gaps/overlaps in a time table : current and previous row question

hello,

let's say that each rows in a table contains a start time and a end
time ("timeinterval" type),
but the index are not ordered nor consecutive, e.g :

$ select * from T order by starttime

index | starttime | endtime
---------+-----------------+-----------------
3 | t1 | t2
1 | t3 | t4
18 | t5 | t6
12 | t7 | t8

I want a result that shows time gaps and overlaps in this table, that is :

delta
---------+
t3 - t2 |
t5 - t4 |
t7 - t6 |

how would I do that ? I guess this could be done with window function and lag()
function but I don't know exactly how. Any suggestion ?

thanks

I guess my question is more about