see things their way,
but humans won't see our parse tree).
. to position our postix in the list,
it is supposed to be placed at
the head of the current term's list;
if there is more than one prefix operator,
it might not apply to the entire list,
so we have to place it with type matching,
starting at the top and working down
until finding that matching type
(that's the way english intuitively reads it:
it's placed at the end because
it applies to everything before it;
that's english's way of
avoiding long parentheticals).
. this might be the end of the term;
or, there could be more postfix;
so recurse: call [find end of term].
# infix:
. we have found end of term;
so we call [build a biop tree](term)
-- the term we just found
is made to be the binary operator's first arg,
and will now find the 2nd arg,
which is a subexpression
(that might either be a term,
or another biop subtree ).

tree a binary operator

. the algorithm for [build a biop tree](term)
is already designed elsewhere .
. actually, that still needs work:
the 1988 version is included below;
and, you can see it uses precedence ordering,
but in our current idea for treebiop
we have the same problem as for postfix placement:
we need to find the matching type;
eg, let b.truth, and let x,y,z,t: num;
then parse ( b or x + y * z = t );
when we get to the x,
there's a type mismatch -- truth OR number --
so we tree-in a place-holder:
(b or { (x ...) })
then for the (x+y*z) we need a precedence table
to tell us that prec(*) < prec(+)
and from that we get ( b or {(x+(y*z)) ...} )
then "=" is taking numbers and returning truth;
so, we parse it as being above num
and also being below truth:
(b or {(x+y*z) = (...)})
and finally (t), a number,
matches the (number = ...):
( b or {(x+y*z) = (t)} ) .]

[ the following is Vax Pascal language:
(I'm not sure if this code works,
but a possibly later version of it
did pass some tests .]
{ disk sys2: parse }{[ENVIRONMENT]}
MODULE parser( parsed, input, output );

letters = ['a'..'z','A'..'Z','_'];
base10 = ['0'..'9'];

N= 0..maxint; Z= integer;
V= VARYING[ 31 ] OF char;

express =^parsing;
parsing =RECORD
CASE node: parse_type OF
   CASE symbolic: boolean OF
    false:(value:N) end;
   inverse: boolean;
   unary, binary: express )
end END;

lexel_ID =( error, number, name, left_par, sign, post_fix, comma, right_par, binary );
precidence_ord = 0..5;

VAR  parsed:text;

FUNCTION fun( meaning:lexel_ID, control, lexel:V ): lexel_ID;
BEGIN fun:= meaning; pro(meaning,control,lexel)
PROCEDURE pro( meaning:lexel_ID, control, lexel:V );
BEGIN write( 'CONTROL: ', control, '   DATA: ', lexel );
writeV(lexel,meaning); writeln( '   ID: ', lexel )

PROCEDURE get_beyond_SP;
BEGIN  while (parsed^ in[''(32),''(9)]) and not eof(parsed) do get(parsed)
FUNCTION Cap( c:char ):char; CONST a=97; z=122; VAR x:N;
BEGIN x:= ord(c); IF (a <=x)and(x<= z) THEN cap:= chr( x-32 ) ELSE Cap:= c
PROCEDURE capV( var T:V ); VAR i:N;
BEGIN  for i:= 1 to T.LENGTH do   T.BODY[i]:= cap(T.BODY[i])
PROCEDURE RDcat( var str:V );
BEGIN    str:= str +parsed^;     get(parsed)

PROCEDURE get_name( var lexel:V );
BEGIN lexel:='';  while (parsed^ in(letters +base10))  and not eof(parsed) do    RDcat( lexel );  get_beyond_SP
PROCEDURE get_N( var lexel:V );
BEGIN lexel:='';  while (parsed^ in(['_']+base10))  and not eof(parsed) do RDcat( lexel );  get_beyond_SP

FUNCTION new_unary( lexel:V; operand: express ): express;
VAR node: express;
{note --inverse of operand is the
'multiplicative inverse: (1/operand),
since this what makes the graph flip
on its identity axis in the graph of m*x }
BEGIN new( node, operation );
WITH node do begin
  unary:= operand;
  binary:= NIL;
  inverse:= false; operation:= lexel;
FUNCTION new_binary( lexel:V; and1, and2: express ): express;
VAR node: express;
BEGIN new( node, operation );
WITH node do begin
  unary:= and1;
  binary:= and2;
  inverse:= false; operation:= lexel
end END;
FUNCTION new_value( number:N ): express; VAR node: express;
BEGIN new( node, operand, false );
  node^.value:= number
FUNCTION new_symbol( lexel:V ): express; VAR node: express;
BEGIN new( node, operand, true );
  node^.symbol:= lexel

FUNCTION p( Q:express ):precidence_ord; VAR T:V;
BEGIN if not( Q^.node=operator ) then
  writeln( 'p(rec variant)' )
    BEGIN T:=Q^.operation; capV( T ); pro( binary, 'p', T );
IF (T='**')or (T='//') THEN
ELSE IF (T='*')or(T='/')or(T='DIV')or(T='MOD')or(T='REM')THEN
ELSE IF (T='+')or(T='-') THEN
ELSE IF (T= '=')or(T='>=')or(T='<=')or (T= '/=')or(T='IN')THEN
ELSE IF (T='AND')or(T='OR')or (T='XOR')or (T='<=>')or(T= '==>')THEN
ELSE p:=0

FUNCTION ID_next( var L:V ):lexel_ID; VAR I:lexel_ID; T:V;
   PROCEDURE getI( ID:lexel_ID );   BEGIN I:= ID; get(parsed) END;

get_beyond_SP; L:=''; I:= error;
CASE parsed^ OF
'(': getI( left_par );
')': getI( right_par );
',': getI( comma );
'a'..'z','A'..'Z':begin   get_name(L); T:=Cap(L);
  IF (T='AND')or(T='OR')or(T='XOR')or(T='DIV')or(T='MOD')or(T='REM')or(T='IN')  THEN
     I:= binary
  ELSE IF parsed^='(' THEN begin
     I:= post_fix; get(parsed) end
     I:= name

'+','-': begin I:= sign; RDcat(L) end;
'*': begin I:= binary; RDcat(L);
   IF parsed^='*' THEN RDcat( L ) end;

'/': begin I:= binary; RDcat(L);
   IF (parsed^= '/')or(parsed^= '=') THEN RDcat( L ) end;

'=': begin RDcat(L);
   IF parsed^ = '=' THEN begin RDcat( L );
    IF parsed^= '>' THEN begin   RDcat( L );   I:= binary  end
   ELSE I:= binary end;
'>':begin I:= binary; RDcat(L);   IF parsed^ = '=' THEN RDcat( L ) end;
'<':begin I:= binary; RDcat(L);
   IF parsed^ = '=' THEN begin
      RDcat( L )
      IF parsed^='>' THEN
    RDcat( L )
   end end
ID_next:= I

PROCEDURE Treebiop( var root:express; leaf: express); FORWARD;

FUNCTION get_operand: express; FORWARD;

FUNCTION subexpress: express;
{--this returns to caller when a right_par
or a comma, or eoln(parsed) is found,
thus its tree is an expressions spanning
,-) or (-) or ,-, or (-,
or from beginning to end of file
since it is the initiating procedure.
The first thing it identifies will not be a biop,
but everything else.
The second thing it identifies
must be a biop or an exit prompt. }
VAR lexel:V; SE:express;
SE:= get_operand;
  SubExpression:= NIL
    CASE fun( ID_next( lexel ), 'subexpress', lexel) OF
    error, comma, right_par:
      SE:= SubExpression;
    binary: begin
      SE:= new_binary( lexel,
        NIL );
      Treebiop( SE,SE ) end;
    left_par, number, name, sign, post_fix:
      writeln( 'subexpress logic')

FUNCTION get_parameter_list: express;
VAR delimiter: express;
new( delimiter, operator );
WITH delimiter do begin
  unary:= subexpress;
  binary:= get_operand;
  inverse:= false; operation:= '' end;
get_parameter_list:= delimiter

FUNCTION get_number; express;
{--finds N.NE-N and parses into
operations on integers }
VAR node:express; L:V; int,frac,exp:N;

get_N(L); readV( L, int );
node:= new_value( int );
IF cap(parsed^) = '.' THEN begin
  get(parsed); get_N(L); readV(L,frac);
  node:= new_binary( '+',
    new_binary( '/'
      new_value( frac ),
      new_value( 10**(L.LENGTH) )
    )) end;
IF cap(parsed^) = 'E' THEN begin
  get(parsed); get_N(L); readV(L,exp);
  node:= new_binary( '*',
    new_binary( '**'
      new_value( 10 ),
      new_value( exp )
    )) end;
get_number:= node

FUNCTION get_operand: express;
VAR lexel:V; GO:express;
    CASE fun( ID_next(lexel), 'get_operand', lexel ) OF
    left_par: GO:= subexpress;
    name: GO:= new_symbol( lexel );
    post_fix: GO:= new_unary( lexel, get_parameter_list );
    binary, comma, error, right_par: GO:= NIL;
    number: GO:= get_number;
    sign: GO:=
      new_unary( lexel, get_operand )
    end get_operand:= GO

PROCEDURE Treebiop( var root:express; leaf: express);
{ --Once a binary operator is
positioned with a unary operand,
this routine uses the following
binary operator's precidence ord
to correctly place it and the
operators' mutually adjacent operand
within the expression tree. }
VAR and2, op1: express;

FUNCTION correct_precidence: boolean;
  BEGIN correct_precidence:=
    (p(op1)<=p(op2)) or (op1=leaf)

  op1:= root; and2:= get_operand;
  IF and2=NIL THEN
    writeln(op1^.operation,'no and2');
  ELSE IF not(fun( ID_next( lexel ),'treebiop', lexel ) = binary )THEN
    leaf^.binary:= and2
    pro( binary, 'treebiop', lexel );
    root_elevated:= correct_precidence;
    WHILE not correct_precidence do
        op1:= op1^.binary;
    IF p(op1)<=p(op2) THEN begin
    { op1 has precidence over op2,
    so op2 is the new root, with op1 as an operand.}
       op1^.binary:= and2;
       op1:= new_binary( lexel,
        NIL );
       IF root_elevated THEN
         root:= op1;
       Treebiop(root,op1) end
    ELSE begin
       op1^.binary:= new_binary( lexel,
        NIL );
       leaf:= op1^.binary;
       Treebiop(root,leaf) end