[GAP Forum] Implementing automatic inheritance of features

[Sebastian Gutsche]

Dear Johannes,

a while ago, I implemented so-called todo-lists in the ToolsForHomalg 
package, which can propagate knowledge (in form of attributes and 
properties) between mathematically related objects (being a subobject is 
a special case). The basic idea is to attach certain tasks to an object, 
which are triggered once a property or an attribute get set (and acquire 
certain values). So they behave like immediate methods, but are much 
more flexible (dynamic inheritance). These todo-lists might be a 
solution for you. Please see the attachment for a commented example. 
Just copy both files to a directory and follow the file example.gi line 
by line for a demo.

Also, there is the possibility to follow how a propagated property was 
set, i.e., building a proof. But this is still very beta, since the 
proof-tree usually grows too large.

An example of a package that uses todo-lists outside of the homalg 
project is Martin Leuner's alcove: https://github.com/martin-leuner/alcove

If you need any help please feel free to contact us.

Best wishes,
Sebastian
-------------- next part --------------
## Reads some definitions. Please look at that file first.

Read( "example_definitions.gi" );

## We first create a group and a subgroup.

G := CreateOrderedGroup( );

H := CreateOrderedSubgroup( );

## Now we create a todo-list entry, which looks up
## if G has an ordering, and then sets the ordering
## of H to the same object.

entry := ToDoListEntry( [ [ G, "Ordering" ] ], H, "Ordering", [ Ordering, G ] );

## Please read this as follows:
## First argument is a list of preconditions.
## Here the two element list means that the todo-list
## looks up if the attribute Ordering is set.
## If this is the case, it sets the Ordering ( 3th argument ) of
## H (2nd argument) to the ordering of G. This is provided by the last
## argument, which is a list. The first entry is a function, at this time
## applied to the rest of the list. We then get the ordering, which is already known,
## and set the ordering of H to it.

## The next step "activates" the entry.

AddToToDoList( entry );

## This should be false

HasOrdering( H );

SetOrdering( G, "lex" );

## Now the background magic happens, and the ordering of H is set to the same thing.

Ordering( H );

## The todo-lists are capable of even more things, for example launching a function.

G2 := CreateOrderedGroup( );

entry := ToDoListEntry( [ [ G2, "Ordering" ] ], function( ) Print( "Hello world!\n" ); end );

AddToToDoList( entry );

SetOrdering( G2, "lex" );

## The passed function is now launched once the attribute is set.

## We also provide the functionality to create todo-list entries by so
## called blueprints. These install todo-list entries for every created object
## in a category.

ToDoListEntryBlueprint( IsOrderedGroup, [ [ ToDoList_this_object, "Ordering", "lex" ] ], [ function() Print( "Yay, I have an order!\n" ); end ] );

## Now every new object should have a todo-list entry.

G3 := CreateOrderedGroup( );

SetOrdering( G3, "lex" );
-------------- next part --------------
LoadPackage( "ToolsForHomalg" );


## Define types etc. for ordered groups

DeclareCategory( "IsOrderedGroup",
                 IsObject );

DeclareCategory( "IsOrderedSubgroup",
                 IsOrderedGroup );

DeclareRepresentation( "IsOrderedGroupRep",
                       IsOrderedGroup and IsAttributeStoringRep,
                       [ ] );

DeclareRepresentation( "IsOrderedSubgroupRep",
                       IsOrderedSubgroup and IsAttributeStoringRep,
                       [ ] );

BindGlobal( "TheFamilyOfOrderedGroups",
        NewFamily( "TheFamilyOfOrderedGroups" ) );

BindGlobal( "TheTypeOfOrderedGroups",
        NewType( TheFamilyOfOrderedGroups,
                IsOrderedGroupRep ) );

BindGlobal( "TheTypeOfOrderedSubgroups",
        NewType( TheFamilyOfOrderedGroups,
                IsOrderedSubgroupRep ) );

## Please note that this is not meant to work in any case.
## Its just a demo. We might need constructors for objects.

DeclareOperation( "CreateOrderedGroup",
                  [ ] );

InstallMethod( CreateOrderedGroup,
               [ ],
  function( )
    local group;
    
    group := rec();
    
    Objectify( TheTypeOfOrderedGroups, group );
    
    return group;
    
end );

## Creating a subgroup.
## Please note that there is currently no connection
## to the containing group. We will do this later by using todo-lists.
## One might solve this in a different manner.

DeclareOperation( "CreateOrderedSubgroup",
                  [ ] );

InstallMethod( CreateOrderedSubgroup,
               [ ],
  function( )
    local group;
    
    group := rec();
    
    Objectify( TheTypeOfOrderedSubgroups, group );
    
    return group;
    
end );

## The attribute we want to share between group and subgroup,
## or better propagate from group to subgroup

DeclareAttribute( "Ordering",
                  IsOrderedGroup );