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/* License in license.txt. */

/* */

/* Adverbs: Inverse & Identity Functions */

#include "j.h"

static F1(jtinvamp);

static B ip(A w,C c,C d){A f,g;V*v;

v=VAV(w); f=v->f; g=v->g;

R CSLASH==ID(f)&&c==ID(VAV(f)->f)&&d==ID(g);

}

static B consf(A w){A f;C c;

c=ID(w);

if(c==CFCONS||c==CQQ&&(f=VAV(w)->f,NOUN&AT(f)))R 1;

R 0;

} /* 1 iff w is a constant function */

static F2(jtfong){A f;C c;V*v;

RZ(a&&w);

v=VAV(a); c=v->id; f=v->f;

R c==CRIGHT ? w : c==CFORK&&(NOUN&AT(f)||CCAP==ID(f)) ? folk(f,v->g,fong(v->h,w)) : folk(ds(CCAP),a,w);

} /* [: f g with simplifications */

static F1(jtinvfork){A f,fi,g,gi,h,k;B b,c;V*v;

RZ(w);

v=VAV(w); RZ(f=unname(v->f)); g=v->g; RZ(h=unname(v->h));

if(CCAP==ID(f))R fong(inv(h),inv(g));

c=1&&NOUN&AT(f); b=c||consf(f);

ASSERT(b!=consf(h),EVDOMAIN);

RZ(k=c?f:df1(zero,b?f:h));

RZ(gi=inv(b?amp(k,g):amp(g,k)));

RZ(fi=inv(b?h:f));

if(CAMP==ID(gi)){

v=VAV(gi);

if (NOUN&AT(v->f))RZ(gi=folk(v->f, v->g, ds(CRIGHT)))

else if(NOUN&AT(v->g))RZ(gi=folk(v->g,swap(v->f),ds(CRIGHT)));

}

R fong(fi,gi);

}

static DF1(jtexpandf){A f; RZ(w&&self); f=VAV(self)->f; R expand(VAV(f)->f,w);}

static DF1(jtexpandg){A f,g,z;V*v;

RZ(w&&self);

f=VAV(self)->f; v=VAV(f); g=v->g;

jt->fill=VAV(g)->g; z=expand(v->f,w); jt->fill=0;

R z;

}

static F2(jtdiag){I d,k,m,p,r,t,*v;

RZ(a&&w);

r=AR(w); t=AT(w); k=bp(t);

v=AS(w); m=0; DO(r, m=MIN(m,v[i]););

v=AS(w)+r; p=1; d=0; DO(r, d+=p; p*=*--v;);

if(t!=AT(a))RZ(a=cvt(t,a));

if(AR(a)){

ASSERT(m==AN(a),EVLENGTH);

ASSERT(0,EVNONCE);

}else{

ASSERT(0,EVNONCE);

}}

static F1(jtbminv){A*wv,x,z=w;I i,j,m,r,*s,t=0,*u,**v,*y,wn,wr,*ws,wd;

RZ(w);

ASSERT(0,EVNONCE);

ASSERT(BOX&AT(w),EVDOMAIN);

wn=AN(w); wr=AR(w); ws=AS(w); wv=AAV(w); wd=(I)w*ARELATIVE(w);

if(1>=wr)R raze(w);

if(!wn)R iota(reshape(sc(wr),zero));

GA(x,INT,wr,1,0); u=AV(x); memset(u,C0,wr*SZI);

GA(x,INT,wr,1,0); v=(I**)AV(x);

DO(wr, m=ws[i]; GA(x,INT,m,1,0); memset(v[i]=AV(x),CFF,m*SZI););

for(i=0;i<wn;++i){

x=WVR(i); r=AR(x); s=AS(x);

if(AN(x)){if(!t)t=AT(x); ASSERT(HOMO(t,AT(x)),EVDOMAIN);}

ASSERT(2>r||r==wr,EVRANK);

if(2>r)z=0;

else DO(wr, y=v[i]+u[i]; if(0>*y)*y=s[i]; else ASSERT(*y==s[i],EVLENGTH););

j=wr; while(1){--j; ++u[j]; if(ws[j]>u[j])break; u[j]=0;}

}

if(!z){A f,h,*zv;I*hv;

GA(z,BOX,wn,2,ws); zv=AAV(z);

GA(h,INT,wr,1,0); hv=AV(h);

GA(f,t,1,1,0); RZ(f=filler(f)); memset(u,C0,wr*SZI);

for(i=0;i<wn;++i){

zv[i]=x=WVR(i);

if(2>AR(x)){DO(wr, hv[i]=*(v[i]+u[i]);); RZ(zv[i]=diag(x,reshape(h,f)));}

j=wr-1; while(1){--j; ++u[j]; if(ws[j]>u[j])break; u[j]=0;}

}}

DO(wr, RZ(z=df1(z,slash(under(qq(ds(CCOMMA),sc(wr-i)),ds(COPE))))););

R ope(z);

} /* <;.1 or <;.2 inverse on matrix argument */

static F1(jtinvamp){A f,ff,g,h,*q,x,y;B nf,ng;C c,d,*yv;I n;V*u,*v;

RZ(w);

v=VAV(w);

f=v->f; nf=!!(NOUN&AT(f));

g=v->g; ng=!!(NOUN&AT(g));

h=nf?g:f; x=nf?f:g; c=ID(h); u=VAV(h);

switch(c){

case CPLUS: R amp(negate(x),h);

case CSTAR: R amp(recip(x), h);

case CMINUS: R nf?w:amp(x,ds(CPLUS));

case CDIV: R nf?w:amp(x,ds(CSTAR));

case CROOT: R amp(ds(nf?CEXP:CLOG),x);

case CEXP: R ng&&equ(x,num[2])?ds(CROOT):amp(x,ds(nf?CLOG:CROOT));

case CLOG: R nf?amp(x,ds(CEXP)):amp(ds(CROOT),x);

case CJDOT: R nf?atop(inv(ds(CJDOT)),amp(ds(CMINUS),x)):amp(ds(CMINUS),jdot1(x));

case CRDOT: R nf?atop(inv(ds(CRDOT)),amp(ds(CDIV ),x)):amp(ds(CDIV ),rdot1(x));

case CLBRACE: R nf?amp(pinv(x),h):amp(x,ds(CIOTA));

case COBVERSE: ff=VAV(h)->g; R amp(nf?x:ff,nf?ff:x);

case CPDERIV: if(!AR(h))R ds(CPDERIV);

case CXCO: RE(n=i0(x)); ASSERT(n&&-3<n&&n<3,EVDOMAIN);

case CROT:

case CCIRCLE:

case CSPARSE: if(nf)R amp(negate(x),h); break;

case CABASE: if(nf)R amp(x,ds(CBASE)); break;

case CIOTA: if(nf)R amp(ds(CLBRACE),x); break;

case CTHORN: if(nf)R ds(CEXEC); break;

case CTILDE:

if(ff=VAV(h)->f,VERB&AT(ff))R invamp(amp(nf?ff:x,nf?x:ff));

else{ff=unname(h); R invamp(amp(nf?x:ff,nf?ff:x));}

case CSCO:

ASSERT(nf,EVDOMAIN);

RE(n=i0(x)); ASSERT(n&&-6<=n&&n<=6,EVDOMAIN);

R amp(sc(-n),h);

case CUCO:

ASSERT(nf,EVDOMAIN);

RE(n=i0(x)); ASSERT(1<=n&&n<=4||7<=n&&n<=8,EVDOMAIN);

R amp(sc(1==n?2L:2==n?1L:3==n?4L:4==n?3L:7==n?8L:7L),h);

case CCANT:

ASSERT(nf,EVDOMAIN);

R obverse(eva(x,"] |:~ x C.^:_1 i.@#@$"),w);

case CPCO:

if(nf){

RE(n=i0(x));

switch(n){

case -4: case 4: R amp(negate(x),h);

case -1: R ds(CPCO);

case 2: R obverse(eval("*/@(^/)\"2"),w);

case 3: R eval("*/");

}}

break;

case CQCO:

if(nf){

ASSERT(!AR(x),EVRANK);

R obverse(eval(all1(lt(x,zero))?"*/@(^/)\"2":"(p:@i.@# */ .^ ])\"1"),w);

}

break;

case CFIT:

ASSERT(nf&&(CPOUND==ID(VAV(g)->f)),EVDOMAIN);

ASSERT(1==AR(x),EVRANK);

R fdef(CPOWOP,VERB, jtexpandg,0L, w,num[-1],0L, 0L, RMAX,0L,0L);

case CPOUND:

ASSERT(nf,EVDOMAIN);

ASSERT(1==AR(x),EVRANK);

R fdef(CPOWOP,VERB, jtexpandf,0L, w,num[-1],0L, 0L, RMAX,0L,0L);

break;

case CPOWOP:

if(VGERL&u->flag){ff=*(1+AAV(u->h)); R amp(nf?x:ff,nf?ff:x);}

break;

case CCOMMA:

n=IC(x);

R obverse(1==n?ds(nf?CDROP:CCTAIL):amp(sc(nf?n:-n),ds(CDROP)),w);

case CBASE:

if(!nf)break;

R AR(x) ? amp(x,ds(CABASE)) :

obverse(evc(x,mag(x),"$&x@>:@(y&(<.@^.))@(1&>.)@(>./)@:|@, #: ]"),w);

case CBANG:

ASSERT(!AR(x),EVRANK);

ASSERT(all1(lt(zero,x)),EVDOMAIN);

GA(y,BOX,9,1,0); q=AAV(y);

q[0]=cstr("3 :'(-("); q[1]=q[3]=lrep(w);

q[2]=cstr("-y\"_)%1e_3&* "); q[4]=cstr("\"0 D:1 ])^:_[");

h=lrep(x);

if(nf){q[5]=over(over(h,cstr("&<@|@{:}")),over(h,cstr(",:"))); q[6]=over(h,cstr("%:y*!")); q[7]=h;}

else {q[5]=cstr("1>.{.@/:\"1|y-/(i.!])"); q[6]=h; q[7]=mtv;}

RE(q[8]=cstr("'")); RZ(y=raze(y));

R obverse(eval(CAV(y)),w);

case CATOMIC:

if(ng){ASSERT(equ(x,nub(x)),EVDOMAIN); R obverse(atop(f,amp(x,ds(CIOTA))),w);}

case CCYCLE:

if(nf&&AR(x)<=(c==CCYCLE))R obverse(eva(w,"/:@x@(i.@#) { ]"),w); break;

case CDROP:

if(!(nf&&1>=AR(x)))break;

RZ(x=cvt(INT,x));

RZ(y=eps(v2(-1L,1L),signum(x))); yv=CAV(y);

f=amp(mag(x),ds(CPLUS));

g=1==AN(x)?ds(CPOUND):atop(amp(tally(x),ds(CTAKE)),ds(CDOLLAR));

h=!yv[1]?f:atop(!yv[0]?ds(CMINUS):amp(negate(signum(x)),ds(CSTAR)),f);

R obverse(hook(swap(ds(CTAKE)),atop(h,g)),w);

case CDOMINO:

if(!(2==AR(x)&&*AS(x)==*(1+AS(x))))break;

ff=eval("+/ .*");

R nf?atop(h,amp(ff,minv(x))):amp(x,ff);

case CDOT:

if(ip(h,CPLUS,CSTAR)){

ASSERT(2==AR(x),EVRANK);

ASSERT(*AS(x)==*(1+AS(x)),EVLENGTH);

R nf?amp(ds(CDOMINO),x):amp(h,minv(x));

}

break;

case CQQ:

if(ng&&equ(x,one)&&equ(f,eval("i.\"1")))R hook(ds(CFROM),ds(CEQ));

break;

case CBSLASH:

if(nf&&(n=i0(x),0>n)&&(d=ID(u->f),d==CLEFT||d==CRIGHT))R slash(ds(CCOMMA));

break;

case CIBEAM:

x=VAV(h)->f; y=VAV(h)->g;

if(NOUN&AT(x)&&equ(x,num[3])&&NOUN&AT(y)){

RE(n=i0(f));

if(all1(eps(y,v2(4L,5L)))){ASSERT(n&&-2<=n&&n<=2,EVDOMAIN); R amp(sc(-n),g);}

if(all1(eps(y,v2(1L,3L)))){ASSERT(0==n||1==n||10==n||11==n,EVDOMAIN); R foreign(x,num[2]);}

}

break;

case CBDOT:

RE(n=i0(x));

switch(i0(VAV(h)->f)){

case 22: case 25: R w;

case 19: case 28: if(ng)R w; break;

case 21: case 26: if(nf)R w; break;

case 32: case 33: case 34: ASSERT(nf,EVDOMAIN); R amp(negate(x),h);

}

break;

case CPOLY:

if(nf&&1==AR(x)&&2==AN(x)&&NUMERIC&AT(x)&&!equ(zero,tail(x))){

RZ(y=recip(tail(x)));

R amp(over(tymes(y,negate(head(x))),y),h);

}}

ASSERT(0,EVDOMAIN);

}

static C invf[2][29] = {

CDIV, CPLUS, CMINUS, CLEFT, CRIGHT, CREV, CCANT, CPOLY,

CNOT, CGRADE, CCYCLE, CDOMINO, COPE, CBOX, CLOG, CEXP,

CGE, CLE, CHALVE, CPLUSCO, CSQRT, CSTARCO, CHEAD, CLAMIN,

CABASE, CBASE, CTHORN, CEXEC, 0,

CDIV, CPLUS, CMINUS, CLEFT, CRIGHT, CREV, CCANT, CPOLY,

CNOT, CGRADE, CCYCLE, CDOMINO, CBOX, COPE, CEXP, CLOG,

CLE, CGE, CPLUSCO, CHALVE, CSTARCO, CSQRT, CLAMIN, CHEAD,

CBASE, CABASE, CEXEC, CTHORN, 0

};

F1(jtinv){A f,ff,g;B b,nf,ng,vf,vg;C id,*s;I p,q;V*v;

RZ(w);

ASSERT(VERB&AT(w),EVDOMAIN);

id=ID(w); v=VAV(w);

if(s=strchr(invf[0],id))R ds(invf[1][s-invf[0]]);

f=v->f; nf=f&&AT(f)&NOUN+NAME; vf=f&&!nf;

g=v->g; ng=g&&AT(g)&NOUN+NAME; vg=g&&!ng;

switch(id){

case CCIRCLE: R eval("1p_1&*");

case CJDOT: R eval("0j_1&*");

case CRDOT: R eval("%&0j1@^.");

case CPLUSDOT: R eval("j./\"1\"_ :. +.");

case CSTARDOT: R eval("r./\"1\"_ :. *.");

case CDGRADE: R eval("/:@|.");

case CWORDS: R eval("}:@;@(,&' '&.>\"1) :. ;:");

case CBANG: R eval("3 :'(-(!-y\"_)%1e_3&* !\"0 D:1 ])^:_ <.&170^:(-:+)^.y' :. !");

case CXCO: R amp(num[-1],w);

case CSPARSE: R fdef(CPOWOP,VERB,jtdenseit,0L, w,num[-1],0L, 0L, RMAX,RMAX,RMAX);

case CPCO: R fdef(CPOWOP,VERB,jtplt, 0L, w,num[-1],0L, 0L, 0L, 0L, 0L );

case CQCO: R eval("*/");

case CUCO: R amp(num[3],w);

case CUNDER: R under(inv(f),g);

case CFORK: R invfork(w);

case CAMP: if(nf!=ng)R invamp(w); /* fall thru */

case CAT: if(vf&&vg)R atop(inv(g),inv(f)); break;

case CAMPCO:

case CATCO: if(vf&&vg)R atco(inv(g),inv(f)); break;

case CSLASH: if(CSTAR==ID(f))R ds(CQCO); break;

case CQQ: if(vf)R qq(inv(f),g); break;

case COBVERSE: if(vf&&vg)R obverse(g,f); break;

case CSCO: R amp(num[5],w);

case CPOWOP:

if(vf&&ng){RE(p=i0(g)); R -1==p?f:1==p?inv(f):powop(0>p?f:inv(f),sc(ABS(p)));}

if(VGERL&v->flag)R*(1+AAV(v->h));

break;

case CTILDE:

if(nf)R inv(symbrd(f));

switch(ID(f)){

case CPLUS: R ds(CHALVE);

case CSTAR: R ds(CSQRT);

case CJDOT: R eval("0.5j_0.5&*");

case CLAMIN: R eval("{. :. (,:~)");

case CSEMICO:R eval(">@{. :. (;~)");

case CCOMMA: R eval("<.@-:@# {. ] :. (,~)");

case CEXP: R eval("3 : '(- -&b@(*^.) % >:@^.)^:_ ]1>.b=.^.y' \" 0 :. (^~)");

}

break;

case CBSLASH:

case CBSDOT:

if(CSLASH==ID(f)&&(ff=VAV(f)->f,ff&&VERB&AT(ff))){

b=id==CBSDOT;

switch(ID(ff)){

case CPLUS: R obverse(eval(b?"- 1&(|.!.0)":" - |.!.0"),w);

case CSTAR: R obverse(eval(b?"% 1&(|.!.1)":" % |.!.1"),w);

case CEQ: R obverse(eval(b?"= 1&(|.!.1)":" = |.!.1"),w);

case CNE: R obverse(eval(b?"~:1&(|.!.0)":" ~:|.!.0"),w);

case CMINUS:R obverse(eval(b?"+ 1&(|.!.0)":"(- |.!.0) *\"_1 $&1 _1@#"),w);

case CDIV: R obverse(eval(b?"* 1&(|.!.1)":"(% |.!.1) ^\"_1 $&1 _1@#"),w);

}}

break;

case CCUT:

if(CBOX==ID(f)&&ng&&(p=i0(g),1==p||2==p))R fdef(CPOWOP,VERB, jtbminv,0L, w,num[-1], 0L,0L, RMAX,RMAX,RMAX);

break;

case CIBEAM:

p=i0(f); q=i0(g);

if(3==p&&1==q)R foreign(f,num[2]);

if(3==p&&2==q)R foreign(f,one );

if(3==p&&3==q)R foreign(f,num[2]);

break;

case CHOOK:

if(CFROM==ID(f)&&CEQ==ID(g))R eval("i.\"1&1");

break;

}

if(!nameless(w))R inv(fix(w));

ASSERT(0,EVDOMAIN);

}

static F1(jtneutral){A x,y;B b;V*v;

RZ(w);

v=VAV(w);

ASSERT(!v->lr&&!v->rr,EVDOMAIN);

RZ(y=v2(0L,1L));

RZ(x=scf(infm)); b=equ(y,CALL2(v->f2,x,y,w)); RESETERR; if(b)R x;

x=ainf; b=equ(y,CALL2(v->f2,x,y,w)); RESETERR; if(b)R x;

x=zero; b=equ(y,CALL2(v->f2,x,y,w)); RESETERR; if(b)R x;

x=one; b=equ(y,CALL2(v->f2,x,y,w)); RESETERR; if(b)R x;

RZ(x=scf(infm)); b=equ(y,CALL2(v->f2,y,x,w)); RESETERR; if(b)R x;

x=ainf; b=equ(y,CALL2(v->f2,y,x,w)); RESETERR; if(b)R x;

x=zero; b=equ(y,CALL2(v->f2,y,x,w)); RESETERR; if(b)R x;

x=one; b=equ(y,CALL2(v->f2,y,x,w)); RESETERR; if(b)R x;

ASSERT(0,EVDOMAIN);

} /* neutral of arbitrary rank-0 function */

F1(jtiden){A f,g,x=0;V*u,*v;

RZ(w=fix(w)); ASSERT(VERB&AT(w),EVDOMAIN);

v=VAV(w); f=v->f; g=v->g;

switch(v->id){

default: RZ(x=neutral(w)); break;

case CCOMMA: R eval("i.@(0&,)@(2&}.)@$");

case CDOT: if(!(ip(w,CPLUS,CSTAR)||ip(w,CPLUSDOT,CSTARDOT)||ip(w,CNE,CSTARDOT)))break;

case CDOMINO: R atop(atop(ds(CEQ),ds(CGRADE)),ds(CHEAD));

case CCYCLE:

case CLBRACE: R atop(ds(CGRADE),ds(CHEAD));

case CSLASH: if(VERB&AT(f))R atop(iden(f),ds(CPOUND)); break;

case CPLUS: case CMINUS: case CSTILE: case CNE:

case CGT: case CLT: case CPLUSDOT: case CJDOT: case CRDOT:

x=zero; break;

case CSTAR: case CDIV: case CEXP: case CROOT: case CBANG:

case CEQ: case CGE: case CLE: case CSTARDOT:

x=one; break;

case CMAX: x=scf(infm); break;

case CMIN: x=ainf; break;

case CUNDER: x=df1(df1(mtv,iden(f)),inv(g)); break;

case CAT:

if(CAMP==ID(f)&&(u=VAV(f),NOUN&AT(u->f)&&!AR(u->f)&&CSTILE==ID(u->g)))switch(ID(g)){

case CSTAR: case CEXP: x=one; break;

case CPLUS: x=zero;

}

break;

case CBDOT:

switch(i0(f)){

case 25: x=num[-1]; break;

case 2: case 4: case 5: case 6: case 7:

case 18: case 20: case 21: case 22: case 23:

x=zero; break;

case 1: case 9: case 11: case 13: case 17:

case 27: case 29:

x=one;

}}

ASSERT(x,EVDOMAIN);

R folk(x,swap(ds(CDOLLAR)),atop(ds(CBEHEAD),ds(CDOLLAR)));

}