Boolean Lists

This chapter describes boolean lists. A boolean list is a list that has no holes and contains only the boolean values true and false (see Chapter ). In function names we call boolean lists blists for brevity.

IsBlist (Filter)
<#Include Label="IsBlist">

Boolean Lists Representing Subsets
<#Include Label="BlistList"> <#Include Label="ListBlist"> <#Include Label="SizeBlist"> <#Include Label="IsSubsetBlist">

Set Operations via Boolean Lists
<#Include Label="UnionBlist"> <#Include Label="IntersectionBlist"> <#Include Label="DifferenceBlist">

Function that Modify Boolean Lists
<#Include Label="UniteBlist"> <#Include Label="UniteBlistList"> <#Include Label="IntersectBlist"> <#Include Label="SubtractBlist">

More about Boolean Lists

We defined a boolean list as a list that has no holes and contains only true and false. There is a special internal representation for boolean lists that needs only 1 bit for each entry. This bit is set if the entry is true and reset if the entry is false. This representation is of course much more compact than the ordinary representation of lists, which needs 32 or 64 bits per entry.

Not every boolean list is represented in this compact representation. It would be too much work to test every time a list is changed, whether this list has become a boolean list. This section tells you under which circumstances a boolean list is represented in the compact representation, so you can write your functions in such a way that you make best use of the compact representation.

If a dense list containing only true and false is read, it is stored in the compact representation. Furthermore, the results of , , and are known to be boolean lists by construction, and thus are represented in the compact representation upon creation.

If an argument of , , , , , , and is a list represented in the ordinary representation, it is tested to see if it is in fact a boolean list. If it is not, an error is signalled. If it is, the representation of the list is changed to the compact representation.

If you change a boolean list that is represented in the compact representation by assignment (see ) or in such a way that the list remains a boolean list it will remain represented in the compact representation. Note that changing a list that is not represented in the compact representation, whether it is a boolean list or not, in such a way that the resulting list becomes a boolean list, will never change the representation of the list.

<#Include Label="IsBlistRep">