Library Coq.FSets.FSetAVL
FSetAVL : Implementation of FSetInterface via AVL trees
This module implements finite sets using AVL trees.
It follows the implementation from Ocaml's standard library,
All operations given here expect and produce well-balanced trees
(in the ocaml sense: heights of subtrees shouldn't differ by more
than 2), and hence has low complexities (e.g. add is logarithmic
in the size of the set). But proving these balancing preservations
is in fact not necessary for ensuring correct operational behavior
and hence fulfilling the FSet interface. As a consequence,
balancing results are not part of this file anymore, they can
now be found in
FSetFullAVL.
Four operations (
union,
subset,
compare and
equal) have
been slightly adapted in order to have only structural recursive
calls. The precise ocaml versions of these operations have also
been formalized (thanks to Function+measure), see
ocaml_union,
ocaml_subset,
ocaml_compare and
ocaml_equal in
FSetFullAVL. The structural variants compute faster in Coq,
whereas the other variants produce nicer and/or (slightly) faster
code after extraction.
This is just a compatibility layer, the real implementation
is now in MSetAVL