/ grouped -> list

P:{
 a:{:[@y;(x;y);(x;_f/y)]}
 p:{
  :[~#z                 ;(x;y;z)
    (*z)_in" \t\r\n"    ;(x;y;1_ z)
    "("=*z              ;(.[x;y;,;,()];y,#x . y;1_ z)
    ")"=*z              ;(.[x;-1_ y;,;()];-1_ y;1_ z)
                         (.[x;y;,;1#z];y;1_ z)]}
 a/*(p .)/(();!0;x," ")}

/ list -> applicative

Q:{:[@x;x;"`",,/_f'x]}

/ applicative -> grouped

R:{:["`"=*x;_f[*d],{:[1=#x;x;"(",x,")"]}_f[*|d:D 1_ x];x]}

/ lambda elimination:

L:{|*(M .)/(();|x)}
M:{:[~#y;(x;y);"."=*y;(|N[y 1;|x];2_ y);(x,*y;1_ y)]}
N:{,/(O[x].)/(();y)}
O:{(:[~#z;y;"`"~*z;y,"``S";x~*z;y,"I";y,"`K",*z];1_ z)}
/ L"x.y.`yx"
/ L"x.`xK"
L"`h.x.`hhh.x.`hh"
/ "```S``S`KSKK``S``S`KSKK"

\

/ combinator optimization:

A:{{`0:,x;B/[x;*Y;Y 1]}/x}

B:{
 i:0;do[1|(#x)-#y
  r:i _ x;if[~r~s:C[r;y;z];:(i#x),s];i+:1]
 x}

C:{
 r:x;d:.();v:_ci 97+!26;while[#y
  if[~(*y)_in v;if[~k:+/&\y=(#y)#r;:x];r:k _ r;y:k _ y]
  if[(*y)_in v;d[`$*y]:*s:D r;r:s 1;y:1_ y]]
 _ssr/[z;$!d;d[]],r}

D:{(0,1+(+\-1 1 x="`")?-1)_ x}

t:"`Y``S``S`KS``S``S`KS``S``S`KS``S`KK`K!``S``S`KS`KK`KK``S``S`KS``S``S`KS``S`KK`KS``S`KK`KK``S`KK`KK`
   `S``S`KS``S``S`KS``S``S`KS``S`KK`KS``S``S`KS``S``S`KS``S`KK`KS``S``S`KS``S`KK`KK``S`KK`KS``S``S`KS``
   S``S`KS``S`KK`KS``S``S`KS``S`KK`KK``S`KK`KK``S``S`KS``S`KK`KK``S`KK`K+``S``S`KS``S``S`KS``S`KK`KS``S
   ``S`KS``S``S`KS``S`KK`KS``S``S`KS``S`KK`KK``S`KK`KS``S``S`KS``S``S`KS``S`KK`KS``S``S`KS``S``S`KS``S`
   KK`KS``S``S`KS``S`KK`KK``S`KK`KS``S``S`KS``S``S`KS``S`KK`KS``S``S`KS``S`KK`KK``S`KK`KK``S``S`KS``S`K
   K`KK``S`KK``SKK``S``S`KS``S``S`KS``S`KK`KS``S``S`KS``S`KK`KK``S`KK`KK``S``S`KS``S``S`KS``S`KK`KS``S`
   KK`KK``S`KK`KK``S``S`KS``S``S`KS``S`KK`KS``S``S`KS``S``S`KS``S`KK`KS``S``S`KS``S`KK`KK``S`KK`KS``S``
   S`KS``S`KK`KK``S`KK`KK``S``S`KS``S`KK`KK``S`KK`KK``S``S`KS``S`KK`K-``S``S`KS`KK`KK"_dvl" \t\r\n"

u:"Y(S(S(KS)(S(S(KS)(S(S(KS)(S(KK)(K!)))(S(S(KS)(KK))(KK))))(S(S(KS)(S(S(KS)(S(KK)(
   KS)))(S(KK)(KK))))(S(KK)(KK)))))(S(S(KS)(S(S(KS)(S(S(KS)(S(KK)(KS)))(S(S(KS)(S(S
   (KS)(S(KK)(KS)))(S(S(KS)(S(KK)(KK)))(S(KK)(KS)))))(S(S(KS)(S(S(KS)(S(KK)(KS)))(S
   (S(KS)(S(KK)(KK)))(S(KK)(KK)))))(S(S(KS)(S(KK)(KK)))(S(KK)(K+)))))))(S(S(KS)(S(S
   (KS)(S(KK)(KS)))(S(S(KS)(S(S(KS)(S(KK)(KS)))(S(S(KS)(S(KK)(KK)))(S(KK)(KS)))))(S
   (S(KS)(S(S(KS)(S(KK)(KS)))(S(S(KS)(S(S(KS)(S(KK)(KS)))(S(S(KS)(S(KK)(KK)))(S(KK)
   (KS)))))(S(S(KS)(S(S(KS)(S(KK)(KS)))(S(S(KS)(S(KK)(KK)))(S(KK)(KK)))))(S(S(KS)(S
   (KK)(KK)))(S(KK)(SKK)))))))(S(S(KS)(S(S(KS)(S(KK)(KS)))(S(S(KS)(S(KK)(KK)))(S(KK
   )(KK)))))(S(S(KS)(S(S(KS)(S(KK)(KS)))(S(KK)(KK))))(S(KK)(KK))))))))(S(S(KS)(S(S(
   KS)(S(KK)(KS)))(S(S(KS)(S(S(KS)(S(KK)(KS)))(S(S(KS)(S(KK)(KK)))(S(KK)(KS)))))(S(
   S(KS)(S(KK)(KK)))(S(KK)(KK))))))(S(S(KS)(S(KK)(KK)))(S(KK)(KK)))))))(S(S(KS)(S(K
   K)(K-)))(S(S(KS)(KK))(KK)))))"_dvl" \t\r\n"

Y:+(("``SKK"            ;,"I")
    ("``S`KxI"          ;,"x")
    ("``S`Kx`Ky"        ;"`K`xy")
    ("``S`Kx``Byz"      ;"```Dxyz")
    ("``S`Kxy"          ;"``Bxy")
    ("``S``Bxy`Kz"      ;"```Exyz")
    ("``Sx`Ky"          ;"``Cxy")
    ("``S``Bxyz"        ;"```Fxyz")
    ("``SxI"            ;"`Wx")
    ("``SI`Kx"          ;"`Tx"))

Y:(P R@)''Y
t:P R t
y:("Y";(("S";"K+");"K0"))
d:{{{e[y;z;x]}/[x;*Y;Y 1]}/x}
e:{:[@z;z;_n~d:f[.();x;z:_f[x;y]'z];z;g[d;y]]}
f:{:[_n~x;x;~@y;:[~@z;_f/[x;y;z]];y _in _ci 97+!26;@[x;`$y;:;z];@y;:[y~z;x]]}
g:{:[4:y;{:[1=#x;*x;x]}@h/[y,"";,/$!x;x[]];_f[x]'y]}
h:{@[x;&x~\:y;:[;z]]}
d t

Z:+(("`Ix"              ;,"x")
    ("``Kcx"            ;,"c")
    ("```Sfgx"          ;"``fx`gx")
    ("```Bfgx"          ;"`f`gx")
    ("```Cfgx"          ;"``fxg")
    ("````Dcfgx"        ;"``c`fx`gx")
    ("````Ecfgx"        ;"``c`fxg")
    ("````Fcfgx"        ;"`c`f`gx")
    ("`Yx"              ;"`x`Yx")
    ("``Wfx"            ;"``fxx")
    ("``Txf"            ;"`fx"))

\

Y(S(S(KS)(S(S(KS)(S(S(KS)(S(KK)(K!)))(S(S(KS)(KK))(KK))))(S(S(KS)(S(S(KS)(S(KK)(
KS)))(S(KK)(KK))))(S(KK)(KK)))))(S(S(KS)(S(S(KS)(S(S(KS)(S(KK)(KS)))(S(S(KS)(S(S
(KS)(S(KK)(KS)))(S(S(KS)(S(KK)(KK)))(S(KK)(KS)))))(S(S(KS)(S(S(KS)(S(KK)(KS)))(S
(S(KS)(S(KK)(KK)))(S(KK)(KK)))))(S(S(KS)(S(KK)(KK)))(S(KK)(K+)))))))(S(S(KS)(S(S
(KS)(S(KK)(KS)))(S(S(KS)(S(S(KS)(S(KK)(KS)))(S(S(KS)(S(KK)(KK)))(S(KK)(KS)))))(S
(S(KS)(S(S(KS)(S(KK)(KS)))(S(S(KS)(S(S(KS)(S(KK)(KS)))(S(S(KS)(S(KK)(KK)))(S(KK)
(KS)))))(S(S(KS)(S(S(KS)(S(KK)(KS)))(S(S(KS)(S(KK)(KK)))(S(KK)(KK)))))(S(S(KS)(S
(KK)(KK)))(S(KK)(SKK)))))))(S(S(KS)(S(S(KS)(S(KK)(KS)))(S(S(KS)(S(KK)(KK)))(S(KK
)(KK)))))(S(S(KS)(S(S(KS)(S(KK)(KS)))(S(KK)(KK))))(S(KK)(KK))))))))(S(S(KS)(S(S(
KS)(S(KK)(KS)))(S(S(KS)(S(S(KS)(S(KK)(KS)))(S(S(KS)(S(KK)(KK)))(S(KK)(KS)))))(S(
S(KS)(S(KK)(KK)))(S(KK)(KK))))))(S(S(KS)(S(KK)(KK)))(S(KK)(KK)))))))(S(S(KS)(S(K
K)(K-)))(S(S(KS)(KK))(KK)))))

Y(S(K(S(S(S(K!)(SKK))(K(SKK)))))(S(S(KS)(S(KK)(S(K(S(K(S(K+)))))(S(S(KS)(S(K(S(K
S)))(S(K(S(KK)))(S(S(KS)(S(KK)(SKK)))(K(SKK))))))(K(K(SKK)))))))(K(S(K-)(SKK))))
)

Y(S(K(S(S!(KI))))(S(S(KS)(S(KK)(S(K(S(K+))))))(K-)))

Y(B(S(C!I))(·B(B(B+))-))