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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
Project: cocalc-sagemath-dev-slelievre
Views: 418346#############################################################################
##
## CAP package
##
## Copyright 2015, Sebastian Gutsche, TU Kaiserslautern
## Sebastian Posur, RWTH Aachen
##
#############################################################################
InstallValue( CATEGORIES_LOGIC_FILES,
rec(
Propositions := rec(
General := [
Filename( DirectoriesPackageLibrary( "CAP", "LogicForCategories" ), "PropositionsForGeneralCategories.tex" )
],
IsEnrichedOverCommutativeRegularSemigroup := [
Filename( DirectoriesPackageLibrary( "CAP", "LogicForCategories" ), "PropositionsForCategoriesEnrichedOverCommutativeRegularSemigroups.tex" )
],
IsAbCategory := [
Filename( DirectoriesPackageLibrary( "CAP", "LogicForCategories" ), "PropositionsForAbCategories.tex" )
],
IsAdditiveCategory := [
Filename( DirectoriesPackageLibrary( "CAP", "LogicForCategories" ), "PropositionsForAdditiveCategories.tex" )
],
IsPreAbelianCategory := [
Filename( DirectoriesPackageLibrary( "CAP", "LogicForCategories" ), "PropositionsForPreabelianCategories.tex" )
],
IsAbelianCategory := [
Filename( DirectoriesPackageLibrary( "CAP", "LogicForCategories" ), "PropositionsForAbelianCategories.tex" )
] ),
Predicates := rec(
General := [
Filename( DirectoriesPackageLibrary( "CAP", "LogicForCategories" ), "PredicateImplicationsForGeneralCategories.tex" )
],
IsEnrichedOverCommutativeRegularSemigroup := [
Filename( DirectoriesPackageLibrary( "CAP", "LogicForCategories" ), "PredicateImplicationsForCategoriesEnrichedOverCommutativeRegularSemigroups.tex" )
],
IsAbCategory := [
Filename( DirectoriesPackageLibrary( "CAP", "LogicForCategories" ), "PredicateImplicationsForAbCategories.tex" )
],
IsAdditiveCategory := [
Filename( DirectoriesPackageLibrary( "CAP", "LogicForCategories" ), "PredicateImplicationsForAdditiveCategories.tex" )
],
IsPreAbelianCategory := [
Filename( DirectoriesPackageLibrary( "CAP", "LogicForCategories" ), "PredicateImplicationsForPreabelianCategories.tex" )
],
IsAbelianCategory := [
Filename( DirectoriesPackageLibrary( "CAP", "LogicForCategories" ), "PredicateImplicationsForAbelianCategories.tex" )
] ),
EvalRules := rec(
General := [
Filename( DirectoriesPackageLibrary( "CAP", "LogicForCategories" ), "RelationsForGeneralCategories.tex" )
],
IsEnrichedOverCommutativeRegularSemigroup := [
Filename( DirectoriesPackageLibrary( "CAP", "LogicForCategories" ), "RelationsForCategoriesEnrichedOverCommutativeRegularSemigroups.tex" )
],
IsAbCategory := [
Filename( DirectoriesPackageLibrary( "CAP", "LogicForCategories" ), "RelationsForAbCategories.tex" )
],
IsAdditiveCategory := [
Filename( DirectoriesPackageLibrary( "CAP", "LogicForCategories" ), "RelationsForAdditiveCategories.tex" )
],
IsPreAbelianCategory := [
Filename( DirectoriesPackageLibrary( "CAP", "LogicForCategories" ), "RelationsForPreabelianCategories.tex" )
],
IsAbelianCategory := [
Filename( DirectoriesPackageLibrary( "CAP", "LogicForCategories" ), "RelationsForAbelianCategories.tex" )
] ),
) );
InstallGlobalFunction( SetCapLogicInfo,
function( arg )
local level;
if Length( arg ) = 0 then
level := 1;
else
level := arg[ 1 ];
fi;
SetInfoLevel( CapLogicInfo, level );
end );
###################################
##
## Logic part 1: theorems
##
###################################
InstallGlobalFunction( AddTheoremFileToCategory,
function( category, filename )
local theorem_list, i;
Add( category!.logical_implication_files.Propositions.General, filename );
theorem_list := READ_THEOREM_FILE( filename );
for i in theorem_list do
ADD_THEOREM_TO_CATEGORY( category, i );
od;
end );
InstallGlobalFunction( ADD_THEOREM_TO_CATEGORY,
function( category, implication_record )
local theorem_record, name;
theorem_record := TheoremRecord( category );
name := implication_record.Function;
if not IsBound( theorem_record.( name ) ) then
theorem_record.( name ) := [ implication_record ];
else
Add( theorem_record.( name ), implication_record );
fi;
end );
InstallGlobalFunction( SANITIZE_RECORD,
function( record, arguments, result_object )
local object, index_list, i, value_function, value;
if not IsBound( record!.Object ) then
object := "result";
else
object := record!.Object;
fi;
if IsString( object ) and LowercaseString( object ) = "result" then
object := [ result_object ];
elif IsString( object ) and LowercaseString( object ) = "all" then
object := arguments;
elif IsInt( object ) then
object := [ arguments[ object ] ];
elif IsList( object ) then
index_list := object;
object := [ arguments ];
for i in index_list do
if IsInt( i ) then
object := List( object, j -> j[ i ] );
elif IsString( i ) and LowercaseString( i ) = "all" then
object := Concatenation( object );
else
Error( "wrong object format: only int and all" );
fi;
od;
else
Error( "wrong object type" );
fi;
if IsBound( record!.ValueFunction ) then
value_function := record!.ValueFunction;
else
value_function := IdFunc;
fi;
if IsBound( record!.Value ) then
value := record!.Value;
else
value := true;
fi;
if not IsBound( record!.compare_function ) then
return List( object, i -> [ i, value_function, value ] );
else
return List( object, i -> [ i, value_function, value, record!.compare_function ] );
fi;
end );
InstallGlobalFunction( INSTALL_TODO_FOR_LOGICAL_THEOREMS,
function( method_name, arguments, result_object, category )
local current_argument, crisp_category, deductive_category, theorem_list,
current_theorem, todo_list_source, range, is_valid_theorem, sanitized_source,
entry, current_source, sanitized_source_list, current_argument_type, i;
if not IsBound( TheoremRecord( category ).( method_name ) ) then
return;
fi;
Info( CapLogicInfo, 1, Concatenation( "Creating todo list for operation ", method_name ) );
theorem_list := TheoremRecord( category ).( method_name );
Info( CapLogicInfo, 1, Concatenation( "Trying to create ", String( Length( theorem_list ) ), " theorems" ) );
for current_theorem in theorem_list do
## check wether argument list matches here
current_argument_type := current_theorem!.Variable_list;
is_valid_theorem := true;
for i in [ 1 .. Length( current_argument_type ) ] do
if current_argument_type[ i ] = 0 then
continue;
fi;
if not IsList( arguments[ i ] ) or not Length( arguments[ i ] ) = current_argument_type[ i ] then
is_valid_theorem := false;
break;
fi;
od;
if not is_valid_theorem then
continue;
fi;
todo_list_source := [ ];
is_valid_theorem := true;
for current_source in current_theorem.Source do
sanitized_source_list := SANITIZE_RECORD( current_source, arguments, result_object );
if IsBound( current_source!.Type ) and LowercaseString( current_source!.Type ) = "testdirect" then
for sanitized_source in sanitized_source_list do
if ( Length( sanitized_source ) = 3 and not sanitized_source[ 2 ]( sanitized_source[ 1 ] ) = sanitized_source[ 3 ] )
or ( Length( sanitized_source ) = 4 and not sanitized_source[ 4 ]( sanitized_source[ 2 ]( sanitized_source[ 1 ] ), sanitized_source[ 3 ] ) ) then
is_valid_theorem := false;
break;
fi;
od;
else
for sanitized_source in sanitized_source_list do
sanitized_source[ 2 ] := NameFunction( sanitized_source[ 2 ] );
Add( todo_list_source, sanitized_source );
od;
fi;
od;
if is_valid_theorem = false then
Info( CapLogicInfo, 1, "Failed" );
continue;
fi;
Info( CapLogicInfo, 1, "Success" );
range := SANITIZE_RECORD( current_theorem!.Range, arguments, result_object );
## NO ALL ALLOWED HERE!
range := range[ 1 ];
if Length( todo_list_source ) = 0 then
Setter( range[ 2 ] )( range[ 1 ], range[ 3 ] );
continue;
fi;
entry := ToDoListEntry( todo_list_source, range[ 1 ], NameFunction( range[ 2 ] ), range[ 3 ] );
SetDescriptionOfImplication( entry, Concatenation( "Implication from ", method_name ) );
AddToToDoList( entry );
od;
end );
InstallImmediateMethod( CAP_CATEGORY_SOURCE_RANGE_THEOREM_INSTALL_HELPER,
IsCapCategoryMorphism and HasCapCategory and HasSource and HasRange,
0,
function( morphism )
if CapCategory( morphism )!.predicate_logic then
INSTALL_TODO_FOR_LOGICAL_THEOREMS( "Source", [ morphism ], Source( morphism ), CapCategory( morphism ) );
INSTALL_TODO_FOR_LOGICAL_THEOREMS( "Range", [ morphism ], Range( morphism ), CapCategory( morphism ) );
fi;
TryNextMethod();
end );
##############################
##
## Logic part 2: predicates
##
##############################
InstallGlobalFunction( AddPredicateImplicationFileToCategory,
function( category, filename )
local theorem_list, i;
Add( category!.logical_implication_files.Predicates.General, filename );
theorem_list := READ_PREDICATE_IMPLICATION_FILE( filename );
for i in theorem_list do
ADD_PREDICATE_IMPLICATIONS_TO_CATEGORY( category, i );
od;
end );
##
InstallGlobalFunction( ADD_PREDICATE_IMPLICATIONS_TO_CATEGORY,
function( category, immediate_record )
INSTALL_PREDICATE_IMPLICATION( category, immediate_record );
if not IsBound( category!.predicate_implication ) then
category!.predicate_implication := [ ];
fi;
Add( category!.predicate_implication, immediate_record );
end );
##
InstallGlobalFunction( INSTALL_PREDICATE_IMPLICATION,
function( category, immediate_record )
local cell_filter;
if LowercaseString( immediate_record!.CellType ) = "obj" then
cell_filter := ObjectFilter( category );
elif LowercaseString( immediate_record!.CellType ) = "mor" then
cell_filter := MorphismFilter( category );
else
cell_filter := TwoCellFilter( category );
fi;
InstallTrueMethod( immediate_record!.Range and cell_filter, immediate_record!.Source and cell_filter );
end );
###############################
##
## Part 3: Eval rule API
##
###############################
##
InstallGlobalFunction( AddEvalRuleFileToCategory,
function( category, filename )
local theorem_list, i;
Add( category!.logical_implication_files.EvalRules.General, filename );
if IsBound( category!.logical_implication_files.EvalRules.general_rules_already_read ) and
category!.logical_implication_files.EvalRules.general_rules_already_read = true then
theorem_list := READ_EVAL_RULE_FILE( filename );
for i in theorem_list do
ADD_EVAL_RULES_TO_CATEGORY( category, i );
od;
fi;
end );
##
InstallGlobalFunction( ADD_EVAL_RULES_TO_CATEGORY,
function( category, rule_record )
local command;
if not IsBound( rule_record!.starting_command ) then
return;
fi;
command := rule_record!.starting_command ;
if not IsBound( category!.eval_rules ) then
category!.eval_rules := rec( );
fi;
if not IsBound( category!.eval_rules.( command ) ) then
category!.eval_rules.( command ) := [ ];
fi;
Add( category!.eval_rules.( command ), rule_record );
end );
###############################
##
## Technical functions
##
###############################
InstallGlobalFunction( INSTALL_LOGICAL_IMPLICATIONS_HELPER,
function( category, current_filter )
local i, theorem_list, current_theorem;
for i in category!.logical_implication_files.Propositions.( current_filter ) do
theorem_list := READ_THEOREM_FILE( i );
for current_theorem in theorem_list do
ADD_THEOREM_TO_CATEGORY( category, current_theorem );
od;
od;
for i in category!.logical_implication_files.Predicates.( current_filter ) do
theorem_list := READ_PREDICATE_IMPLICATION_FILE( i );
for current_theorem in theorem_list do
ADD_PREDICATE_IMPLICATIONS_TO_CATEGORY( category, current_theorem );
od;
od;
end );
InstallImmediateMethod( INSTALL_LOGICAL_IMPLICATIONS,
IsCapCategory and IsEnrichedOverCommutativeRegularSemigroup,
0,
function( category )
INSTALL_LOGICAL_IMPLICATIONS_HELPER( category, "IsEnrichedOverCommutativeRegularSemigroup" );
TryNextMethod( );
end );
InstallImmediateMethod( INSTALL_LOGICAL_IMPLICATIONS,
IsCapCategory and IsAdditiveCategory,
0,
function( category )
INSTALL_LOGICAL_IMPLICATIONS_HELPER( category, "IsAdditiveCategory" );
TryNextMethod( );
end );
InstallImmediateMethod( INSTALL_LOGICAL_IMPLICATIONS,
IsCapCategory and IsPreAbelianCategory,
0,
function( category )
INSTALL_LOGICAL_IMPLICATIONS_HELPER( category, "IsPreAbelianCategory" );
TryNextMethod( );
end );
InstallImmediateMethod( INSTALL_LOGICAL_IMPLICATIONS,
IsCapCategory and IsAbelianCategory,
0,
function( category )
INSTALL_LOGICAL_IMPLICATIONS_HELPER( category, "IsAbelianCategory" );
TryNextMethod( );
end );
InstallImmediateMethod( INSTALL_LOGICAL_IMPLICATIONS,
IsCapCategory and IsAbCategory,
0,
function( category )
INSTALL_LOGICAL_IMPLICATIONS_HELPER( category, "IsAbCategory" );
TryNextMethod( );
end );