Add documentation for object numbering

Author: smowton

src/pointer-analysis/README.md

@@ -3,7 +3,7 @@
 
 # Folder pointer-analysis
 
-\author Martin Brain
+\author Martin Brain, Chris Smowton
 
 To perform symbolic execution on programs with dereferencing of
 arbitrary pointers, some alias analysis is needed.  `pointer-analysis`
@@ -15,7 +15,20 @@ subtle and sophisticated and thus there may be bugs.
 
 \subsection pointer-analysis-object-numbering Object / expression numbering (object_numberingt)
 
-To be documented.
+Object numbering assigns numbers to expressions, allowing other pointer-analysis
+classes to use small, cheap to compare, cheap to sort numbers in place of
+\ref exprt instances. Numbering also saves memory, as two identical exprt
+objects will be assigned the same number, eliminating redundant storage of the
+same data.
+
+Alternative approaches to the same problem include \ref irept sharing (but this
+only shares when a copy is taken; two identical irepts arrived at by different
+routes will not be shared) and \ref merge_irept (which does merge identical
+ireps, but is still more expensive to compare than numbers).
+
+Object numbering is used by \ref value_sett and cousins (such as
+\ref value_set_fit) in an effort to reduce the memory dedicated to value-set
+storage.x
 
 \subsection pointer-analysis-pointer-offset-sum Pointer-offset sum (pointer_offset_sum)
 

src/pointer-analysis/object_numbering.h

@@ -1,13 +1,23 @@
 /*******************************************************************\
 
-Module: Value Set
+Module: Object Numbering
 
 Author: Daniel Kroening, kroening@kroening.com
 
 \*******************************************************************/
 
 /// \file
-/// Value Set
+/// Object Numbering
+///
+/// This is used to abbreviate identical expressions by number: for example,
+/// an object_numberingt instance might maintain the map:
+/// ```
+/// 1 -> constant_exprt("Hello", string_typet())
+/// 2 -> constant_exprt("World", string_typet())
+/// ```
+/// Then any users that agree to use the same object_numberingt instance as a
+/// common reference source can use '1' and '2' as shorthands for "Hello" and
+/// "World" respectively.
 
 #ifndef CPROVER_POINTER_ANALYSIS_OBJECT_NUMBERING_H
 #define CPROVER_POINTER_ANALYSIS_OBJECT_NUMBERING_H