\d e
\l d
\l s

/ X.S:{[f;g;x]p:S x;(A;(A;f;p);(A;g;p))}
X.S:{[f;g;x](A;(A;f;x);(A;g;x))}
X.K:{[x;y](A;`I;x)}
X.I:{[x]x}
X.B:{[f;g;x](A;f;(A;g;x))}
X.C:{[f;g;x](A;(A;f;x);g)}
/ X.S_:{[c;f;g;x]p:S x;(A;(A;c;(A;f;p));(A;g;p))}
X.S_:{[c;f;g;x](A;(A;c;(A;f;x));(A;g;x))}
X.B_:{[c;f;g;x](A;c;(A;f;(A;g;x)))}
X.C_:{[c;f;g;x](A;(A;c;(A;f;x));g)}
/ X.Y:{[f]p:S(A;`Y;f);(A;f;p)}
X.Y:{[f](A;f;(A;`Y;f))}
/ X.U:{[f;z]p:S z;(A;(A;f;(A;H;p));(A;T;p))}
X.U:{[f;z](A;(A;f;(A;H;z));(A;T;z))}

Trace:0
trace:{[v;r;t]if[v=Trace;`0:(40$rep r),{:[" "=*x;x;" ",x]} -40$rep t;if[#0:`;Trace::0]]}

i:{(A;I;x)}
S:{(A;i G;:[x _in Z;Z?x;-1+#Z,:,({};x)])}
G:{if[{}~*p:Z x;p:reduce p 1;Z[x]:p];p}
left:{[b]:[~@b;step . b;b _in!X;X b;b]}
sys:{[b;f](2#b)~(A;f)}
step:{[a;b;c]trace[2;()](a;b;c);case[a;b]c}
case:{[a;b;c]:[sys[b]I;func b[2][strict c];sys[b]O;cond[b 2;c];b~H;hd c;b~T;tl c;exe[left b]c]}
list:{[i;c]:[@c:reduce c;c;~#c;*c;sys[c]G;c[1]c 2;c . i]}
hd:list[1 2]
tl:list[2]
exe:{[b;c]:[7=4:b;b[c];_n~b;c;(A;b;c)]}
func:{[t]:[7=4:t;i t;t]}
cond:{[i;t;e]:[strict i;reduce t;reduce e]}
reduce:{[t](A~*:)(step .)/t}
lazy:{[r;t]trace[1;r]t;:[~#t;(r;t);split[r]reduce t]}
split:{[r;t]:[(@t)&~#r;(t;());(r,i#t;(i:t?A)_ t)]}
strict:{[t]*(lazy .)/(();t)}
eval:{[t]Z::();strict(A;t;`I)}

\d ^
eval:e.eval

\

initialize Z, t to common subexpressions