/ bitemporality

d:{(_dj _ x%86400.;100_sv 24 60 60_vs _ x!86400.)}
t:{(24 60 60_sv 0 100 100_vs y)+86400.*_jd x}
sp:{1_'(&x=*x)_ x}
dt:{{t . 100_sv'0$(sp"-",x;sp":",y)}. 2#sp" ",x," 0"}
na:(;0N;0n;;`)@__abs 4::

ti:{[o;a;p]						/ individual index
 k:!p[`o]_bin o						/ assertions made on times < o
 k@:&a>p[`f;k]						/ assertions about a time beginning a
 k@:&~a>p[`t;k]						/ assertions about a time ending on or after a
 k@(*|:)'=p[`i;k]}					/ latest assertion for each individual

qi:{[o;a;p;v]						/ query index
 k:ti[o;a]p						/ temporal indices
 k:[~_n~v;&v p[`v;k]]}					/ assertions which satisfy non-null f[x]

id:{[p;k]p[`i;k]}					/ indices and property -> individuals which are subjects of
is:{:[#x;{x@&x _lin y}/x@<#:'x;x]}			/ intersection of vectors

iq:{[o;a;q]is(!q)id'qi[o;a]'[!q;q[]]}			/ individual query

pq:{[o;a;p;i]						/ property query
 k:ti[o;a;p]v						/ temporal indices
 (p[`v;k],na p`v)p[`i;k]?/:i}				/ property values for individuals

ih:{[o;p;i]						/ individual history query
 k:!p[`o]_bin o						/ assertions <= o
 k@:&i=p[`i;k]						/ assertions about i
 hi . tl . p[`v`f`t;k]}					/ history of timeline

tl:{[v;f;t]tu[u]tv[u@:<u:?f,t;v;f]t}			/ timeline

tv:{[u;v;f;t]						/ time vector
 j:i+!:'(u _binl t)-i:u _binl f				/ enumerated t-f
 @[(#u)#na v;j;:;v]}					/ amend value state

tu:{[u;s](u;s)@\:&~0(=;~)[~4:s]':s}			/ fuse partial assertions

hi:{[u;s](,-1_ s),+{y,x}':u}				/ history

it:{@[_n;`v`f`t;:;x]}					/ matrix (v;f;t) -> table[`v`f`t]