\d p

parse:{value flat ternary unary elevate tree type group x}

/ (x) -> ,x

group:{*(group_ .)/(();x)}
group_:{:[~#y;(x;y);"("~**y;{(x,,group 1_ y;1_ z)}[x]. par y;(x,,*y;1_ y)]}
lr:{:[x[0]~*y;(0,(=/+\'y~\:/:x)?1)_ y;(+,x),'(y;())]}
par:lr[+,"()"]

/ "x" -> (`c;"x")

type:{:[~4:x;_f'x;x[0]_in A;({`a};x);&/x _lin V;({`v};x);L~*x;({`l};x);R~*x;({`r};x);({`n};x)]}
V:".-_~!@#$%^&*=+|<,>?:"
A:"'/\\"
L:"{"
R:"}"

/ x is the type of the result of binding y and z

S:(`nnn
   `vvv`vuv`vvu`vuu
   `nvn
   `nun
   `unv
   `vna`vva`vua`vnb`vvb`vub
   `vrn`aru`arv`ara`brb`nln`nlu`nlv`vla`vlb)

/ "xyz" -> B[y;z]=index of yz in S, C[y;z]=x

abc:{
 s:`$'''$(),/:x
 j:,/s[;;1 2];k:,/l:s[;;0];i:,/a,\:/:a:?,//s
 b:./[./[_n;i;:;-1];j;:;&#:'l]
 c:./[./[_n;i;:;_n];j;:;(. 1!"}{`",)'$k]
 (b;c)}

@[_d;`B`C;:;abc S];

/ parse 2x2

tree:{*(1<#:)(bind . drop@)/|@[x;&term'x;_f@]}          / token-list -> parse-tree
term:{:[1=#x;1;~4:x 1]}                                 / nested token-list
bind:{,/.[(0,y+0 2)_ x;1;pair;C_ . x[1 0+y;0]]}         / ..xy.. -> ..(t;yx)..  
drop:{(x;(<':B_':*:'x)?1)}                              / drop in strength
pair:{,(y;|x)}                                          / binding operation
B_:{B[x[]]y[]}                                          / binding strength
C_:{C[x[]]y[]}                                          / result category

/ eliminate elevator:  x(e(y;z)) -> xz

elevate:{:[4:x 1;x;elevate_ ..[x;(1;);_f]]}
elevate_:{:[y[0;0][]_in`l`r;(x;y[1]1);(x;y)]}

/ n(vn) -> n(v:n)

unary:{:[4:x 1;u . x;unary_ .[x;(1;);_f]]}
unary_:{:[vn x;u0;vu x;uu;vv x;u0;::]x}
u:{:[(`v~x[])&(1<#y)&":"=*-1#y;({`u};y);(x;y)]}
vv:{(`v=x[0][])&(`v=x[1;0;0][])&(~~4:x[1;0;1])&`v=x[1;1;0][]}
vu:{(`v=x[0][])&(`v=x[1;0;0][])&(~~4:x[1;0;1])&`u=x[1;1;0][]}
uu:{({`u};.[x;1 0;:;({`u};:[x[1;0;1;0]_in V;x[1;0;1],":";x[1;0;1]])])}
vn:{(`v=x[1;0;0][])&(x[1;1;0][]_in`n`u)&~~4:x[1;0;1]}
u0:{.[x;1 0;:;({`u};:[x[1;0;1;0]_in V;x[1;0;1],":";x[1;0;1]])]}

/ n(v(va)) -> n(v(vb))

ternary:{:[4:x 1;b . x;ternary_ .[x;(1;);_f]]}
ternary_:{:[va x 1;vb x;x]}
b:{:[(`a~x[])&(1<#y)&(&/y _lin A)&"."=*-1#y;({`b};y);(x;y)]}
va:{:[~`n=x[0;0][];0;~`v=x[1;0][];0;4:x[1;1];0;(x[1;1;0;0][]_in`n`v)&`a=x[1;1;1;0][]]}
vb:{.[x;1 1 1 1 0;:;{`b}]}

/ eliminate derived types

flat:{:[4:x 1;x;_f'x 1]}

/ "x" -> x

value:{:[4:x 1;@[x;1;k[x[0][]]];_f'x]}
k[`n`v`u]:{:["`"=*x;sym x;"\""=*x;. x;x[0]_in V,"0123456789";. x;&/x _lin A,":";k.a x;(x[0]_in A)&"."_in x;k.b x;`$x]}
k.a:{:[x[0]_in A;. 1!"}{x",x;`$x]}
k.b:{:[x[0]_in A;. 2!"z}{y x",_dv[x;"."];`$x]}
sym:{atom`$1_'(&x="`")_ x}
atom:{:[1=#x;*x;x]}

\d ^
parse:p.parse