Replace operation_weights in CategoryConstructor by a better mechanism

When using the string "default" for create_func_*, one must now set the
option `underlying_category`, from which the weight is determined. If
create_func_* is a function, one can (optionally) set a weight by returning
a pair of a string and an integer (instead of only a string).

CAP/gap/CategoryConstructor.gd

@@ -36,10 +36,10 @@ DeclareInfoClass( "InfoCategoryConstructor" );
 #!  * `morphism_constructor` (optional): function added as an installation of <Ref Oper="MorphismConstructor" Label="for IsCapCategoryObject, IsObject, IsCapCategoryObject" /> to the category
 #!  * `morphism_datum` (optional): function added as an installation of <Ref Oper="MorphismDatum" Label="for IsCapCategoryMorphism" /> to the category
 #!  * `list_of_operations_to_install` (mandatory): a list of names of &CAP; operations which should be installed for the category
-#!  * `operation_weights` (optional): a record mapping operations in `list_of_operations_to_install` to their weights
 #!  * `is_computable` (optional): whether the category can decide `IsCongruentForMorphisms`
 #!  * `supports_empty_limits` (optional): whether the category supports empty lists in inputs to operations of limits and colimits
 #!  * `underlying_category_getter_string` (optional): see below
+#!  * `underlying_category` (optional): see below
 #!  * `underlying_object_getter_string` (optional): see below
 #!  * `underlying_morphism_getter_string` (optional): see below
 #!  * `top_object_getter_string` (optional): see below
@@ -53,8 +53,9 @@ DeclareInfoClass( "InfoCategoryConstructor" );
 #!
 #!  The values of the keys `create_func_*` should be either the string `"default`" or functions which accept the category and the name of a &CAP; operation
 #!  of the corresponding `return_type`. Values for return types occuring for operations in `list_of_operations_to_install` are mandatory.
-#!  The functions must return strings, which (after some replacements described below) will be evaluated and added as an installation of the corresponding operation to the category.
-#!  The value `"default"` chooses a suitable default string, see the implementation for details.
+#!  The functions must return either strings or pairs of a string and an integer:
+#!  The strings (after some replacements described below) will be evaluated and added as installations of the corresponding operations to the category with weights given by the integer (if provided).
+#!  The value `"default"` chooses a suitable default string (see the implementation for details) and gets the weights from `underlying_category`.
 #!  The following placeholders may be used in the strings and are replaced automatically:
 #!  * `operation_name` will be replaced by the name of the operation
 #!  * `input_arguments...` will be replaced by the `input_arguments_names` specified in the method name record (see <Ref Sect="Section_method_name_record_entries" />)

CAP/gap/CategoryConstructor.gi

@@ -9,7 +9,7 @@ InstallMethod( CategoryConstructor,
                [ IsRecord ],
 
   function( options )
-    local known_options_with_filters, name, object_datum_type, morphism_datum_type, is_computable, filter, CC, default_func_strings, info, unknown_filters, create_func_name, create_func, func_string, underlying_arguments, add, func, option_name, prop;
+    local known_options_with_filters, name, object_datum_type, morphism_datum_type, is_computable, filter, CC, underlying_category, default_func_strings, info, unknown_filters, create_func_name, create_func, func_string, weight, func_string_and_weight, underlying_arguments, add, func, option_name, prop;
 
     ## check given options
     known_options_with_filters := rec(
@@ -27,10 +27,10 @@ InstallMethod( CategoryConstructor,
         morphism_constructor := IsFunction,
         morphism_datum := IsFunction,
         list_of_operations_to_install := IsList,
-        operation_weights := IsRecord,
         is_computable := IsBool,
         supports_empty_limits := IsBool,
         underlying_category_getter_string := IsString,
+        underlying_category := IsCapCategory,
         underlying_object_getter_string := IsString,
         underlying_morphism_getter_string := IsString,
         top_object_getter_string := IsString,
@@ -290,11 +290,32 @@ InstallMethod( CategoryConstructor,
 
         if create_func = "default" then
 
+            if not IsBound( options.underlying_category ) then
+
+                Error( "when using \"default\" for some `create_func_*`, the option `underlying_category` must be set" );
+
+            fi;
+
             func_string := default_func_strings.(info.return_type);
 
+            # the default strings simply apply the operation in the underlying category
+            weight := OperationWeight( options.underlying_category, info.function_name );
+
         elif IsFunction( create_func ) then
 
-            func_string := create_func( name, CC );
+            func_string_and_weight := create_func( name, CC );
+
+            if IsList( func_string_and_weight ) and Length( func_string_and_weight ) = 2 and IsInt( func_string_and_weight[2] ) then
+
+                func_string := func_string_and_weight[1];
+                weight := func_string_and_weight[2];
+
+            else
+
+                func_string := func_string_and_weight;
+                weight := -1;
+
+            fi;
 
         else
 
@@ -464,9 +485,9 @@ InstallMethod( CategoryConstructor,
 
         func := EvalString( func_string );
 
-        if IsBound( options.operation_weights ) and IsBound( options.operation_weights.(name) ) then
+        if weight <> -1 then
 
-            add( CC, func, options.operation_weights.(name) );
+            add( CC, func, weight );
 
         else
 

CAP/gap/DummyImplementations.gi

@@ -166,13 +166,13 @@ InstallMethod( DummyCategory,
 
     fi;
 
-    dummy_function := { operation_name, dummy } -> """
+    dummy_function := { operation_name, dummy } -> Pair( """
         function ( input_arguments... )
             
             Error( "this is a dummy category without actual implementation" );
             
         end
-    """;
+    """, 1 );
 
     category_constructor_options.create_func_bool := dummy_function;
     category_constructor_options.create_func_object := dummy_function;

CAP/gap/ReinterpretationOfCategory.gi

@@ -85,6 +85,7 @@ InstallMethod( ReinterpretationOfCategory,
     # the methods for ModelingObject et al. will be installed later once we have a category instance filter
     category_constructor_options := rec(
         underlying_category_getter_string := "ModelingCategory",
+        underlying_category := C,
         underlying_object_getter_string := "ModelingObject",
         underlying_morphism_getter_string := "ModelingMorphism",
         top_object_getter_string := "ReinterpretationOfObject",
@@ -138,14 +139,6 @@ InstallMethod( ReinterpretationOfCategory,
 
     category_constructor_options.list_of_operations_to_install := list_of_operations_to_install;
 
-    category_constructor_options.operation_weights := rec( );
-
-    for operation in list_of_operations_to_install do
-
-        category_constructor_options.operation_weights.(operation) := OperationWeight( C, operation );
-
-    od;
-
     if IsBound( C!.supports_empty_limits ) then
 
         category_constructor_options.supports_empty_limits := C!.supports_empty_limits;

CAP/gap/TerminalCategory.gi

@@ -24,7 +24,7 @@ BindGlobal( "IsCapTerminalCategoryMorphismRep", IsMorphismInCapTerminalCategoryW
 
 InstallGlobalFunction( CAP_INTERNAL_CONSTRUCTOR_FOR_TERMINAL_CATEGORY,
   function( input_record )
-    local completed_record, list_of_operations_to_install, skip, info, properties, excluded_properties, T, operation_name;
+    local completed_record, list_of_operations_to_install, skip, info, properties, excluded_properties, T, operation_name, operation;
 
     completed_record := ShallowCopy( input_record );
 
@@ -104,7 +104,7 @@ InstallGlobalFunction( CAP_INTERNAL_CONSTRUCTOR_FOR_TERMINAL_CATEGORY,
         ## equality of source and target is part of the specification of the input and checked by the pre-function
         return true;
 
-    end );
+    end, 1 );
 
     return T;
 
@@ -147,27 +147,27 @@ InstallGlobalFunction( TerminalCategoryWithSingleObject, FunctionWithNamedArgume
     create_func_object :=
         function( name, T )
 
-            return """
+            return Pair( """
                 function( input_arguments... )
                     
                     return ObjectConstructor( cat, fail );
                     
                 end
-            """;
+            """, 1 );
 
         end;
 
     ## e.g., IdentityMorphism, PreCompose
     create_func_morphism :=
         function( name, T )
 
-            return """
+            return Pair( """
                 function( input_arguments... )
                     
                     return MorphismConstructor( cat, top_source, fail, top_range );
                     
                 end
-            """;
+            """, 1 );
 
         end;
 
@@ -211,39 +211,39 @@ InstallGlobalFunction( TerminalCategoryWithSingleObject, FunctionWithNamedArgume
 
         return true;
 
-    end );
+    end, 1 );
 
     ##
     AddIsWellDefinedForMorphisms( T,
       function( T, morphism )
 
         return true;
 
-    end );
+    end, 1 );
 
     ##
     AddIsEqualForObjects( T,
       function( T, object1, object2 )
 
         return true;
 
-    end );
+    end, 1 );
 
     ##
     AddIsEqualForMorphisms( T,
       function( T, morphism1, morphism2 )
 
         return true;
 
-    end );
+    end, 1 );
 
     ##
     AddMorphismsOfExternalHom( T,
       function( T, object_1, object_2 )
 
         return [ TerminalCategoryWithSingleObjectUniqueMorphism( T ) ];
 
-    end );
+    end, 2 );
 
     if CAP_NAMED_ARGUMENTS.FinalizeCategory then
 
@@ -321,27 +321,27 @@ InstallGlobalFunction( TerminalCategoryWithMultipleObjects, FunctionWithNamedArg
     create_func_object :=
         function( name, T )
 
-            return """
+            return Pair( """
                 function( input_arguments... )
                     
                     return ObjectConstructor( cat, "operation_name" );
                     
                 end
-            """;
+            """, 1 );
 
         end;
 
     ## e.g., IdentityMorphism, PreCompose
     create_func_morphism :=
         function( name, T )
 
-            return """
+            return Pair( """
                 function( input_arguments... )
                     
                     return MorphismConstructor( cat, top_source, "operation_name", top_range );
                     
                 end
-            """;
+            """, 1 );
 
         end;
 
@@ -432,50 +432,50 @@ InstallGlobalFunction( TerminalCategoryWithMultipleObjects, FunctionWithNamedArg
 
         return true;
 
-    end );
+    end, 1 );
 
     ##
     AddSomeIsomorphismBetweenObjects( T,
       function( T, object_1, object_2 )
 
         return MorphismConstructor( T, object_1, "SomeIsomorphismBetweenObjects", object_2 );
 
-    end );
+    end, 1 );
 
     AddDistinguishedObjectOfHomomorphismStructure( T,
       function( T )
 
         return TerminalCategoryWithSingleObjectUniqueObject( RangeCategoryOfHomomorphismStructure( T ) );
 
-    end );
+    end, 2 );
 
     AddHomomorphismStructureOnObjects( T,
       function( T, source, target )
 
         return TerminalCategoryWithSingleObjectUniqueObject( RangeCategoryOfHomomorphismStructure( T ) );
 
-    end );
+    end, 2 );
 
     AddHomomorphismStructureOnMorphismsWithGivenObjects( T,
       function( T, source, morphism_1, morphism_2, target )
 
         return TerminalCategoryWithSingleObjectUniqueMorphism( RangeCategoryOfHomomorphismStructure( T ) );
 
-    end );
+    end, 2 );
 
     AddInterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructureWithGivenObjects( T,
       function( T, distinguished_object, morphism, target )
 
         return TerminalCategoryWithSingleObjectUniqueMorphism( RangeCategoryOfHomomorphismStructure( T ) );
 
-    end );
+    end, 2 );
 
     AddInterpretMorphismFromDistinguishedObjectToHomomorphismStructureAsMorphism( T,
       function( T, source, target, iota  )
 
         return MorphismConstructor( T, source, "InterpretMorphismFromDistinguishedObjectToHomomorphismStructureAsMorphism", target );
 
-    end );
+    end, 1 );
 
     if CAP_NAMED_ARGUMENTS.FinalizeCategory then