patriciaLib.PTREE

STRUCTURE

SYNOPSIS

Conversion for evaluating Patricia tree operations.

DESCRIPTION

The conversion PTREE_CONV evaluates Patricia tree operations such as ADD, ADD_LIST, REMOVE, SIZE, PEEK and FIND. These evaluations work for constants that are defined using Define_mk_ptree. When adding to, or removing from, a Patricia tree a new contant will be defined after patriciaLib.ptree_new_defn_depth operations. By default ptree_new_defn_depth is ~1, which means that new constants are never defined.

EXAMPLE

Consider the following Patricia tree:

val ptree = Define_mk_ptree "ptree" (int_ptree_of_list [(1,``1``), (2, ``2``)]);
<<HOL message: Saved IS_PTREE theorem for new constant "ptree">>
val ptree = |- ptree = Branch 0 0 (Leaf 1 1) (Leaf 2 2): thm

Adding a list of updates expands into applications of ADD:

> real_time PTREE_CONV ``ptree |++ [(3,3); (4,4); (5,5); (6,6); (7,7)]``;
realtime: 0.000s
val it =
   |- ptree |++ [(3,3); (4,4); (5,5); (6,6); (7,7)] =
   ptree |+ (3,3) |+ (4,4) |+ (5,5) |+ (6,6) |+ (7,7):
   thm

However, setting ptree_new_defn_depth will cause new definitions to be made:

> ptree_new_defn_depth := 2;
val it = (): unit
> real_time PTREE_CONV ``ptree |++ [(3,3); (4,4); (5,5); (6,6); (7,7)]``;
<<HOL message: Defined new ptree: ptree1>>
<<HOL message: Defined new ptree: ptree2>>
realtime: 0.006s
val it = |- ptree |++ [(3,3); (4,4); (5,5); (6,6); (7,7)] = ptree2 |+ (7,7):
   thm

New definitions will also be made when removing elements:

> real_time PTREE_CONV ``ptree2 \\ 6 \\ 5``;
<<HOL message: Defined new ptree: ptree3>>
realtime: 0.001s
val it = |- ptree2 \\ 6 \\ 5 = ptree3: thm

Here, the conversion is not smart enough to work out that ptree3 is the same as ptree1.

> (DEPTH_CONV PTREE_DEFN_CONV THENC EVAL) ``ptree1 = ptree3``;
val it = |- (ptree1 = ptree3) <=> T: thm

Look-up behaves as expected:

> real_time PTREE_CONV ``ptree1 ' 2``;
realtime: 0.001s
val it = |- ptree1 ' 2 = SOME 2: thm
> real_time PTREE_CONV ``ptree1 ' 5``;
realtime: 0.001s
val it = |- ptree1 ' 5 = NONE: thm

COMMENTS

The conversion PTREE_CONV is automatically added to the standard compset. Thus, EVAL will have the same behaviour when patriciaLib is loaded.

Run-times should be respectable when working with large Patricia trees. However, this is predicated on the assumption that relatively small numbers of updates are made following an initial application of Define_mk_ptree. In this sense, the Patricia tree development is best suited to situations where users require fast "read-only" look-up; where the work of building the look-up tree can be performed outside of the logic (i.e. in ML).

SEEALSO

Define_mk_ptree, PTREE_DEFN_CONV