module mathpr; % Header module for mathpr package.
% Author: Anthony C. Hearn.
create!-package('(mathpr mprint sqprint ratprin dfprin % prend specprin
fortpri),
nil);
endmodule;
module mprint; % Basic output package for symbolic expressions.
% Authors: Anthony C. Hearn and Arthur C. Norman.
% Copyright (c) 1991 RAND. All rights reserved.
fluid '(!*fort
!*list
!*nat
!*nosplit
!*ratpri
!*revpri
overflowed!*
orig!*
pline!*
posn!*
p!*!*
testing!-width!*
ycoord!*
ymax!*
ymin!*);
global '(!*eraise initl!* nat!*!* obrkp!* spare!*);
switch list,ratpri,revpri,nosplit;
% Global variables initialized in this section.
% SPARE!* should be set in the system dependent code module.
!*eraise := t;
!*nat := nat!*!* := t;
!*nosplit := t; % Expensive, maybe??
obrkp!* := t;
orig!*:=0;
posn!* := 0;
ycoord!* := 0;
ymax!* := 0;
ymin!* := 0;
initl!* := append('(orig!* pline!*),initl!*);
put('orig!*,'initl,0);
flag('(linelength),'opfn); %to make it a symbolic operator;
symbolic procedure mathprint l;
<< terpri!* t;
maprin l;
terpri!* t >>;
symbolic procedure maprin u;
if not overflowed!* then maprint(u,0);
symbolic procedure maprint(l,p!*!*);
% Print expression l at bracket level p!*!* without terminating
% print line. Special cases are handled by:
% pprifn: a print function that includes bracket level as 2nd arg.
% prifn: a print function with one argument.
begin scalar p,x,y;
p := p!*!*; % p!*!* needed for (expt a (quotient ...)) case.
if null l then return nil
else if atom l
then <<if not numberp l or (not l<0 or p<=get('minus,'infix))
then prin2!* l
else <<prin2!* "("; prin2!* l; prin2!* ")">>;
return l >>
else if stringp l then return prin2!* l
else if not atom car l then maprint(car l,p)
else if ((x := get(car l,'pprifn)) and
not(apply2(x,l,p) eq 'failed)) or
((x := get(car l,'prifn)) and
not(apply1(x,l) eq 'failed))
then return l
else if x := get(car l,'infix) then <<
p := not x>p;
if p then <<
y := orig!*;
prin2!* "(";
orig!* := if posn!*<18 then posn!* else orig!*+3 >>;
% (expt a b) was dealt with using a pprifn sometime earlier than this
inprint(car l,x,cdr l);
if p then <<
prin2!* ")";
orig!* := y >>;
return l >>
else prin2!* car l;
prin2!* "(";
obrkp!* := nil;
y := orig!*;
orig!* := if posn!*<18 then posn!* else orig!*+3;
if cdr l then inprint('!*comma!*,0,cdr l);
obrkp!* := t;
orig!* := y;
prin2!* ")";
return l
end;
symbolic procedure exptpri(l,p);
% Prints expression in an exponent notation.
begin scalar !*list,x,pp,q,w1,w2;
if not !*nat or !*fort then return 'failed;
pp := not((q:=get('expt,'infix))>p); % Need to parenthesize
w1 := cadr l;
w2 := caddr l;
if !*eraise and not atom w1 and
(x := get(car w1, 'prifn)) and
get(x, 'expt) = 'inbrackets then
% Special treatment here to avoid muddle between exponents and
% raised indices
w1 := layout!-formula(w1, 0, 'inbrackets)
% Very special treatment for things that will be displayed with
% subscripts
else if x = 'indexprin and not (indexpower(w1, w2)='failed)
then return nil
else w1 := layout!-formula(w1, q, nil);
if null w1 then return 'failed;
begin scalar !*ratpri;
% I do not display fractions with fraction bars in exponent
% expressions, since it usually seems excessive. Also (-p)/q gets
% turned into -(p/q) for printing here
if eqcar(w2,'quotient) and eqcar(cadr w2,'minus)
then w2 := list('minus,list(car w2,cadadr w2,caddr w2))
else w2 := negnumberchk w2;
w2 := layout!-formula(w2, if !*eraise then 0 else q, nil)
end;
if null w2 then return 'failed;
l := cdar w1 + cdar w2;
if pp then l := l + 2;
if l > linelength nil - spare!* - orig!* then return 'failed;
if l > linelength nil - spare!* - posn!* then terpri!* t;
if pp then prin2!* "(";
putpline w1;
if !*eraise then l := 1 - cadr w2
else << oprin 'expt; l := 0 >>;
putpline ((update!-pline(0, l, caar w2) . cdar w2) .
((cadr w2 + l) . (cddr w2 + l)));
if pp then prin2!* ")"
end;
put('expt,'pprifn,'exptpri);
symbolic procedure inprint(op,p,l);
begin scalar x,y;
if op eq 'plus and !*revpri then l := reverse l;
% print sum arguments in reverse order.
if not get(op,'alt) then <<
if op eq 'setq and not atom (x := car reverse l)
and idp car x and (y := getrtype x)
and (y := get(get(y,'tag),'setprifn))
then return apply2(y,car l,x);
if null atom car l and idp caar l
and !*nat and
((x := get(caar l,'prifn)) or (x := get(caar l,'pprifn)))
and (get(x,op) eq 'inbrackets)
% to avoid mix up of indices and exponents.
then<<prin2!* "("; maprint(car l,p); prin2!* ")">>
else if !*nosplit and not testing!-width!* then
prinfit(car l, p, nil)
else maprint(car l, p);
l := cdr l >>;
if !*nosplit and not testing!-width!* then
% The code here goes to a certain amount of trouble to try to arrange
% that terms are never split across lines. This will slow
% printing down a bit, but I hope the improvement in formatting will
% be worth that.
for each v in l do
if atom v or not(op eq get(car v,'alt))
then <<
% It seems to me that it looks nicer to put +, - etc on the second
% line, but := and comma usually look better on the first one when I
% need to split things.
if op memq '(setq !*comma!*) then <<
oprin op;
prinfit(negnumberchk v, p, nil) >>
else prinfit(negnumberchk v, p, op) >>
else prinfit(v, p, nil)
else for each v in l do <<
if atom v or not(op eq get(car v,'alt))
then <<oprin op; maprint(negnumberchk v,p)>>
% difficult problem of negative numbers needing to be in
% prefix form for pattern matching.
else maprint(v,p) >>
end;
symbolic procedure flatsizec u;
if null u then 0
else if atom u then lengthc u
else flatsizec car u + flatsizec cdr u + 1;
symbolic procedure oprin op;
(lambda x;
if null x then <<prin2!* " "; prin2!* op; prin2!* " ">>
else if !*fort then prin2!* x
else if !*list and obrkp!* and op memq '(plus minus)
then if testing!-width!* then overflowed!* := t
else <<terpri!* t; prin2!* x>>
else if flagp(op,'spaced)
then <<prin2!* " "; prin2!* x; prin2!* " ">>
else prin2!* x)
get(op,'prtch);
symbolic procedure prin2!* u;
begin integer m,n;
if overflowed!* then return 'overflowed
else if !*fort then return fprin2 u
else if !*nat then <<
if u = 'pi then u := symbol '!.pi
else if u = 'infinity then u := symbol 'infinity >>;
n := lengthc u;
if n<=(linelength nil-spare!*) then <<
m := posn!*+n;
% I somewhat dislike having the side-effect of a call to
% terpri!* in the condition tested here, but that is maybe what
% the problem calls for.
if m<=(linelength nil-spare!*) or
(not testing!-width!* and
<< terpri!* t;
(m := posn!*+n)<=(linelength nil-spare!*) >>)
then <<if not !*nat then %fjw% prin2 u
% output should be REDUCE-readable %% begin{fjw}
if stringp u or get(u,'switch!*) or digit u
or get(car explode2 u,'switch!*) then prin2 u
else prin1 u %% end{fjw}
else pline!* := (((posn!* . m) . ycoord!*) . u)
. pline!*;
return (posn!* := m)>>>>;
%identifier longer than one line;
if testing!-width!* then <<
overflowed!* := t;
return 'overflowed >>
else if !*fort
then rerror(mathpr,1,list(u,"too long for FORTRAN"));
% Let LISP print the atom.
terpri!* nil;
prin2t u;
% if !*clisp then m := posn() else
% I think this is what is really wanted.
m := remainder(n,(linelength nil-spare!*));
return (posn!* := m)
end;
symbolic procedure terpri!* u;
begin integer n;
if testing!-width!* then return overflowed!* := t
else if !*fort then return fterpri(u)
else if !*nat and pline!*
then <<
pline!* := reverse pline!*;
for n := ymax!* step -1 until ymin!* do <<
scprint(pline!*,n);
terpri() >>;
pline!* := nil >>;
if u then terpri();
posn!* := orig!*;
ycoord!* := ymax!* := ymin!* := 0
end;
symbolic procedure scprint(u,n);
begin scalar m;
posn!* := 0;
for each v in u do <<
if cdar v=n then <<
if not((m:= caaar v-posn!*)<0) then spaces m;
prin2 cdr v;
posn!* := cdaar v >> >>
end;
% Definition of some symbols and their access function.
symbolic procedure symbol s;
get(s,'symbol!-character);
put('!.pi, 'symbol!-character, 'pi);
put('bar, 'symbol!-character, '!-);
put('int!-top, 'symbol!-character, '!/);
put('int!-mid, 'symbol!-character, '!|);
put('int!-low, 'symbol!-character, '!/);
put('d, 'symbol!-character, '!d); % This MUST be lower case
%%put('sqrt, 'symbol!-character, 'sqrt);% No useful fallback here
put('vbar, 'symbol!-character, '!|);
put('sum!-top, 'symbol!-character, "---");
put('sum!-mid, 'symbol!-character, "> ");
put('sum!-low, 'symbol!-character, "---");
put('prod!-top, 'symbol!-character, "---");
put('prod!-mid, 'symbol!-character, "| |");
put('prod!-low, 'symbol!-character, "| |");
put('infinity, 'symbol!-character, 'infinity);
% In effect nothing special
put('mat!-top!-l, 'symbol!-character, '![);
put('mat!-top!-r, 'symbol!-character, '!]);
put('mat!-low!-l, 'symbol!-character, '![);
put('mat!-low!-r, 'symbol!-character, '!]);
% The following definitions allow for more natural printing of
% conditional expressions within rule lists.
symbolic procedure condpri(u,p);
<<if p>0 then prin2!* "(";
while (u := cdr u) do
<<if not(caar u eq 't)
then <<prin2!* 'if; prin2!* " "; maprin caar u;
prin2!* " "; prin2!* 'then; prin2!* " ">>;
maprin cadar u;
if cdr u then <<prin2!* " "; prin2!* 'else; prin2!* " ">>>>;
if p>0 then prin2!* ")">>;
put('cond,'pprifn,'condpri);
symbolic procedure revalpri u;
maprin eval cadr u;
put('aeval,'prifn,'revalpri);
put('reval,'prifn,'revalpri);
symbolic procedure boolvalpri u;
maprin cadr u;
put('boolvalue!*,'prifn,'boolvalpri);
endmodule;
module sqprint; % Routines for printing standard forms and quotients.
% Author: Anthony C. Hearn.
% Copyright (c) 1991 RAND. All rights reserved.
% Modified by A. C. Norman, 1987.
fluid '(!*fort
!*nat
!*nero
!*pri
!*prin!#
overflowed!*
orig!*
posn!*
testing!-width!*
ycoord!*
ymax!*
ymin!*
wtl!*);
testing!-width!* := overflowed!* := nil;
global '(!*eraise !*horner);
% When nat is enabled I use some programmable characters to
% draw pi, fraction bars and integral signs. (symbol 's) returns
% a character-object, and I use
% .pi pi
% bar solid horizontal bar -
% int-top top hook of integral sign /
% int-mid vertical mid-stroke of integral sign |
% int-low lower hook of integral sign /
% d curly-d for use with integral display d
% sqrt square root sign sqrt
% sum-top ---
% sum-mid > for summation
% sum-low ---
% prod-top ---
% prod-mid | | for products
% prod-low | |
% infinity infinity sign
% mat!-top!-l / for display of matrices
% mat!-top!-r \
% mat!-low!-l \
% mat!-low!-r /
% vbar |
symbolic procedure !*sqprint u;
sqprint cadr u;
put('!*sq, 'prifn, '!*sqprint);
symbolic procedure printsq u;
<< terpri!* t;
sqprint u;
terpri!* u;
u >>;
symbolic procedure sqprint u;
%mathprints the standard quotient U;
begin scalar flg,w,z,!*prin!#;
!*prin!# := t;
z := orig!*;
if !*nat and posn!*<20 then orig!* := posn!*;
if !*pri or wtl!* then <<
if null !*horner
or errorp(w:=errorset!*(list('horner,mkquote u),nil))
then w := prepsq!* u
else w := prepsq car w;
maprin w >>
else if cdr u neq 1 then <<
flg := not domainp numr u and red numr u;
if flg then prin2!* "(";
xprinf(car u,nil,nil);
if flg then prin2!* ")";
prin2!* " / ";
flg:= not domainp denr u and (red denr u or lc denr u neq 1);
% flg:= not domainp denr u and red denr u;
if flg then prin2!* "(";
xprinf(cdr u,nil,nil);
if flg then prin2!* ")" >>
else xprinf(car u,nil,nil);
return (orig!* := z)
end;
symbolic procedure printsf u;
<< prinsf u;
terpri!* nil;
u >>;
symbolic procedure prinsf u;
if null u then prin2!* 0 else xprinf(u,nil,nil);
symbolic procedure xprinf(u,v,w);
%U is a standard form.
%V is a flag which is true if a term has preceded current form.
%W is a flag which is true if form is part of a standard term;
%Procedure prints the form and returns NIL;
<< while not domainp u do <<
xprint(lt u,v);
u := red u;
v := t >>;
if not null u then xprid(u,v,w)
else nil >>;
symbolic procedure xprid(u,v,w);
%U is a domain element.
%V is a flag which is true if a term has preceded element.
%W is a flag which is true if U is part of a standard term.
%Procedure prints element and returns NIL;
begin
if minusf u then <<oprin 'minus; u := !:minus u>>
else if v then oprin 'plus;
if not w or u neq 1
then if atom u then prin2!* u else maprin u
end;
symbolic procedure xprint(u,v);
%U is a standard term.
%V is a flag which is true if a term has preceded this term.
%Procedure prints the term and returns NIL;
begin scalar flg,w;
flg := not domainp tc u and red tc u;
if flg then <<
if v then oprin 'plus;
prin2!* "(" >>;
xprinf(tc u,if flg then nil else v,not flg);
if flg then prin2!* ")";
if not atom tc u or not abs tc u=1 then oprin 'times;
w := tpow u;
if atom car w then prin2!* car w
else if not atom caar w or caar w eq '!*sq then <<
prin2!* "(";
if not atom caar w then xprinf(car w,nil,nil)
else sqprint cadar w;
prin2!* ")" >>
else if caar w eq 'plus then maprint(car w,100)
else maprin car w;
if not (cdr w=1) then <<
if !*nat and !*eraise
then <<ycoord!* := ycoord!*+1;
if ycoord!*>ymax!* then ymax!* := ycoord!*>>
else prin2!* get('expt,'prtch);
prin2!* if numberp cdr w and minusp cdr w then list cdr w
else cdr w;
if !*nat and !*eraise
then <<ycoord!* := ycoord!*-1;
if ymin!*>ycoord!* then ymin!* := ycoord!*>> >>
end;
symbolic procedure varpri(u,v,w);
begin scalar x;
%U is expression being printed
%V is the original form that was evaluated.
%W is an id that indicates if U is the first, only or last element
% in the current set (or NIL otherwise).
testing!-width!* := overflowed!* := nil;
if null u then u := 0;
if !*nero and u=0 then return nil;
v := setvars v;
if (x := getrtype u) and flagp(x,'sprifn)
then return if null v then apply1(get(get(x,'tag),'prifn),u)
else maprin list('setq,car v,u);
if w memq '(first only) then terpri!* t;
if !*fort then return fvarpri(u,v,w);
if v then u := 'setq . aconc(v,u);
maprin u;
if null w or w eq 'first then return nil
else if not !*nat then prin2!* "$";
terpri!*(not !*nat);
return nil
end;
symbolic procedure setvars u;
if atom u then nil
else if car u memq '(setel setk)
then lispeval cadr u . setvars caddr u
else if car u eq 'setq then cadr u . setvars caddr u
else nil;
endmodule;
module ratprin; % Printing standard quotients.
% Author: Eberhard Schruefer.
% Modifications by: Anthony C. Hearn & A. C. Norman.
fluid '(!*fort
!*list
!*mcd
!*nat
!*ratpri
dmode!*
ycoord!*
ymin!*
ymax!*
orig!*
pline!*
posn!*
p!*!*);
global '(spare!*);
switch ratpri;
!*ratpri := t; % default value if this module is loaded.
put('quotient,'prifn,'quotpri);
put('quotpri, 'expt, 'inbrackets);
symbolic procedure quotpri u;
% *mcd is included here since it uses rational domain elements.
begin scalar dmode;
if null !*ratpri or null !*nat or !*fort or !*list or null !*mcd
then return 'failed
else if flagp(dmode!*,'ratmode)
then <<dmode := dmode!*; dmode!* := nil>>;
u := ratfunpri1 u;
if dmode then dmode!* := dmode;
return u
end;
symbolic procedure ratfunpri1 u;
begin scalar x,y,ch,pln,pld;
integer heightnum,heightden,orgnum,orgden,fl,w;
spare!* := spare!* + 2;
if (pln := layout!-formula(cadr u, 0, nil)) and
(pld := layout!-formula(caddr u, 0, nil)) then <<
spare!* := spare!* - 2;
fl := 2 + max(cdar pln, cdar pld);
if fl>(linelength nil - spare!* - posn!*) then terpri!* t;
w := (cdar pln - cdar pld); % Width difference num vs. den
if w > 0 then << orgnum := 0; orgden := w / 2 >>
else << orgnum := (-w) / 2; orgden := 0 >>;
heightnum := cddr pln - cadr pln + 1;
heightden := cddr pld - cadr pld + 1;
pline!* :=
append(
update!-pline(orgnum + posn!* + 1 - orig!*,
1 - cadr pln + ycoord!*,
caar pln),
append(update!-pline(orgden + posn!* + 1 - orig!*,
ycoord!* - cddr pld - 1,
caar pld),
pline!*));
ymin!* := min(ymin!*, ycoord!* - heightden);
ymax!* := max(ymax!*, ycoord!* + heightnum);
ch := symbol 'bar;
for j := 1:fl do prin2!* ch >>
else <<
% Here the miserable thing will not fit on one line
spare!* := spare!* - 2; % Restore
u := cdr u;
x := get('quotient,'infix);
if p!*!* then y := p!*!*>x else y := nil;
if y then prin2!* "(";
maprint(car u,x);
oprin 'quotient;
maprint(negnumberchk cadr u,x);
if y then prin2!* ")">>
end;
symbolic procedure layout!-formula(u, p, op);
% This procedure forms a pline!* structure for an expression that
% will fit upon a single line. It returns the pline* together with
% height, depth and width information. If the line would not fit
% it returns nil. Note funny treatment of orig!* and width here.
% If op is non-nil oprin it too - if it is 'inbrackets do that.
begin
scalar ycoord!*, ymin!*, ymax!*, posn!*, pline!*,
testing!-width!*, overflowed!*;
pline!* := overflowed!* := nil;
ycoord!* := ymin!* := ymax!* := 0;
posn!* := orig!*;
testing!-width!* := t;
if op then <<
if op = 'inbrackets then prin2!* "("
else oprin op >>;
maprint(u, p);
if op = 'inbrackets then prin2!* ")";
if overflowed!* then return nil
else return (pline!* . (posn!* - orig!*)) . (ymin!* . ymax!*)
end;
symbolic procedure update!-pline(x,y,pline);
% Adjusts origin of expression in pline by (x,y).
if x=0 and y=0 then pline
else for each j in pline collect
(((caaar j #+ x) . (cdaar j #+ x)) . (cdar j #+ y)) . cdr j;
symbolic procedure prinfit(u, p, op);
% Display u (as with maprint) with op in front of it, but starting
% a new line before it if there would be overflow otherwise.
begin
scalar w;
if not !*nat or testing!-width!* then <<
if op then oprin op;
return maprint(u, p) >>;
w := layout!-formula(u, p, op);
if w = nil then <<
if op then oprin op;
return maprint(u, p) >>;
putpline w
end;
symbolic procedure putpline w;
begin
if posn!* #+ cdar w > linelength nil #- spare!* then terpri!* t;
pline!* :=
append(update!-pline(posn!* #- orig!*, ycoord!*, caar w),
pline!*);
posn!* := posn!* #+ cdar w;
ymin!* := min(ymin!*, cadr w #+ ycoord!*);
ymax!* := max(ymax!*, cddr w #+ ycoord!*)
end;
endmodule;
module dfprin; % Printing for derivatives plus other options
% suggested by the Twente group
% Author: A. C. Norman, reconstructing ideas from Ben Hulshof,
% Pim van den Heuvel and Hans van Hulzen.
fluid '(!*fort !*nat depl!* posn!*);
global '(!*dfprint
!*noarg
farglist!*);
switch dfprint,noarg;
!*dfprint := nil; % This is OFF by default because switching it on
% changes Reduce output in a way that might upset
% customers who have not found out about this switch.
% Perhaps in later releases of the code (and when the
% manual reflects this upgrade) it will be possible
% to make 'on dfprint' the default. Some sites may of
% course wish to arrange things otherwise...
!*noarg := t; % If dfprint is enabled I am happy for noarg to be
% the expected option.
farglist!* := nil;
symbolic procedure dfprintfn u;
% Display derivatives - if suitable flags are set this uses
% subscripts to denote differentiation and loses the arguments to
% functions.
if not !*nat or !*fort or not !*dfprint then 'failed
else begin
scalar w;
w := layout!-formula('!!df!! . cdr u, 0, nil);
if w = nil then return 'failed
else putpline w
end;
put('df, 'prifn, 'dfprintfn);
symbolic procedure dflayout u;
% This is a prifn for !!df!!, which is used internally when I am
% formatting derivatives, but which should only ever be seen in
% testing!-width!* mode and never at all by the end-user.
begin
scalar op, args, w;
w := car (u := cdr u);
u := cdr u;
if !*noarg then <<
if atom w then <<
op := w;
args := assoc(op, depl!*); % Implicit args
if args then args := cdr args >>
else <<
op := car w;
args := cdr w >>; % Explicit args
remember!-args(op, args);
w := op >>;
maprin w;
if u then <<
u := layout!-formula('!!dfsub!! . u, 0, nil); % subscript line
if null u then return 'failed;
w := 1 + cddr u;
putpline((update!-pline(0, -w, caar u) . cdar u) .
((cadr u - w) . (cddr u - w))) >>
end;
symbolic procedure dfsublayout u;
% This is a prifn for !!dfsub!!, which is used internally when I am
% formatting derivatives, but which should only ever be seen in
% testing!-width!* mode and never at all by the end-user.
begin
scalar dfcase, firstflag, w;
% This is used as a prifn for both df and other things with
% subscripts - dfcase remembers which.
dfcase := (car u = '!!dfsub!!);
u := cdr u;
firstflag := t;
while u do <<
w := car u;
u := cdr u;
if firstflag then firstflag := nil
else prin2!* ",";
if dfcase and u and numberp car u then <<
prin2!* car u;
u := cdr u >>;
maprin w >>
end;
put('!!df!!, 'prifn, 'dflayout);
put('!!dfsub!!, 'prifn, 'dfsublayout);
symbolic procedure remember!-args(op, args);
% This records information that can be displayed by the user
% issuing the command 'FARG'.
begin
scalar w;
w := assoc(op, farglist!*);
if null w then farglist!* := (op . args) . farglist!*
end;
symbolic procedure farg;
% Implementation of FARG: display implicit argument data
begin
scalar newname;
prin2!* "The operators have the following ";
prin2!* "arguments or dependencies";
terpri!* t;
for each p in farglist!* do <<
prin2!* car p;
prin2!* "=";
% To avoid clever pieces of code getting rid of argument displays
% here I convert the name of the function into a string so that
% maprin produces a simple but complete display. Since I expect
% farg to be called but rarely this does not seem overexpensive
newname := compress ('!" . append(explodec car p, '(!")));
maprin(newname . cdr p);
terpri!* t >>
end;
put('farg, 'stat, 'endstat);
symbolic procedure clfarg;
% Clear record of implicit args
farglist!* := nil;
put('clfarg, 'stat, 'endstat);
symbolic procedure setprifn(u, fn);
% Establish (or clear) prifn property for a list of symbols
for each n in u do
if idp n then <<
% Things listed here will be declared operators now if they have
% not been so declared earlier.
if not operatorp n then mkop n;
if fn then put(n, 'prifn, fn)
else remprop(n, 'prifn) >>
else lprim list(n, "not an identifier");
symbolic procedure indexprin u;
% Print helper-function when integer-valued arguments are to be shown as
% subscripts
if not !*nat or !*fort then 'failed
else begin
scalar w;
w := layout!-formula('!!index!! . u, 0, nil);
if w = nil then return 'failed
else putpline w
end;
symbolic procedure indexpower(u, n);
% Print helper-function when integer-valued arguments are to be shown as
% subscripts with exponent n
begin
scalar w;
w := layout!-formula('!!indexpower!! . n . u, 0, nil);
if w = nil then return 'failed
else putpline w
end;
symbolic procedure indexlayout u;
% This is a prifn for !!index!!, which is used internally when I am
% formatting index forms, but which should only ever be seen in
% testing!-width!* mode and never at all by the end-user.
begin
scalar w;
w := car (u := cdr u);
u := cdr u;
maprin w;
if u then <<
u := layout!-formula('!!indexsub!! . u, 0, nil);
% subscript line
if null u then return 'failed;
w := 1 + cddr u;
putpline((update!-pline(0, -w, caar u) . cdar u) .
((cadr u - w) . (cddr u - w))) >>
end;
symbolic procedure indexpowerlayout u;
% Format a subscripted object raised to some power.
begin
scalar n, w, pos, maxpos;
n := car (u := cdr u); % The exponent
w := car (u := cdr u);
u := cdr u;
maprin w;
w := layout!-formula(n, 0, nil);
pos := posn!*;
putpline((update!-pline(0, 1 - cadr w, caar w) . cdar w) .
(1 . (1 + cddr w - cadr w)));
maxpos := posn!*;
posn!* := pos;
if u then <<
u := layout!-formula('!!indexsub!! . u, 0,nil);
% subscript line
if null u then return 'failed;
w := 1 + cddr u;
putpline((update!-pline(0, -w, caar u) . cdar u) .
((cadr u - w) . (cddr u - w))) >>;
posn!* := max(posn!*, maxpos)
end;
put('!!index!!, 'prifn, 'indexlayout);
put('!!indexpower!!, 'prifn, 'indexpowerlayout);
put('!!indexsub!!, 'prifn, 'dfsublayout);
symbolic procedure noargsprin u;
% Print helper-function when arguments for a function are to be hidden,
% but remembered for display via farg
if not !*nat or !*fort then 'failed
else <<
remember!-args(car u, cdr u);
maprin car u >>;
symbolic procedure doindex u;
% Establish some function names to have args treated as index values
setprifn(u, 'indexprin);
symbolic procedure offindex u;
% Clear effect of doindex
setprifn(u, nil);
symbolic procedure donoargs u;
% Identify functions where args are to be hidden
setprifn(u, 'noargsprin);
symbolic procedure offnoargs u;
% Clear effect of donoargs
setprifn(u, nil);
put('doindex, 'stat, 'rlis);
put('offindex, 'stat, 'rlis);
put('donoargs, 'stat, 'rlis);
put('offnoargs, 'stat, 'rlis);
endmodule;
module fortpri; % FORTRAN output package for expressions.
% Author: Anthony C. Hearn.
% Modified by: James Davenport after Francoise Richard, April 1988.
% Copyright (c) 1991 RAND. All rights reserved.
fluid '(!*fort
!*period
scountr
explis
fbrkt
fvar
nchars
svar
posn!*);
global '(cardno!*
fortwidth!*
spare!*
varnam!*);
%Global variables initialized in this section;
% SPARE!* should be set in the system dependent code module.
cardno!*:=20;
fortwidth!* := 70;
posn!* := 0;
varnam!* := 'ans;
flag ('(cardno!* fortwidth!*),'share);
symbolic procedure varname u;
%sets the default variable assignment name;
varnam!* := car u;
rlistat '(varname);
symbolic procedure flength(u,chars);
if chars<0 then chars
else if atom u
then chars-if numberp u then if fixp u then flatsizec u+1
else flatsizec u
else flatsizec((lambda x; if x then x else u)
get(u,'prtch))
else flength(car u,flenlis(cdr u,chars)-2);
symbolic procedure flenlis(u,chars);
if null u then chars
else if chars<0 then chars
else if atom u then flength(u,chars)
else flenlis(cdr u,flength(car u,chars));
symbolic procedure fmprint(l,p);
begin scalar x;
if null l then return nil
else if atom l then <<
if l eq 'e then return fprin2 "EXP(1.0)";
if not numberp l or
not l<0 then return fprin2 l;
fprin2 "(";
fbrkt := nil . fbrkt;
fprin2 l;
fprin2 ")";
return fbrkt := cdr fbrkt >>
else if stringp l then return fprin2 l
else if not atom car l then fmprint(car l,p)
% else if x := get(car l,'specprn)
% then return apply1(x,cdr l)
else if ((x := get(car l,'pprifn))
and not((x := apply2(x,l,p)) eq 'failed)) or
((x := get(car l,'prifn))
and not((x := apply1(x,l)) eq 'failed))
then return x
else if x := get(car l,'infix) then <<
p := not x>p;
if p then <<fprin2 "("; fbrkt := nil . fbrkt>>;
fnprint(car l,x,cdr l);
if p then <<fprin2 ")"; fbrkt := cdr fbrkt>>;
return >>
else fprin2 car l;
fprin2 "(";
fbrkt := nil . fbrkt;
x := !*period;
% Assume no period printing for non-operators (e.g., matrices).
if gettype car l neq 'operator then !*period := nil;
if cdr l then fnprint('!*comma!*,0,cdr l);
!*period := x;
fprin2 ")";
return fbrkt := cdr fbrkt
end;
symbolic procedure fnprint(op,p,l);
begin
if op eq 'expt then return fexppri(p,l)
else if not get(op,'alt) then <<
fmprint(car l,p);
l := cdr l >>;
for each v in l do <<
if atom v or not (op eq get(car v,'alt)) then foprin op;
fmprint(v,p) >>
end;
symbolic procedure fexppri(p,l);
% Next line added by James Davenport after Francoise Richard.
if car l eq 'e then fmprint('exp . cdr l,p)
else begin scalar pperiod;
fmprint(car l,p);
foprin 'expt;
pperiod := !*period;
if numberp cadr l then !*period := nil else !*period := t;
fmprint(cadr l,p);
!*period := pperiod
end;
symbolic procedure foprin op;
(lambda x; if null x then fprin2 op else fprin2 x) get(op,'prtch);
symbolic procedure fvarpri(u,v,w);
%prints an assignment in FORTRAN notation;
begin integer scountr,llength,nchars; scalar explis,fvar,svar;
llength := linelength nil;
if not posintegerp cardno!*
then typerr(cardno!*,"FORTRAN card number");
if not posintegerp fortwidth!*
then typerr(fortwidth!*,"FORTRAN line width");
linelength fortwidth!*;
if stringp u
then return <<fprin2 u;
if w eq 'only then fterpri(t);
linelength llength>>;
if eqcar(u,'!*sq) then u := prepsq!* cadr u;
scountr := 0;
nchars := ((linelength nil-spare!*)-12)*cardno!*;
%12 is to allow for indentation and end of line effects;
svar := varnam!*;
fvar := if null v then svar else car v;
if posn!*=0 and w then fortpri(fvar,u,w)
else fortpri(nil,u,w);
% should mean expression preceded by a string.
linelength llength
end;
symbolic procedure fortpri(fvar,xexp,w);
begin scalar fbrkt;
if eqcar(xexp,'list)
then <<posn!* := 0;
fprin2 "C ***** INVALID FORTRAN CONSTRUCT (";
fprin2 car xexp;
return fprin2 ") NOT PRINTED">>;
if flength(xexp,nchars)<0
then xexp := car xexp . fout(cdr xexp,car xexp,w);
if fvar
then <<posn!* := 0;
fprin2 " ";
fmprint(fvar,0);
fprin2 "=">>;
fmprint(xexp,0);
if w then fterpri(w)
end;
symbolic procedure fout(args,op,w);
begin integer ncharsl; scalar distop,x,z;
ncharsl := nchars;
if op memq '(plus times) then distop := op;
while args do
<<x := car args;
if atom x and (ncharsl := flength(x,ncharsl))
or (null cdr args or distop)
and (ncharsl := flength(x,ncharsl))>0
then z := x . z
else if distop and flength(x,nchars)>0
then <<z := fout1(distop . args,w) . z;
args := list nil>>
else <<z := fout1(x,w) . z;
ncharsl := flength(op,ncharsl)>>;
ncharsl := flength(op,ncharsl);
args := cdr args>>;
return reversip!* z
end;
symbolic procedure fout1(xexp,w);
begin scalar fvar;
fvar := genvar();
explis := (xexp . fvar) . explis;
fortpri(fvar,xexp,w);
return fvar
end;
% If we are in a comment, we want to continue to stay in one,
% Even if there's a formula. That's the purpose of this flag
% Added by James Davenport after Francoise Richard.
global '(Comment!*);
symbolic procedure fprin2 u;
% FORTRAN output of U;
begin integer m,n;
if posn!*=0 then Comment!*:=
stringp u and cadr(explode u) eq 'C;
n := flatsizec u;
m := posn!*+n;
if fixp u and !*period then m := m+1;
if m<(linelength nil-spare!*) then posn!* := m
else <<terpri();
if Comment!* then << prin2 "C"; spaces 4 >>
else spaces 5;
prin2 ". "; posn!* := n+7>>;
prin2 u;
if fixp u and !*period then prin2 "."
end;
symbolic procedure fterpri(u);
<<if not posn!*=0 and u then terpri();
posn!* := 0>>;
symbolic procedure genvar;
intern compress append(explode svar,explode(scountr := scountr + 1));
endmodule;
end;