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Icl maps differ in their behavior dependent on how they handle identity elements of the associated
type CodomainT
.
In the pseudo code snippets below 0
will be used to denote identity elements
,
which can be different objects like const
double 0.0
,
empty sets, empty strings, nullvectors etc. dependent of the instance type
for parameter CodomainT
.
The existence of an identity element
wrt. an operator+=
is a requirement for template type CodomainT
.
type 
operation 
identity element 


addition 


concatenation 


union 

In these cases the identity element
value is delivered by the default
constructor of the maps CodomainT
type. But there are well known exceptions like e.g. numeric multiplication:
type 
operation 
identity element 


multiplication 

Therefore icl functors, that serve as Combiner
parameters of icl Maps implement a static function identity_element()
to make sure that the correct identity_element()
is used in the implementation of aggregate on overlap.
inplace_times<int>::identity_element() == 1 // or more general inplace_times<T>::identity_element() == unit_element<T>::value()
There are two properties or traits
of icl maps that can be chosen by a template parameter Traits
.
The first trait relates
to the definedness
of the map. Icl maps can be partial or
total on the set of values given by domain
type DomainT
.
The second trait is
related to the representation of identity
elements
in the map. An icl map
can be a identity absorber
or a identity enricher.
(k,0)
that carry identity elements.
(k,0)
.
For the template parameter Traits
of icl Maps we have the following four values.

identity absorber 
identity enricher 

partial 
partial_absorber (default) 
partial_enricher 
total 
total_absorber 
total_enricher 
Map traits are a late extension to the icl. Interval maps have been used for a couple of years in a variety of applications at Cortex Software GmbH with an implementation that resembled the default trait. Only the deeper analysis of the icl's aggregating Map's concept in the course of preparation of the library for boost led to the introduction of map Traits.
Constitutional for the absorber/enricher propery is a little antinomy.
We can insert value pairs to the map by adding
them to the map via operations add, +=
or +
:
{} + {(k,1)} == {(k,1)} // addition
Further addition on common keys triggers aggregation:
{(k,1)} + {(k,1)} == {(k,2)} // aggregation for common key k
A subtraction of existing pairs
{(k,2)}  {(k,2)} == {(k,0)} // aggregation for common key k
yields value pairs that are associated with 0values or identity
elements
.
So once a value pair is created for a key k
it can not be removed from the map via subtraction (subtract, =
or 
).
The very basic fact on sets, that we can remove what we have previously added
x  x = {}
does not apply.
This is the motivation for the identity absorber Trait. A identity absorber map handles value pairs that carry identity elements as nonexistent, which saves the law:
x  x = {}
Yet this introduces a new problem: With such a identity absorber
we are by definition unable to store a value (k,0)
in the map.
This may be unfavorable because it is not inline with the behavior of stl::maps
and this is not necessarily expected by clients of the library.
The solution to the problem is the introduction of the identity enricher Trait, so the user can choose a map variant according to her needs.
The idea of a identity absorbing map is, that an associated
identity element value of a pair (k,0)
codes nonexistence
for it's key k
. So the pair
(k,0)
immediately tunnels from a map where it may emerge into the realm of non
existence.
{(k,0)} == {}
If identity elements do not code nonexistence
but existence with null quantification,
we can also think of a map that has an associated identity element for every key k
that has no associated value different from 0. So in contrast to modelling
all neutral value pairs (k,0)
as being nonexistent
we can model all neutral value pairs (k,0)
as being
implicitly existent.
A map that is modelled in this way, is one large vector with a value v
for every key k
of it's domain type DomainT
.
But only nonidentity values are actually stored. This is the motivation
for the definednessTrait on icl
Maps
.
A partial map models the intuitive view that only value pairs are existent, that are stored in the map. A total map exploits the possibility that all value pairs that are not stored can be considered as being existent and quantified with the identity element.
From a pragmatic perspective value pairs that carry identity
elements
as mapped values can often
be ignored. If we count, for instance, the number of overlaps of inserted
intervals in an interval_map
(see example overlap counter),
most of the time, we are not interested in whether an overlap has been counted
0
times or has not been counted
at all. A identity enricher map is only needed, if we want to distinct between
nonexistence and 0quantification.
The following distinction can not be made
for a partial_absorber
map but it can be made for an partial_enricher
map:
(k,v) does not exist in the map: Pair (k,v) has NOT been dealt with (k,0) key k carries 0 : Pair (k,v) has been dealt with resulting in v=0
Sometimes this subtle distinction is needed. Then a partial_enricher
is the right choice. Also, If we want to give two icl::Maps
a common set of keys in order to, say, iterate synchronously over both maps,
we need enrichers.