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- % Description: This module contains both functions for passing MathML to the Intermediate
- % representation and from the intermediate representation to MathML.
- % Both main functions are: mml2ir() and ir2mml().
- %
- % Date: 2 May 2000
- %
- % Author: Luis Alvarez Sobreviela
- %
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- % Here start the functions in charge of parsing MathML and printing %
- % it out in REDUCE intermediate representation. MathML->REDUCE IR %
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- % WN global '(f);
- fluid '(constructors!* !*f!*);
- % This is the function for reading from a file. It is given the name of a file which contains
- % the mathml input. It launches the program by calling mml2ir().
- symbolic procedure mml(f);
- begin;
- FILE!*:=t;
- !*f!*:= open(f, 'input);
- !*f!*:= rds(!*f!*);
- mml2ir();
- close rds !*f!*;
- FILE!*:=nil;
- end;
- % This function starts the parsing mechanism, which is a recursive descent
- % parsing. Begins at the <math> token.
- symbolic procedure mml2ir();
- begin scalar res;
- res:=nil;
- mmlatts:=nil;
- space:=int2id(32);
- count:=0;
- ch:=readch();
- temp2:=nil;
- lex();
- if char='(m a t h) then
- res:=mathML()
- else errorML("<math>",2);
- lex();
- if char='(!/ m a t h) then
- terpri()
- else errorML("</math>",19);
- return res;
- end;
- % The two next functions differ in that one of them parses from the next
- % token onwards, and the other one from the actual token onwards.
- % It is necessary to have both since some functions end their task one
- % token ahead (eg getargs()).
- symbolic procedure mathML();
- begin scalar a;
- a:=nil;
- lex();
- return sub_math();
- end;
- symbolic procedure mathML2();
- begin scalar a;
- a:=nil;
- return sub_math();
- end;
- % Parses all tokens which legally follow a <math> token.
- % These tokens have to be constructors.
- symbolic procedure sub_math();
- begin scalar a, aa;
- a:=nil;
- if char='(i d e n t !/) then return list 'ident;
- % The reason why we perform an individual test to see if we are dealing with a vector tag
- % is because REDUCE changes vector in the list to ~vector when compressing (v e c t o r)
- % and then it doesnt work anymore...
- if char='(v e c t o r) then
- <<a:=vectorRD();
- if char neq '(!/ v e c t o r) then
- errorML("</vector>",2);
- return a>>;
- if (aa:=assoc(compress!* char, constructors!*)) then <<
- a:=apply(cadr aa, nil );
- if PAIRP a then if car a = 'csymbol then a:=cddr a;
- if PAIRP a then if car a = 'fn then a:=cddr a;
- if compress!* char neq third aa then
- errorML(third cdr aa, 2);
- return a>>;
- return nil;
- end;
- % The next two functions parse the <cn> and <ci> tokens and extract its
- % content to be used by the function calling it. It will have different
- % behaviours according to the attributes contained.
- symbolic procedure cnRD();
- begin scalar type, sep, tt, base;
- % Must check that what is being returned is an int.
- type:=nil;
- sep:=nil;
- type:=intern find(atts, 'type);
- base:=find(atts, 'base);
- lex();
- tt := char;
-
- lex();
- if type='constant then return compress!* tt;
- if type=nil then return compress!* tt;
- if member(type, '(real integer)) neq nil then <<
- if base eq nil then return compress!* tt
- else return 'based_integer . nil . base . list ('string . list compress!* tt)
- >>;
- if member(intern type, '(rational complex!-cartesian complex!-polar)) neq nil then
- << sep:=sepRD();
- if type='rational then <<
- lex();
- return rational(compress!* tt, sep)
- >>
- else
- if type='complex!-cartesian then
- << lex();return 'complex_cartesian . nil . compress!* tt . list sep >>
- else
- if type='complex!-polar then
- << lex();return 'complex_polar . nil . compress!* tt . list sep >>
- >>;
- end;
- symbolic procedure ciRD();
- begin scalar test, type,aa, tt, ats;
- aa:=nil; type:=nil; test:=nil;
- ats:=retattributes(atts, '(type));
- lex();
- tt := char;
- lex();
- << test:=compress tt;
- if NUMBERP test then errorML(test, 4);
- test := compress!* tt;
- if ats = nil then return test;
- return list('ci, ats, test)>>
- end;
- % returns the value of the constant values.
- % !!!!!!!!!! USELESS
- %symbolic procedure consts(c);
- %begin;
- % if c='(quote i) then return 'i;
- % if c='(quote d) then return 'd;
- % if c='(quote e) then return 'e;
- % if c='(quote p) then return 'pi;
- % if c='(quote infinity) then return 'infinity;
- % if c='(quote gamma) then return 'gamma;
- %end;
- % Constructs a rational number in intermediate representation
- symbolic procedure rational(a,b);
- begin;
- return 'rational . nil . a . list b;
- end;
- % Reads through values seperated by <sep/> tags and
- % returns them in a list
- symbolic procedure sepRD();
- begin scalar p1, p2;
- p1:=nil; p2:=nil;
- if char neq '(s e p !/) then errorML("<sep/>",2);
- lex();
- p2:=compress!* char;
- return p2;
- end;
- % Creates a vector by using function matrix_row.
- symbolic procedure vectorRD();
- begin scalar a, ats;
- ats:=retattributes(atts, '(type other));
- a:=nil;
- a:=matrixrowRD();
- a:=cons('vectorml,cons(ats, a));
- return a;
- end;
- % The following functions constructs the matrix from the mathml information.
- symbolic procedure matrixRD();
- begin scalar b1, stop, ats, b2;
- ats:=retattributes(atts, '(type));
- stop:=0;
- b1:='();
- b2:=nil;
- while stop=0 do
- <<
- lex();
- if char='(m a t r i x r o w) then
- <<b2:=matrixrowRD();
- if b1 neq nil then b1:=append(b1, list b2)
- else b1:=list b2;
- if char neq '(!/ m a t r i x r o w) then
- errorML("</matrixrow>",2)>>
- else stop:=1
- >>;
- return cons('matrix, cons(ats,cons('matrixrow, list b1)));
- end;
- symbolic procedure matrixrowRD();
- begin scalar a;
- a:=nil;
- a:=mathML();
- return if a=nil then nil
- else cons(a, matrixrowRD());
- end;
- % returns a lambda function constructed from the information supplied.
- symbolic procedure lambdaRD();
- begin scalar b1, b2, ats;
- ats:=retattributes(atts, '(type definitionURL encoding));
- lex();
- b1:=getargsRD();
- b2:=mathML2();
- lex();
- return cons('lambda, cons(ats, append (b1, list b2)));
- end;
- % returns a set constructed from the information supplied.
- symbolic procedure setRD();
- begin scalar setvars, ats;
- ats:=retattributes(atts, '(type));
- setvars:= cons('set, cons(ats, stats_getargs()));
- return setvars;
- end;
- % returns a list constructed from the information supplied.
- symbolic procedure listRD();
- begin scalar ats;
- ats:=retattributes(atts, '(order));
- return cons('list, cons(ats , stats_getargs()));
- end;
- symbolic procedure fnRD();
- begin scalar b1;
- lex();
- if char neq '(c i) then errorML(compress char,20)
- else b1:= mathML2();
- lex();
- return b1;
- end;
- % Reads the declare construct and sets the value of the given variable to
- % the given value.
- symbolic procedure declareRD();
- begin scalar b1, b2, ats;
- ats:=retattributes(atts, '(type nargs occurence scope definitionURL));
- lex();
- if char='(c i) then
- << b1:=ciRD()>>
- else errorML("<ci>", 8);
- lex();
- if char neq '(!/ d e c l a r e) then <<b2 :=mathML2(); lex()>>;
-
- return cons('declare, list(ats, b1, b2));
- end;
- % This function will determine if the next token is a valid token following
- % an apply token. It then calls the appropriate function if succesful.
- symbolic procedure applyRD();
- begin scalar aa, fun;
- lex();
- % This following _if_ statement relates the mathml tag to its entry in functions!*
- % It then returns a list starting with the name of the function followed by its
- % arguments: eg: (plus 1 2 3).
- % It uses the table in functions!* to find the function name (the third entry) and
- % the arguments to send the RD function.
- mmlatts:=retattributes(atts, '(type definitionURL encoding));
- if (aa:=assoc(compress!* char, functions!*)) then <<
- fun:=apply(cadr aa, nil);
- fun:=mmlatts . fun;
- mmlatts:=nil;
- return cons(cadr rest aa, fun);
- >>;
- errorML(compress char, 17);
- end;
- % Reads through a select construct and acts accordingly.
- symbolic procedure selectRD();
- begin scalar a1, b2, b3;
- a1:=mathml();
- if car a1 = 'matrix then <<
- b2:=mathml();
- lex();
- if char neq '(!/ a p p l y) then <<b3:=MathML2(); lex()>>;
- return cons(a1, list(b2, b3))
- >>;
- if car a1 = 'list OR car a1 = 'vectorml then <<
- b2:=mathml();
- lex();
- return cons(a1, list b2)
- >>;
-
- end;
- % Returns the transpose of the element contained in the transpose tags.
- symbolic procedure transposeRD();
- begin scalar a;
- a:=mathML();
- lex();
- return list a;
- end;
- % Returns the determinant of the given element.
- symbolic procedure determinantRD();
- begin scalar a;
- a:=mathML();
- lex();
- return list a;
- end;
- % Takes the given function name, makes it an operator, and then
- % applies it to the arguments specified in the mathml input.
- symbolic procedure applyfnRD();
- begin scalar b1, b2, c1;
- b1:=nil; b2:=nil; c1:=nil;
- b1:=fnRD();
- b2:=stats_getargs();
- return b1 . nil . b2;
- end;
- % Introduces the new csymbol element of MathML 2.0
- symbolic procedure csymbolRD();
- begin scalar b1, b2, c1;
- b1:=nil; b2:=nil; c1:=nil;
- b1:=fnRD();
- b2:=stats_getargs();
- return b1 . nil . b2;
- end;
- % Reads the condition tag.
- symbolic procedure conditionRD();
- begin scalar a;
- a:=mathml();
- lex();
- if char neq '(!/ c o n d i t i o n) then errorML("</condition>", 2);
- return cons('condition, list a);
- end;
- % This function will read all legal tags following the <reln> tag.
- fluid '(relations!*);
- symbolic procedure relnRD();
- begin scalar aa, ats;
- lex();
- ats:=retattributes(atts, '(type definitionURL));
- if (aa:=assoc(compress!* char, relations!*)) then return cons(cadr rest aa, cons(ats, apply(cadr aa, nil)));
- end;
- symbolic procedure relationRD( type );
- begin scalar args;
- args:=stats_getargs();
- return cons(cadr type, args);
- end;
- %!!!!!!!! PROBABLY USELESS FUNCTION!!!!!
- symbolic procedure binaryrelationRD( type );
- begin scalar arg1, arg2;
- arg1 := MathML();
- arg2 := MathML();
- lex();
- return cons(type, list (arg1, arg2));
- end;
- % The following functions do all the necessay actions in order to evaluate
- % what should be by the tags.
- symbolic procedure subsetRD();
- begin scalar abc1;
- abc1:=nil;
- abc1:=mathML();
- return if abc1 = nil then '()
- else cons(abc1, subsetRD());
- end;
- symbolic procedure prsubsetRD();
- begin scalar abc1;
- abc1:=nil;
- abc1:=mathML();
- return if abc1 = nil then '()
- else cons(abc1, prsubsetRD());
- end;
- % These functions parse through most MathML elements,
- % since many fall in the unary, binary and nary categories.
- symbolic procedure unaryRD();
- begin scalar a;
- a:= mathML();
- lex();
- return list a;
- end;
- symbolic procedure binaryRD();
- begin scalar a1, a2;
- a1:=mathML();
- a2:=mathML();
- lex();
- return cons(a1, list a2);
- end;
- symbolic procedure naryRD();
- begin scalar a;
- a:=mathML();
- return if a = nil then '()
- else cons(a, naryRD());
- end;
- symbolic procedure setFuncsNaryRD();
- begin scalar a;
- a:=mathML();
- if PAIRP a then <<if cadr a neq nil then if intern cadr car cadr a = 'multiset then mmlatts:='multiset;>>;
- return if a = nil then '()
- else cons(a, setFuncsnaryRD());
- end;
- symbolic procedure setFuncsBinRD();
- begin scalar flag,a1,a2;
- flag:=nil;
- a1:=mathML();
- if PAIRP a1 then <<if cadr a1 neq nil then if intern cadr car cadr a1 = 'multiset then flag:=t;>>;
- a2:=mathML();
- if PAIRP a2 then <<if cadr a2 neq nil then if intern cadr car cadr a2 = 'multiset then flag:=t else flag:=nil;>>;
- lex();
- if flag=t then mmlatts:='multiset;
- return cons(a1, list a2);
- end;
- % Encodes information given in a <limit/> tag.
- symbolic procedure limitRD();
- begin scalar var, condi, low, exp, ats;
- ats:=retattributes(atts, '(definitionurl));
- low:=nil;
- lex();
- if char='(b v a r) then
- << var:=bvarRD();
- if (caddr var neq 1) then errorML("<degree>",8);
- lex()>>
- else var:=nil;
- if char='(l o w l i m i t) then
- << low:=lowlimitRD();
- >>
- else if char='(c o n d i t i o n) then
- << condi:=conditionRD()
- >>
- else condi:=nil;
- exp:=mathML();
- lex();
- if condi=nil then
- return list(var, low, exp);
- if low=nil then
- return list(var, condi, exp);
- end;
- % Returns the partial derivative.
- symbolic procedure partialdiffRD();
- begin scalar res, bvar, express;
- lex();
- bvar:=getargsRD();
- express:=mathML2();
- lex();
- % res:=cons(express, bvar);
- res:=append(bvar, list express);
- return res;
- end;
-
- % Returns the derivative.
- symbolic procedure diffRD();
- begin scalar bvar, express;
- lex();
- if char='(b v a r) then
- <<bvar:=bvarRD();
- lex()>>
- else bvar:=nil;
- express:=mathML2();
- lex();
- return diff2 list(bvar, express);
- end;
- % This function restructures the IR when we are differentiating
- % more than degree 1 so the translation is possible to OM
- symbolic procedure diff2(elem);
- begin scalar fun, res, deg, var;
- deg:=caddr car elem;
- var:=cadr car elem;
- if deg=1 then return elem;
- fun:=car reverse elem;
- res:='diff . nil . ('bvar . var .list 1) . list fun;
- deg:=deg-1;
- while deg > 0 do <<
- res:='diff . nil . ('bvar . var .list 1) . list res;
- deg:=deg-1;
- >>;
- return cddr res;
- end;
- % This function reads through the a series of <bvar> tags and extracts the
- % variables.
- symbolic procedure getargsRD();
- begin scalar a;
- % Dont forget. This function leaves the file pointer on
- % the next token after the last bvar. So you need to use mathML2 after.
- if char='(b v a r) then
- <<a:=bvarRD();
- lex();
- return cons (a,getargsRD())>>;
- end;
- % Parses through MathML quantifiers
- symbolic procedure quantifierRD();
- begin scalar bvars, condi, exp;
- lex();
- bvars:=getargsRD();
- if char='(c o n d i t i o n) then
- condi:=conditionRD()
- else condi:=nil;
- if condi neq nil then exp:=MathML()
- else exp:=MathML2();
- lex();
- return append(bvars, list(condi, exp));
- end;
- % This function will parse through the sum, product and int tags. Takes in the expression, then
- % the bound variable, and finally the limits, conditions or intervals if they exist.
- symbolic procedure symbolsRD();
- begin scalar bvar, low, upper, int, exp, result, cond;
- low:=nil;
- upper:=nil;
- int:=nil;
- exp:=nil;
- result:=nil;
- cond:=nil;
- lex();
- if char='(b v a r) then
- <<bvar:=bvarRD();
- if (caddr bvar eq 1) then bvar:=bvar
- else
- errorML("",13);
- lex()>>
- else errorML("<bvar>",14);
- if char='(l o w l i m i t) then <<low:=lowupperlimitRD(); lex()>>
- else low:=nil;
- if char='(i n t e r v a l) then
- <<int:=intervalRD();
- lex()>>
- else int:=nil;
- if char='(c o n d i t i o n) then
- <<cond:=conditionRD();
- lex()>>
- else cond:=nil;
- exp:=mathML2();
- lex();
- if (low neq nil) then return list(bvar, low, exp);
- if (int neq nil) then return list(bvar, int, exp);
- if (cond neq nil) then return list(bvar, cond, exp);
- return list(bvar, nil, exp);
- end;
- % Here we parse bound variables. The function reads the variable as well as
- % the degree if there is one.
- symbolic procedure bvarRD();
- begin scalar var, deg;
- lex();
- if char='(d e g r e e) then
- errorML("<bvar>",15);
- var:=mathML2();
- lex();
- if char='(d e g r e e) then
- << deg:=mathML();
- lex();
- if char neq '(!/ d e g r e e) then
- error("</degree>",2);
- lex()>>
- else deg:=1;
- if char='(!/ b v a r) then return cons('bvar , list(var, deg))
- else errorML("</bvar>", 2);
- end;
- % Functions used to parse the limits of an integral, sum, or product.
- symbolic procedure lowupperlimitRD();
- begin scalar lowlimit, upperlimit;
- lowlimit:=mathML();
- lex();
- if char='(!/ l o w l i m i t) then upperlimit:=upperlimitRD()
- else errorML("</lowlimit>", 2);
- return cons('lowupperlimit, list (lowlimit, upperlimit))
- end;
- symbolic procedure lowlimitRD();
- begin scalar lowlimit;
- lowlimit:=mathML();
- lex();
- if char neq '(!/ l o w l i m i t) then errorML("</lowlimit>", 2);
- return cons('lowlimit, list lowlimit);
- end;
- symbolic procedure upperlimitRD();
- begin scalar upperlimit;
- lex();
- if char neq '(u p l i m i t) then errorML("<uplimit>", 10);
- upperlimit:=mathML();
- lex();
- if char='(!/ u p l i m i t) then return upperlimit
- else errorML("</uplimit>", 2);
- end;
- symbolic procedure intervalRD();
- begin scalar l,u, ats;
- ats:=retattributes(atts, '(closure));
- l:=mathML();
- u:=mathML();
- lex();
- if char='(!/ i n t e r v a l) then return cons('interval, list(ats, l,u))
- else errorML("</interval>", 2);
- end;
- % Following functions just evaluate calculus functions.
- symbolic procedure logRD();
- begin scalar a1, base;
- base:=nil;
- lex();
- if char='(l o g b a s e) then
- <<base:=logbaseRD();
- lex()>>;
- a1:=mathML2();
- lex();
- return cons(base, list a1);
- end;
- symbolic procedure logbaseRD();
- begin scalar a;
- a:=mathML();
- lex();
- if char='(!/ l o g b a s e) then return a
- else errorML("</logbase>",2);
- end;
- % % Work on here. Make sure you can have either one or two arguments...
- symbolic procedure minusRD();
- begin scalar c,b;
- c:=mathML();
- b:=mathML();
- if b=nil then c:= cons(c,'())
- else <<
- c:=cons(c, cons(b, '()));
- lex()>>;
- return c;
- end;
- symbolic procedure rootRD();
- begin scalar b,deg;
- lex();
- if char='(d e g r e e) then
- << deg:=mathML();
- lex();
- if char neq '(!/ d e g r e e) then
- error("</degree>","Syntax ERROR: Missing end tag");
- lex()>>
- else deg:=2;
- b:=mathML2();
- lex();
- return list(cons('degree, list deg), b);
- end;
- symbolic procedure minmaxRD();
- begin scalar a, bvar, cond, flag;
- lex();
- flag:=0;
- if char = '(b v a r) then <<bvar:=bvarRD(); flag:=1; lex();>> else bvar:=nil;
- if char = '(c o n d i t i o n) then <<cond:=conditionRD()>>
- else <<
- a:=mathml2();
- a:=cons(a, stats_getargs());
- cond:=nil
- >>;
- if flag=1 then << a:=MathML2(); lex()>>;
- if bvar neq nil then return cons(bvar, append(list cond, list a));
- if cond neq nil then return list(cond);
- return a;
- end;
- % Following function are in charge of parsing statistics related mathml.
- symbolic procedure momentRD( );
- begin scalar deg, child;
- lex();
- if char='(d e g r e e) then
- << deg:=mathML();
- lex();
- if char neq '(!/ d e g r e e) then
- error("</degree>",2);
- lex()>>
- else deg:=nil;
- child:=mathml2();
- lex();
- return list(cons('degree, list deg), child);
- end;
- % The following function gets all arguments from the mathml input.
- symbolic procedure stats_getargs();
- begin scalar ww;
- ww:=nil;
- ww:=mathML();
- if ww neq nil then <<
- return cons (ww,stats_getargs())>>;
- end;
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- % Here start the functions in charge of parsing reduce's output and printing %
- % it out in MathML. REDUCE->MathML %
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- % The following function takes an IR expression and produces a MathML equivalent
- symbolic procedure ir2mml( u );
- begin;
- FLUID '(indent);
- ind:=3;
- indent:=0$
- printout("<math>");
- indent!* t;
- expression u;
- indent!* nil;
- printout( "</math>" );
- end;
- % Prints out vectors.
- symbolic procedure vectorML( elem );
- begin;
- printout("<vector");
- attributesML(car elem, "");
- indent!* t;
- multi_elem(cdr elem);
- indent!* nil;
- printout("</vector>");
- end;
- % Following functions print out matrices.
- symbolic procedure matrixML( elem );
- begin;
- printout("<matrix");
- attributesML(car elem, "");
- indent!* t;
- if cadr elem = 'matrixrow then matrix_rows(caddr elem)
- else matrix_rows(cols2rows caddr elem);
- indent!* nil;
- printout("</matrix>")
- end;
- symbolic procedure matrix_rows( elem );
- begin;
- if (elem neq()) then
- << printout("<matrixrow>");
- indent!* t;
- row(car elem);
- indent!* nil;
- printout("</matrixrow>");
- matrix_rows( cdr elem ); >>
- end;
- symbolic procedure row( elem );
- begin;
- if (elem neq()) then
- << expression(car elem); row(cdr elem);>>
- end;
- symbolic procedure identML(elem);
- begin;
- printout( "<ident/>" );
- end;
- % This function takes in an intermediate representation expression, parses it and prints it
- % in MathML.
- fluid '(ir2mml!*);
- symbolic procedure expression( elem );
- begin scalar aa;;
- if elem neq nil then
- if (ATOM elem) then constsML( elem ) else
- <<
- if (aa:=assoc(car elem, ir2mml!*)) then <<
- if caddr aa = nil then
- apply(cadr aa, list cdr elem)
- else
- apply(cadr aa, list(cdr elem, car elem))
- >>
- else
- if ((car elem)= '!*sq) then expression (PREPSQ (cadr elem))
- else operator_fn(elem);>>;
- end;
- symbolic procedure tendstoML( elem );
- begin;
- printout("<apply><tendsto");
- attributesML(car elem, "/");
- indent!* t;
- expression(cadr elem);
- expression(caddr elem);
- indent!* nil;
- printout("</apply>");
- end;
- % Prints out derivatives.
- symbolic procedure dfml( elem );
- begin scalar test;
- test:=cdr elem;
- if length test=1 OR (length test=2 AND NUMBERP
- cadr test) then
- printout("<apply><diff/>")
- else
- printout("<apply><partialdiff/>");
- indent!* t;
- dfargs(cdr elem);
- expression(car elem);
- indent!* nil;
- printout("</apply>");
- end;
- symbolic procedure dfargs( elem );
- begin;
- if elem neq nil then
- << if length elem>1 then
- << if NUMBERP cadr elem then
- <<printout("<bvar>");
- indent!* t;
- expression car elem;
- degreeML(cadr elem);
- indent!* nil;
- printout("</bvar>");
- dfargs(cddr elem)>>
- else
- <<printout("<bvar>");
- indent!* t;
- expression car elem;
- indent!* nil;
- printout("</bvar>");
- dfargs(cdr elem)>>; >>
- else
- << printout("<bvar>");
- indent!* t;
- expression car elem;
- indent!* nil;
- printout("</bvar>");
- dfargs(cdr elem)>> >>;
- end;
- % Prints out degree statements.
- symbolic procedure degreeML( elem );
- begin;
- if car elem neq nil then <<
- printout("<degree>");
- indent!* t;
- expression( car elem );
- indent!* nil;
- printout("</degree>") >>;
- end;
-
- symbolic procedure rationalML(elem);
- begin scalar a, b;
- a:=cadr elem;
- b:=caddr elem;
- printout("<cn type=""rational"">");
- princ a; princ "<sep/>"; princ b; princ "</cn>";
- end;
- % Prints out relns.
- symbolic procedure reln(elem, tty);
- begin;
- printout("<apply>");
- princ "<"; princ tty;
- attributesML(car elem, "/");
- indent!* t;
- multi_elem( cdr elem );
- indent!* nil;
- printout("</apply>");
- end;
- % Prints out a set.
- symbolic procedure containerML( elem, tty );
- begin;
- if tty = 'integer_interval then tty:='interval;
- printout("<"); princ tty;
- attributesML(car elem, "");
- indent!* t;
- multi_elem( cdr elem );
- indent!* nil;
- printout("</"); princ tty; princ ">";
- end;
- % Prints out set theory related functions.
- symbolic procedure sets(elem, tty);
- begin;
- printout("<apply>");
- princ "<"; princ tty;
- attributesML(car elem, "/");
- indent!* t;
- multi_elem( cdr elem );
- indent!* nil;
- printout("</apply>");
- end;
- symbolic procedure listML( elem );
- begin;
- printout( "<list" );
- attributesML(car elem,"");
- indent!* t;
- multilists( cdr elem );
- indent!* nil;
- printout( "</list>" );
- end;
- symbolic procedure multilists( elem );
- begin;
- if elem neq nil then
- if ((LENGTH elem)=1) then expression (car elem)
- else <<expression(car elem); multilists(cdr elem);>>
- end;
- % Prints out unknown functions as a function. It prints out all variables
- % declared as operators.
- symbolic procedure csymbol_fn( elem );
- begin;
- printout("<apply>");
- indent!* t;
- printout("<csymbol");
- if car elem neq nil then attributesML(car elem, "")
- else princ ">";
- indent!* t;
- printout("<ci>");
- princ cadr elem;
- princ "</ci>";
- indent!* nil;
- printout("</csymbol>");
- multi_args(cddr elem);
- indent!* nil;
- printout("</apply>");
- end;
- symbolic procedure operator_fn( elem );
- begin;
- printout("<apply>");
- indent!* t;
- printout("<csymbol>");
- indent!* t;
- printout("<ci>");
- princ car elem;
- princ "</ci>";
- indent!* nil;
- printout("</csymbol>");
- multi_args(cdr elem);
- indent!* nil;
- printout("</apply>");
- end;
- % Reads through a list and prints out each component.
- symbolic procedure multi_args( elem );
- begin;
- if (elem neq ()) then <<expression(car elem); multi_args( cdr elem );>>
- end;
- % Prints out logs with a base.
- symbolic procedure log_baseML(elem, type);
- begin;
- printout("<apply><log");
- attributesML(car elem, "/");
- indent!* t;
- if car reverse elem neq nil then <<
- printout("<logbase>");
- indent!* t;
- expression(cadr elem);
- indent!* nil;
- printout("</logbase>")>>;
- expression(caddr elem);
- indent!* nil;
- printout("<apply>");
- end;
- % Prints out equal relns.
- symbolic procedure equalML( elem );
- begin;
- printout( "<reln><eq/>" );
- indent!* t;
- expression(car elem);
- expression(cadr elem);
- indent!* nil;
- printout( "</reln>" );
- end;
- % Prints out square roots and moments.
- symbolic procedure degreetoksML( elem, tty );
- begin;
- printout( "<apply><" ); princ tty;
- attributesML(car elem, "/");
- indent!* t;
- degreeML(cdadr elem);
- expression( caddr elem );
- indent!* nil;
- printout( "</apply>" );
- end;
- symbolic procedure bvarML(elem);
- begin;
- printout("<bvar>");
- indent!* t;
- expression(car elem);
- if cadr elem neq 1 then <<
- degreeML(list cadr elem);
- >>;
- indent!* nil;
- printout("</bvar>")
- end;
-
- % This function prints a series of bvar statements
- symbolic procedure xbvarML(elem);
- begin;
- if elem neq nil then <<bvarML cdar elem; xbvarML cdr elem>>;
- end;
-
- symbolic procedure conditionML( elem );
- begin;
- printout("<condition>");
- indent!* t;
- expression(car elem);
- indent!* nil;
- printout("</condition>")
- end;
- symbolic procedure lambdaML( elem );
- begin;
- printout("<lambda");
- attributesml(car elem, "");
- indent!* t;
- multi_elem(cdr elem);
- indent!* nil;
- printout("</lambda>")
- end;
- symbolic procedure attributesML( a, s );
- begin;
- if a eq nil then <<princ s; princ ">">>
- else <<
- princ " ";
- princ caar a;
- princ "=""";
- if caar a neq 'definitionurl then <<
- if cadar a = 'vectorml then princ "vector"
- else princ cadar a;
- >>
- else list2string(cadar a);
- princ"""";
- attributesML(cdr a, s);
- >>;
- end;
- symbolic procedure list2string(a);
- begin;
- if a neq nil then <<princ car a; list2string(cdr a)>>;
- end;
- symbolic procedure declareML( elem );
- begin;
- printout("<declare");
- attributesML(car elem, "");
- indent!* t;
- multi_elem(cdr elem);
- indent!* nil;
- printout("</declare>")
- end;
- symbolic procedure lowupperlimitML( elem );
- begin;
- printout("<lowlimit>");
- indent!* t;
- expression(cadr elem);
- indent!* nil;
- printout("</lowlimit>");
- printout("<uplimit>");
- indent!* t;
- expression(caddr elem);
- indent!* nil;
- printout("</uplimit>");
- end;
- symbolic procedure lowlimitML( elem );
- begin;
- printout("<lowlimit>");
- indent!* t;
- expression(car elem);
- indent!* nil;
- printout("</lowlimit>");
- end;
- % Prints out quotients.
- symbolic procedure quotientML( elem , tty);
- begin;
- if (NUMBERP car elem) AND (NUMBERP cadr elem) then <<
- if !*web=nil then printout("<cn type=""rational""> ")
- else printout("<cn type="rational"> ");
- princ car elem;
- princ " <sep/> ";
- princ cadr elem;
- princ " </cn>">>
- else <<
- printout( "<apply>" );
- princ "<"; princ tty; princ "/>";
- indent!* t;
- expression( cadr elem );
- expression( caddr elem );
- indent!* nil;
- printout( "</apply>" )>>;
- end;
- % Prints out all nary functions.
- symbolic procedure nary( elem, type );
- begin;
- if car elem = 'e AND type = 'power then unary(cdr elem, 'exp)
- else <<
- printout( "<apply>" );
- princ "<";
- princ type;
- attributesml(car elem, "/");
- indent!* t;
- multi_elem( cdr elem );
- indent!* nil;
- printout( "</apply>" )>>
- end;
- symbolic procedure multi_elem( elem );
- begin;
- if ((length elem)=1) then expression( car elem )
- else <<expression car elem ; multi_elem( cdr elem );>>
- end;
- symbolic procedure minusML( elem );
- begin;
- printout( "<apply><minus/>" );
- indent!* t;
- multiminus( cdr elem );
- indent!* nil;
- printout( "</apply>" );
- end;
- symbolic procedure multiminus( elem );
- begin;
- expression(car elem);
- if ((length elem)=2) then expression cadr elem;
- end;
- symbolic procedure ciML(elem);
- begin;
- printout("<ci");
- attributesML(car elem, "");
- princ(cadr elem);
- princ("</ci>");
- end;
- symbolic procedure cnML(elem);
- begin;
- printout("<cn");
- attributesML(car elem, "");
- princ(cadr elem);
- princ("</cn>");
- end;
- symbolic procedure semanticML(elem);
- begin;
- if length elem > 1 then <<
- printout("<apply>");
- indent!* t;
- printout("<fn>");
- indent!* t;
- >>;
- printout("<semantic>");
- indent!* t;
- printout("<ci><mo>"); princ caar elem; princ "</mo></ci>";
- printout("<annotation-xml encoding=""OpenMath"">");
- indent!* t;
- printout"<"; list2string cadar elem; princ ">";
- indent!* nil;
- printout("</annotation-xml>");
- indent!* nil;
- printout("</semantic>");
- if length elem > 1 then <<
- indent!* nil;
- printout("</fn>");
- multi_elem(cdr elem);
- indent!* nil;
- printout("</apply>");
- >>;
- end;
- symbolic procedure numML(elem, type);
- begin;
- if type='based_integer then <<
- printout "<cn type=""integer"" base="""; princ cadr elem; princ """> "; princ cadr caddr elem; princ " </cn>";
- >>;
- if type='complex_cartesian then <<
- printout "<cn type=""complex-cartesian""> "; princ cadr elem; princ " <sep/> "; princ caddr elem; princ " </cn>";
- >>;
- if type='complex_polar then <<
- printout "<cn type=""complex-polar""> "; princ cadr elem; princ " <sep/> "; princ caddr elem; princ " </cn>";
- >>;
-
- end;
- % Prints out all pieces of data: i.e terminal symbols.
- % They can be numbers, identifiers, or constants.
- symbolic procedure constsML(exp);
- begin;
- if (NUMBERP exp) then
- << printout "<cn";
- if (FLOATP exp) then princ " type=""real""> "
- else
- if (FIXP exp) then princ " type=""integer""> "
- else princ "> ";
- princ exp;
- princ " </cn>">>;
- if (IDP exp) then
- <<
- if member(intern exp, constants!*) neq nil then
- % <<printout "<cn type=""constant""> "; princ exp; princ " </cn>"; return nil>>
- <<printout "<cn type=""constant""> "; princ exp; princ " </cn>">>
- else << printout "<ci";
- if (listp exp) then princ " type=""list""> "
- else
- if (vectorp exp) then princ " type=""vector""> "
- else princ "> ";
- princ exp;
- princ " </ci>">>; >>;
- end;
- % Functions used to print out variables with a subscript.
- % Prints out expressions in math form. Plagiarised from reduce code of
- % mathprint
- symbolic procedure ma_print l;
- begin scalar temp;
- temp:=outputhandler!*;
- outputhandler!*:=nil;
- terpri!* nil;
- if !*web=nil then maprin "<cn type=""real"">"
- else maprin "<cn type="real">";
- maprin l;
- maprin "</cn>";
- terpri!* nil;
- outputhandler!*:=temp;
- end;
- % Function in charge of doing all printing in order to make sure the
- % indentation is always correct.
- symbolic procedure printout( str );
- begin;
- if !*web = nil then terpri();
- if !*web = nil then for i := 1:indent
- do << princ " " >>;
- if PAIRP str then
- <<if car str='!:rd!: OR car str='!:rn!: then ma_print str
- else princ str>>
- else princ str;
- end;
- lisp operator mml;
- lisp operator mml2ir;
- algebraic operator g_eq;
- algebraic operator l_eq;
- algebraic operator gt;
- algebraic operator lt;
- lisp operator plusRD;
- symbolic procedure test();
- begin scalar a;
- a:=mml2ir();
- terpri!* t;
- princ "Intermediate representation: ";
- terpri!* t;
- print a;
- ir2mml a;
- end;
- end;
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