Artifact b3d8493742d62e4a86a5dbba9da59132f1466f39570c8fb6111ff3b1898a07dd:
- Executable file
r37/packages/misc/boolean.red
— part of check-in
[f2fda60abd]
at
2011-09-02 18:13:33
on branch master
— Some historical releases purely for archival purposes
git-svn-id: https://svn.code.sf.net/p/reduce-algebra/code/trunk/historical@1375 2bfe0521-f11c-4a00-b80e-6202646ff360 (user: arthurcnorman@users.sourceforge.net, size: 5841) [annotate] [blame] [check-ins using] [more...]
- Executable file
r38/packages/misc/boolean.red
— part of check-in
[f2fda60abd]
at
2011-09-02 18:13:33
on branch master
— Some historical releases purely for archival purposes
git-svn-id: https://svn.code.sf.net/p/reduce-algebra/code/trunk/historical@1375 2bfe0521-f11c-4a00-b80e-6202646ff360 (user: arthurcnorman@users.sourceforge.net, size: 5841) [annotate] [blame] [check-ins using]
module boolean; % Propositional calculus support. % Author: Herbert Melenk % Konrad Zuse Zentrum Berlin % A form in propositional calculus is transformed to a canonical DNF % (disjuinct normal form) and then converted back to a or-not-form. % Polynomials are used as intermediate form mapping or to plus and % and to times. The variables are embedded in kernels prop* and % negated variables are represented as not_prop* operators. create!-package('(boolean),'(contrib misc)); algebraic operator prop!*, not_prop!*; algebraic infix implies; algebraic infix equiv; algebraic precedence equiv,=>; algebraic precedence implies,equiv; algebraic let prop!*(~x)*prop!*(x)=>prop!*(x), not_prop!*(~x)*not_prop!*(x)=>not_prop!*(x), prop!*(~x)*not_prop!*(x)=>0; fluid '(propvars!* !'and !'or !'true !'false); symbolic procedure simp!-prop u; begin scalar propvars!*,w,opt; % convert to intermediate standard form. opt:=for each f in cdr u collect reval f; if member('and,opt) then <<!'and:='or; !'or:='and; !'true:=0; !'false:=1;>> else <<!'and:='and; !'or:='or; !'true:=1; !'false:=0;>>; w:=reval prepf simp!-prop1(car u,t); if w=0 then return simp !'false; % add for each variable a true value "and (x or not x)". for each x in propvars!* do w:=reval{'times,w,prepf simp!-prop1({!'or,x,{'not,x}},t)}; % transform to distributive. w:=simp!-prop!-dist w; if not member('full,opt) then w:=simp!-prop2 w; w :=simp!-prop!-form w; if numberp w then return w ./ 1; if not atom w then w:={'boolean,w}; return (w .**1 .*1 .+nil) ./ 1; end; put('boolean,'simpfn,'simp!-prop); symbolic procedure simp!-prop1(u,m); % Convert logical form to polynomial. begin scalar w; if atom u then goto z; if car u = !'and and m or car u=!'or and not m then <<w:=1; for each q in cdr u do w:=multf(w,simp!-prop1(q,m))>> else if car u=!'or and m or car u=!'and and not m then <<w:=nil; for each q in cdr u do w:=addf(w,simp!-prop1(q,m))>> else if car u='not then w:=simp!-prop1(cadr u,not m) else if car u ='implies then (if m then w:=simp!-prop1({'or,{'not,cadr u},caddr u},t) else w:=simp!-prop1({'or,{'not,caddr u},cadr u},t)) else if car u= 'equiv then w:=simp!-prop1( {'or,{'and,cadr u,caddr u},{'and,{'not,cadr u},{'not,caddr u}}},m) else goto z1; return w; z: if u=1 or u=t or u='true then u:=m else if u=0 or u=nil or u='false then u:=not m; if u=t then return simp!-prop1('(or !*true (not !*true)),t); if u=nil then return simp!-prop1('(and !*true (not !*true)),t); z1: u:=reval u; if eqcar(u,'boolean) then return simp!-prop1(cadr u,m); w:= numr simp{if m then 'prop!* else 'not_prop!*,u}; if not member(u,propvars!*) then propvars!*:=u.propvars!*; return w; end; symbolic procedure simp!-prop2 w; % Remove redundant elements, convert back. begin scalar y,z,o,q1,q2,term,old; for each x in propvars!* do <<old:=nil; while w do <<term := car w; w := cdr w; q1:={'prop!*,x}; q2:={'not_prop!*,x}; if not member(q1,term) then <<y:=q2;q2:=q1;q1:=y>>; z:=subst(q2,q1,term); old:=term.old; if (o:=member(z,w)) then << if o then <<w:=delete(car o,w); old:=car o . old>>; term:=delete(q1,term); old:=union({term},old); >>; >>; w:=old; >>; return simp!-prop!-condense w; end; symbolic procedure simp!-prop!-condense u; begin scalar w,r; u:=sort(u,function(lambda(v1,v2);length(v1)<length(v2))); while u do <<w:=car u; u:=cdr u; r:=w.r; for each q in u do if subsetp(w,q) then u:=delete(q,u); >>; return ordn r; end; symbolic procedure simp!-prop!-dist w; % convert to a distributive form. <<if eqcar(w,'plus) then w :=cdr w else w:={w}; w:=for each term in w collect <<term:=if eqcar(term,'times) then cdr term else {term}; if numberp car term then term:=cdr term; sort(term,function(lambda(p1,p2); ordp(cadr p1,cadr p2))) >>; sort(w,function simp!-prop!-order) >>; symbolic procedure simp!-prop!-order(a,b); if null a then nil else if caar a = caar b then simp!-prop!-order(cdr a,cdr b) else if caar a = 'prop!* then t else nil; symbolic procedure simp!-prop!-form u; if u='(nil) then !'true else <<u:=for each term in u collect <<term := for each x in term collect if eqcar(x,'not_prop!*) then {'not,cadr x} else cadr x; if cdr term then !'and . term else car term>>; if cdr u then !'or . u else car u >>; fluid '(bool!-break!*); %symbolic procedure boolean!-eval u; % <<v:=boolean!-eval1 u; % if bool!-break!* then % rederr(u,"boolean evaluation"); % v>> where v=nil,bool!-break!*=nil; % %put('boolean,'boolfn,'boolean!-eval); symbolic procedure test!-bool u; mk!*sq simp!-prop list boolean!-eval1 car u; put('testbool,'psopfn,'test!-bool); symbolic procedure boolean!-eval1 u; begin scalar v; return if eqcar(u,'sq!*) and cddr u and eqcar(v:=prespsq cadr u,'boolean) then boolean!-eval2 cadr v else boolean!-eval2 prepf numr simp!-prop list u; end; symbolic procedure boolean!-eval2 u; if eqcar(u,'boolean) then boolean!-eval2 cadr u else if eqcar(u,'and) or eqcar(u,'or) or eqcar(u,'not) then car u. for each x in cdr u collect boolean!-eval2 x else <<r:=errorset(formbool(u,nil,'algebraic),nil,nil) where !*protfg=t; if errorp r then <<bool!-break!*:=t;erfg!*:=nil; u>> else car r>> where r=nil; put('and,'prtch,"/\"); put('or,'prtch," \/ "); endmodule; end;