module showrule; % Display rules for an operator.
% Author: Herbert Melenk, ZIB, Berlin. E-mail: melenk@zib.de.
% Copyright (c) 1992 ZIB Berlin. All rights reserved.
% Modified by: Francis J. Wright <F.J.Wright@Maths.QMW.ac.uk>
% Time-stamp: <10 November 1998>
% $Id: showrule.red 1.2 1998-11-10 08:33:09+00 fjw Exp $
global '(!*match);
fluid '(asymplis!* powlis!*);
% All let-rules for an operator are collected as rule set.
% Usage in algebraic mode:
% e.g. SHOWRULES SIN;
% The rules for exponentiation can be listed by
% SHOWRULES EXPT;
symbolic procedure showrules opr;
begin scalar r;
r := showruleskvalue opr;
r:=append(r,showrulesopmtch opr);
r:=append(r,showrules!*match opr);
r:=append(r,showrulesdfn opr);
if opr eq 'expt then
<<r:=append(r,showrulespowlis!*());
r:=append(r,showrulespowlis1!*());
r:=append(r,showrulesasymplis!*())>>
else
%% FJW: Show rules for powers of opr:
<<r:=append(r,showrulespowlis!*opr opr);
r:=append(r,showrulespowlis1!*opr opr);
r:=append(r,showrulesasymplis!*opr opr)>>;
return 'list.r;
end;
symbolic procedure showruleskvalue opr;
for each rule in get(opr,'kvalue) collect
begin scalar pattern, vars, target;
pattern := car rule;
vars := selectletvars pattern;
vars := arbvars vars;
pattern := subla(vars,pattern);
target := cadr rule;
target := subla(vars,target);
return mkrule(nil,pattern,target)
end;
symbolic procedure showonerule(test,pattern,target);
% central routine produces one rule.
begin scalar vars;
vars := selectletvars pattern;
vars := arbvars vars;
pattern := subla(vars,pattern);
test := subla(vars,test);
target := subla(vars,target);
test := simpletsymbolic test;
if test=t then test:=nil;
target := simpletsymbolic target;
return mkrule(test,pattern,target)
end;
symbolic procedure showrulesopmtch opr;
for each rule in get(opr,'opmtch) collect
showonerule(cdadr rule,opr . car rule,caddr rule);
symbolic procedure showrulesdfn opr;
append(showrulesdfn1 opr, showrulesdfn2 opr);
symbolic procedure showrulesdfn1 opr;
for i:=1:5 join showrulesdfn1!*(opr,i);
symbolic procedure showrulesdfn1!*(opr,n);
% simple derivatives
begin scalar dfn,pl,rule,pattern,target;
dfn:=dfn_prop(for j:=0:n collect j);
if(pl:=get(opr,dfn)) then return
for j:=1:n join
if (rule:=nth(pl,j)) then
<< pattern := car rule;
pattern := {'df,opr . pattern,nth(pattern,j)};
target := cdr rule;
{showonerule(nil,pattern,target)}
>>;
end;
symbolic procedure mkrule(c,a,b);
<<b:=strip!~ b; c:=strip!~ c;
{'replaceby,separate!~ a,if c then {'when,b,c} else b}>>;
symbolic procedure strip!~ u;
if null u then u else
if idp u then
(if eqcar(w,'!~) then intern compress cdr w else u)
where w=explode2 u
else if atom u then u
else if car u = '!~ then strip!~ cadr u
else strip!~ car u . strip!~ cdr u;
symbolic procedure separate!~ u;
if null u or u='!~ then u else
if idp u then
(if eqcar(w,'!~) then {'!~,intern compress cdr w} else u)
where w=explode2 u
else if atom u then u
else separate!~ car u . separate!~ cdr u;
symbolic procedure showrulesdfn2 opr;
% collect possible rules from df
for each rule in get('df,'opmtch) join
if eqcar(caar rule,opr) then
{showonerule(cdadr rule,'df . car rule,caddr rule)};
symbolic procedure showrules!*match opr;
for each rule in !*match join if smember(opr,rule) then
begin scalar pattern,target,test,p1,p2;
pattern := car rule;
p1 := car pattern;
p2 := cadr pattern;
pattern := list('times,prepsq !*p2q p1,
prepsq !*p2q p2);
test := cdadr rule;
target := caddr rule;
return {showonerule(test,pattern,target)}
end;
symbolic procedure showrulespowlis!*();
for each rule in powlis!* collect
begin scalar pattern,target;
pattern := list ('expt,car rule,cadr rule);
target := cadddr rule;
return mkrule(nil,pattern,target);
end;
symbolic procedure showrulespowlis1!*();
for each rule in powlis1!* collect
begin scalar pattern,target,test,p1,p2;
pattern := car rule;
p1 := car pattern;
p2 := cdr pattern;
pattern := list ('expt, p1, p2);
test := cdadr rule;
target := caddr rule;
return showonerule(test,pattern,target);
end;
symbolic procedure showrulesasymplis!*();
for each rule in asymplis!* collect
mkrule(nil,{'expt,car rule,cdr rule},0);
symbolic procedure showrulespowlis!*opr opr;
%% FJW: Pick rules in powlis!* for operator opr:
for each rule in powlis!* join
if eqcar(car rule, opr) then
begin scalar pattern,target;
pattern := list ('expt,car rule,cadr rule);
target := cadddr rule;
return mkrule(nil,pattern,target) . nil
end;
symbolic procedure showrulespowlis1!*opr opr;
%% FJW: Pick rules in powlis1!* for operator opr:
for each rule in powlis1!* join
if eqcar(caar rule, opr) then
begin scalar pattern,target,test,p1,p2;
pattern := car rule;
p1 := car pattern;
p2 := cdr pattern;
pattern := list ('expt, p1, p2);
test := cdadr rule;
target := caddr rule;
return showonerule(test,pattern,target) . nil
end;
symbolic procedure showrulesasymplis!*opr opr;
%% FJW: Pick rules in asymplis!* for operator opr:
for each rule in asymplis!* join
if eqcar(car rule, opr) then
mkrule(nil,{'expt,car rule,cdr rule},0) . nil;
symbolic procedure selectletvars u;
if null u then nil else
if memq(u,frlis!*) then {u} else
if atom u then nil else
union (selectletvars car u, selectletvars cdr u);
symbolic procedure simpletsymbolic u;
if atom u then u else
if car u eq 'quote then simpletsymbolic cadr u else
if car u memq '(aeval reval revalx boolvalue!*) then
if needs!-lisp!-tag cadr u
then {'symbolic,simpletsymbolic cadr u}
else simpletsymbolic cadr u
else
if car u eq 'list then simpletsymbolic cdr u else
if isboolfn car u then simpletsymbolic (isboolfn car u . cdr u)
else simpletsymbolic car u . simpletsymbolic cdr u;
symbolic procedure needs!-lisp!-tag u;
if numberp u then nil else
if atom u then t else
if car u memq '(aeval reval revalx boolvalue!* quote) then nil else
if car u eq 'list then needs!-lisp!-tag1 cdr u
else if car u eq 'cons then
needs!-lisp!-tag cadr u or needs!-lisp!-tag caddr u
else t;
symbolic procedure needs!-lisp!-tag1 u;
if null u then nil else
needs!-lisp!-tag car u or needs!-lisp!-tag1 cdr u;
fluid '(bool!-functions!*);
bool!-functions!* :=
for each x in {'equal,'greaterp,'lessp,'geq,'leq,'neq,'numberp}
collect get(x,'boolfn).x;
symbolic procedure isboolfn u;
if idp u and (u:=assoc(u,bool!-functions!*)) then cdr u;
symbolic procedure arbvars vars;
for each var in vars collect
var . {'!~, intern compress cddr explode var};
symbolic operator showrules;
endmodule;
end;