/ example
\d .k.q
a:100
i:{[x]r:0;do[1000000;r+:g x];r}
g:{[x]a+x}
h:(3;{x+y})
m:,.+(`b`c`d`i;(10;{x*y};20;{z+y-x}))
f..i:{x*y}
z:.()
\d .k

/ path from symbol
ps:{[s]
 a:{[f;p;v]:[f[p;v]&7=t:4:v;p;(t=6)|~t _in 0 5;();p,/:,/'_f[f]'[:[0=t;!#:;!:]v;v[]]_dv()]}
 d:{[f;p;v]if[(v~.())|~5=4:v;:a[f;p]v];m:. v;p,/:,/(_f[f]'[m[;0];m[;1]]),_f[f]'[~m[;0];m[;2]]}
 d[{[s;p;v]s~*|p}[s];()]@.`}

/ path from object
po:{[o]
 a:{[o;p;v]:[o~v;p;(t=6)|~(t:4:v)_in 0 5;();p,/:,/'_f[o]'[:[0=t;!#:;!:]v;v[]]_dv()]}
 d:{[o;p;v]if[(v~.())|~5=4:v;:a[o;p]v];m:. v;p,/:,/(_f[o]'[m[;0];m[;1]]),_f[o]'[~m[;0];m[;2]]}
 d[o;();.`]}

/ path from k-type(s)
pt:{[k]
 a:{[k;p;v]:[(t:4:v)_in k;p;(t=6)|~t _in 0 5;();p,/:,/'_f[k]'[:[0=t;!#:;!:]v;v[]]_dv()]}
 d:{[k;p;v]if[(v~.())|~5=4:v;:a[k;p]v];m:. v;p,/:,/(_f[k]'[m[;0];m[;1]]),_f[k]'[~m[;0];m[;2]]}
 d[(),k;();.`]}

\

pt 7
ps`i
po(.())
po{x*y}

\

ps`i:

(`k `q `i
 (`k;`q;`m;0;`i)
 `k `q `f. `i)

po{x*y}:

((`k;`q;`m;0;`c)
 `k `q `f. `i)

\

the k tree is a set of associations from symbols in a dictionary to objects or indices in a list to objects.

it follows that given a symbol it should be possible find all the paths in the k tree which terminate in that symbol.

if also follows that given an object (which might be a symbol) it should be possible to find all variables in the k tree which have that object as their value.

given a symbol s the function ps returns a list of paths in the k tree which terminate in s.

given an object o the function po returns a list of paths in the k tree which have o as their value.