<ManSection>
<Attr Arg="functor" Name="ObjectCache" Label="for IsCapFunctor"/>
<Returns>IsCachingObject
</Returns>
<Description>
Retuns the caching object which stores the results of the functor <A>functor</A> applied to objects.
</Description>
</ManSection>
<ManSection>
<Attr Arg="functor" Name="MorphismCache" Label="for IsCapFunctor"/>
<Returns>IsCachingObject
</Returns>
<Description>
Retuns the caching object which stores the results of the functor <A>functor</A> applied to morphisms.
</Description>
</ManSection>
<ManSection>
<Func Arg="specification, func" Name="FunctionWithNamedArguments" />
<Returns>a function
</Returns>
<Description>
Simulates named arguments in &GAP; as follows:
<List>
<Item>
<A>specification</A> is a list of pairs with first entry the name of the argument and second entry a default value (which must be immutable).
</Item>
<Item>
<A>func</A> must be a function with first argument <Code>CAP_NAMED_ARGUMENTS</Code>.
</Item>
<Item>
The return value is a function with one argument fewer than <A>func</A>.
</Item>
</List>
<P/>
When calling the returned function, the arguments are passed on to <A>func</A>.
To simulate named arguments, any &GAP; options appearing in <A>specification</A> are consumed and put into the record <Code>CAP_NAMED_ARGUMENTS</Code>.
</Description>
</ManSection>
<ManSection>
<Func Arg="filter_string[, category]" Name="CAP_INTERNAL_GET_DATA_TYPE_FROM_STRING"/>
<Returns>a record
</Returns>
<Description>
The function takes one of the strings listed under <Code>filter_list</Code> in <Ref Sect="Section_method_name_record_entries" /> as input
and returns the corresponding data type (see <Ref BookName="CompilerForCAP" Func="CapJitInferredDataTypes" /> for details).
If no category is given, data types with generic filters (<Code>IsCapCategoryObject</Code>, <Code>IsCapCategoryMorphism</Code> etc.) are returned.
However, those cannot be used in the context of <Code>CompilerForCAP</Code> because the component <Code>category</Code> cannot be set in this case.
</Description>
</ManSection>
<ManSection>
<Func Arg="list_of_strings[, category]" Name="CAP_INTERNAL_GET_DATA_TYPES_FROM_STRINGS" />
<Returns>a list
</Returns>
<Description>
Applies <Ref Func="CAP_INTERNAL_GET_DATA_TYPE_FROM_STRING" /> to all elements of <A>list</A> and returns the result.
</Description>
</ManSection>
<ManSection>
<Func Arg="filter_string[, category]" Name="CAP_INTERNAL_REPLACED_STRING_WITH_FILTER" />
<Returns>a filter
</Returns>
<Description>
The function takes one of the strings listed under <Code>filter_list</Code> in <Ref Sect="Section_method_name_record_entries" /> as input.
The corresponding filter of the category <A>category</A> is returned.
If no category is given, generic filters (<Code>IsCapCategoryObject</Code>, <Code>IsCapCategoryMorphism</Code> etc.) are used.
</Description>
</ManSection>
<ManSection>
<Func Arg="list[, category]" Name="CAP_INTERNAL_REPLACED_STRINGS_WITH_FILTERS" />
<Returns>Replaced list
</Returns>
<Description>
Applies <Ref Func="CAP_INTERNAL_REPLACED_STRING_WITH_FILTER" /> to all elements of <A>list</A> and returns the result.
</Description>
</ManSection>
<ManSection>
<Func Arg="string, value" Name="CAP_INTERNAL_RETURN_OPTION_OR_DEFAULT" />
<Returns>option value
</Returns>
<Description>
Returns the value of the option with name string, or, if this value is fail,
the object value.
</Description>
</ManSection>
<ManSection>
<Func Arg="function, symbol_list, loop_multiple, replacement_record" Name="CAP_INTERNAL_FIND_APPEARANCE_OF_SYMBOL_IN_FUNCTION" />
<Returns>a list of symbols with multiples
</Returns>
<Description>
The function searches for the appearance of the strings in symbol list on the function function
and returns a list of pairs, containing the name of the symbol and the number of appearance.
If the symbol appears in a loop, the number of appearance is counted times the loop multiple.
Moreover, if appearances of found strings should be replaced by collections of other strings, then
these can be specified in the replacement record.
</Description>
</ManSection>
<ManSection>
<Func Arg="list1, list2" Name="CAP_INTERNAL_MERGE_PRECONDITIONS_LIST" />
<Returns>merge list
</Returns>
<Description>
The function takes two lists containing pairs of symbols (strings) and multiples.
The lists are merged that pairs where the string only appears in one list is then
added to the return list, if a pair with a string appears in both lists, the resulting
lists only contains this pair once, with the higher multiple from both lists.
</Description>
</ManSection>
<ManSection>
<Func Arg="data_type, human_readable_identifier_getter" Name="CAP_INTERNAL_ASSERT_VALUE_IS_OF_TYPE_GETTER" />
<Returns>a function
</Returns>
<Description>
Returns a function <Code>f</Code> which throws an error if its first argument is not of type <A>data_type</A>.
<A>human_readable_identifier_getter</A> is a function returning a string which is used to refer to the first argument of <Code>f</Code> in the error message.
The arguments of <Code>f</Code> except the first argument are passed on to <A>human_readable_identifier_getter</A>.
</Description>
</ManSection>
<ManSection>
<Func Arg="cell, category, human_readable_identifier_getter" Name="CAP_INTERNAL_ASSERT_IS_CELL_OF_CATEGORY" />
<Description>
The function throws an error if <A>cell</A> is not a cell of <A>category</A>.
If <A>category</A> is the boolean <C>false</C>, only general checks not specific to a concrete category are performed.
<A>human_readable_identifier_getter</A> is a 0-ary function returning a string which is used to refer to <A>cell</A> in the error message.
</Description>
</ManSection>
<ManSection>
<Func Arg="object, category, human_readable_identifier_getter" Name="CAP_INTERNAL_ASSERT_IS_OBJECT_OF_CATEGORY" />
<Description>
The function throws an error if <A>object</A> is not an object of <A>category</A>.
If <A>category</A> is the boolean <C>false</C>, only general checks not specific to a concrete category are performed.
<A>human_readable_identifier_getter</A> is a 0-ary function returning a string which is used to refer to <A>cell</A> in the error message.
</Description>
</ManSection>
<ManSection>
<Func Arg="morphism, category, human_readable_identifier_getter" Name="CAP_INTERNAL_ASSERT_IS_MORPHISM_OF_CATEGORY" />
<Description>
The function throws an error if <A>morphism</A> is not a morphism of <A>category</A>.
If <A>category</A> is the boolean <C>false</C>, only general checks not specific to a concrete category are performed.
<A>human_readable_identifier_getter</A> is a 0-ary function returning a string which is used to refer to <A>cell</A> in the error message.
</Description>
</ManSection>
<ManSection>
<Func Arg="two_cell, category, human_readable_identifier_getter" Name="CAP_INTERNAL_ASSERT_IS_TWO_CELL_OF_CATEGORY" />
<Description>
The function throws an error if <A>two_cell</A> is not a <Math>2</Math>-cell of <A>category</A>.
If <A>category</A> is the boolean <C>false</C>, only general checks not specific to a concrete category are performed.
<A>human_readable_identifier_getter</A> is a 0-ary function returning a string which is used to refer to <A>cell</A> in the error message.
</Description>
</ManSection>
<ManSection>
<Func Arg="category[, operation]" Name="CachingStatistic" />
<Description>
Prints statistics for all caches in <A>category</A>.
If <A>operation</A> is given (as a string), only statistics
for the given operation cache is stored.
</Description>
</ManSection>
<ManSection>
<Func Arg="category" Name="BrowseCachingStatistic" />
<Description>
Displays statistics for all caches in <A>category</A>.
in a Browse window. Here "status" indicates if the cache is weak, strong, or inactive, "hits" is the number of successful cache accesses, "misses" the number of unsuccessful cache
accesses, and "stored" the number of objects currently stored in the cache.
</Description>
</ManSection>
<ManSection>
<Func Arg="alias_name, function_name, deprecation_date" Name="InstallDeprecatedAlias" />
<Description>
Makes the function given by <A>function_name</A> available under the alias <A>alias_name</A>
with a deprecation warning including the date <A>deprecation_date</A>.
</Description>
</ManSection>
<ManSection>
<Func Arg="filter1, filter2" Name="IsSpecializationOfFilter" />
<Description>
Checks if <A>filter2</A> is more special than <A>filter1</A>,
i.e. if <A>filter2</A> implies <A>filter1</A>.
<A>filter1</A> and/or <A>filter2</A> can also be one of the strings listed under <Code>filter_list</Code> in <Ref Sect="Section_method_name_record_entries" /> and
in this case are replaced by the corresponding filters (e.g. <Code>IsCapCategory</Code>, <Code>IsCapCategoryObject</Code>, <Code>IsCapCategoryMorphism</Code>, ...).
</Description>
</ManSection>
<ManSection>
<Func Arg="filter_list1, filter_list2" Name="IsSpecializationOfFilterList" />
<Description>
Checks if <A>filter_list2</A> is more special than <A>filter_list1</A>,
i.e. if both lists have the same length and any element of <A>filter_list2</A> is more special than
the corresponding element of <A>filter_list1</A> in the sense of <Ref Func="IsSpecializationOfFilter" />.
<A>filter_list1</A> and <A>filter_list2</A> can also be the string <Code>"any"</Code>, respresenting a most general filter list of any length.
</Description>
</ManSection>
<ManSection>
<Func Arg="same as for InstallMethod" Name="InstallMethodForCompilerForCAP" />
<Description>
Installs a method via <Code>InstallMethod</Code> and adds it to the list of methods known to the compiler.
See <Ref Func="CapJitAddKnownMethod" /> for requirements.
</Description>
</ManSection>
<ManSection>
<Func Arg="same as for InstallOtherMethod" Name="InstallOtherMethodForCompilerForCAP" />
<Description>
Installs a method via <Code>InstallOtherMethod</Code> and adds it to the list of methods known to the compiler.
See <Ref Func="CapJitAddKnownMethod" /> for requirements.
</Description>
</ManSection>
<ManSection>
<Func Arg="operation, filters, method" Name="CapJitAddKnownMethod" />
<Description>
Adds a method to the list of methods known to the compiler.
If the first filter implies <Code>IsCapCategory</Code>,
method selection only takes the number of arguments and the first filter into account.
This allows to resolve operations even in the case that the syntax tree cannot fully be typed.
If the first filter does not imply <Code>IsCapCategory</Code>,
method selection takes all filters into account.
To strictly distinguish between the two cases, <Code>IsCapCategory</Code> must not imply the first filter
(except if the first filter is equal to <Code>IsCapCategory</Code>).
Method selection is strict in the sense that two different methods for the same operation
must not be comparable. That is, they must have a different number of filters or the filters
at at least one position must not be related via implication.
In particular, adding two methods with a CAP category as first argument (or a convenience method for a CAP operation)
with the same number of arguments and one category filter implying the other is not supported.
</Description>
</ManSection>
<ManSection>
<Func Arg="name, input_filters, output_data_type" Name="CapJitAddTypeSignature" />
<Description>
(experimental) Adds a type signature for the global function or operation given by <A>name</A> to the compiler.
<A>input_filters</A> must be a list of filters, or the string '"any"' representing a most general filter list of any length.
<A>output_data_type</A> must be a filter, a data type, or a function.
If it is a function with one argument, it must accept a list of input types and return the corresponding data type of the output.
If it is a function with two arguments, it must accept the arguments of a function call of <A>name</A> (as syntax trees)
and the function stack and return a record with components <Code>args</Code> (the possibly modified arguments) and <Code>output_type</Code>
(the data type of the output).
See <Ref BookName="CompilerForCAP" Func="CapJitInferredDataTypes" /> for more details on data types.
</Description>
</ManSection>
<ManSection>
<Func Arg="element_type" Name="CapJitDataTypeOfListOf" />
<Description>
(experimental) Returns the data type of a list whose elements are of type <A>element_type</A>.
<A>element_type</A> must be a filter or a data type.
</Description>
</ManSection>
<ManSection>
<Func Arg="n, element_types..." Name="CapJitDataTypeOfNTupleOf" />
<Description>
(experimental) Returns the data type of an <A>n</A>-tuple whose entries are of types corresponding to <A>element_types</A>.
<A>element_types...</A> must be filters or data types.
</Description>
</ManSection>
<ManSection Label="AutoDoc_generated_group301">
<Func Arg="group" Name="CapJitDataTypeOfGroup" />
<Func Arg="group" Name="CapJitDataTypeOfElementOfGroup" />
<Description>
(experimental) Returns the data type of the group (or elements of the group) <A>group</A>.
<P/>
</Description>
</ManSection>
<ManSection Label="AutoDoc_generated_group302">
<Func Arg="ring" Name="CapJitDataTypeOfRing" />
<Func Arg="ring" Name="CapJitDataTypeOfElementOfRing" />
<Description>
(experimental) Returns the data type of the ring (or elements of the ring) <A>ring</A>.
<P/>
</Description>
</ManSection>
<ManSection Label="AutoDoc_generated_group303">
<Func Arg="category" Name="CapJitDataTypeOfCategory" />
<Func Arg="category" Name="CapJitDataTypeOfObjectOfCategory" />
<Func Arg="category" Name="CapJitDataTypeOfMorphismOfCategory" />
<Func Arg="category" Name="CapJitDataTypeOfTwoCellOfCategory" />
<Description>
(experimental) Returns the data type of the category (or objects, morphisms, or two cells in the category) <A>category</A>.
<P/>
</Description>
</ManSection>
<ManSection>
<Func Arg="value, data_type_getter" Name="CapJitTypedExpression" />
<Description>
(experimental) Simply returns <A>value</A>, but allows to specify the data type of <A>value</A> for CompilerForCAP.
<A>data_type_getter</A> must be a literal function or a global variable pointing to a function.
The function must accept no arguments or a single argument, and return a valid data type.
If the function accepts a single argument, it must be inside a CAP operation or method known to CompilerForCAP (for example, see <Ref Func="InstallMethodForCompilerForCAP" />),
and the current category (i.e. the first argument of the CAP operation or method known to CompilerForCAP) will be passed to the function.
IMPORTANT: If <A>data_type_getter</A> is a literal function, it must not contain references to variables in its context.
Otherwise the code might access random memory locations.
See <Ref BookName="CompilerForCAP" Func="CapJitInferredDataTypes" /> for more details on data types.
</Description>
</ManSection>
<ManSection>
<Func Arg="predicate, func, initial_value" Name="CapFixpoint" />
<Description>
Computes a fixpoint of <A>func</A> with regard to equality given by <A>predicate</A>, starting with <A>initial_value</A>.
If no such fixpoint exists, the execution does not terminate.
</Description>
</ManSection>
<ManSection>
<Func Arg="package_name" Name="TransitivelyNeededOtherPackages" />
<Description>
Returns a list of package names which are transitively needed other packages of the package <A>package_name</A>.
</Description>
</ManSection>
<ManSection>
<Func Arg="operation_name" Name="PackageOfCAPOperation" />
<Description>
Returns the name of the package to which the CAP operation given by <A>operation_name</A> belongs or fail if the package is not known.
</Description>
</ManSection>
<ManSection>
<Oper Arg="list, obj" Name="SafePosition" Label="for IsList, IsObject"/>
<Returns>an integer
</Returns>
<Description>
Returns <Code>Position( <A>list</A>, <A>obj</A> )</Code> while asserting that this value is not <Code>fail</Code>.
</Description>
</ManSection>
<ManSection>
<Oper Arg="list, obj" Name="SafeUniquePosition" Label="for IsList, IsObject"/>
<Returns>an integer
</Returns>
<Description>
Returns <Code>Position( <A>list</A>, <A>obj</A> )</Code> while asserting that this value is not <Code>fail</Code> and the position is unique.
</Description>
</ManSection>
<ManSection>
<Oper Arg="list, func" Name="SafePositionProperty" Label="for IsList, IsFunction"/>
<Returns>an integer
</Returns>
<Description>
Returns <Code>PositionProperty( <A>list</A>, <A>func</A> )</Code> while asserting that this value is not <Code>fail</Code>.
</Description>
</ManSection>
<ManSection>
<Oper Arg="list, func" Name="SafeUniquePositionProperty" Label="for IsList, IsFunction"/>
<Returns>an integer
</Returns>
<Description>
Returns a position in <A>list</A> for which <A>func</A> returns <Code>true</Code> when applied to the corresponding entry while asserting that there exists exactly one such position.
</Description>
</ManSection>
<ManSection>
<Oper Arg="list, func" Name="SafeFirst" Label="for IsList, IsFunction"/>
<Returns>an element of the list
</Returns>
<Description>
Returns <Code>First( <A>list</A>, <A>func</A> )</Code> while asserting that this value is not <Code>fail</Code>.
</Description>
</ManSection>
<ManSection>
<Oper Arg="list, func" Name="SafeUniqueEntry" Label="for IsList, IsFunction"/>
<Returns>an element of the list
</Returns>
<Description>
Returns a value in <A>list</A> for which <A>func</A> returns <Code>true</Code> while asserting that there exists exactly one such entry.
</Description>
</ManSection>
<ManSection>
<Func Arg="n, args..." Name="NTuple" />
<Returns>a list
</Returns>
<Description>
Returns <A>args</A> while asserting that its length is <A>n</A>.
</Description>
</ManSection>
<ManSection>
<Func Arg="first, second" Name="Pair" />
<Returns>a list
</Returns>
<Description>
Alias for <Code>NTuple( 2, <A>first</A>, <A>second</A> )</Code>.
</Description>
</ManSection>
<ManSection>
<Func Arg="first, second, third" Name="Triple" />
<Returns>a list
</Returns>
<Description>
Alias for <Code>NTuple( 3, <A>first</A>, <A>second</A>, <A>third</A> )</Code>.
</Description>
</ManSection>
<ManSection>
<Func Arg="nr_rows, nr_cols, listlist" Name="TransposedMatWithGivenDimensions" />
<Returns>a list (of lists)
</Returns>
<Description>
The arguments are two integers <A>nr_rows</A>, <A>nr_cols</A> and a list of lists <A>listlist</A> such that
<A>nr_rows</A> = <C>Length</C>(<A>listlist</A>) and <A>nr_cols</A> = <C>Length</C>(<A>listlist</A><Math>[i]</Math>) for <Math>i=1</Math> to <A>nr_rows</A>.
The output is the transpose of <A>listlist</A> as a list consisting of <A>nr_cols</A> rows and <A>nr_rows</A> columns.
</Description>
</ManSection>
<ManSection>
<Func Arg="category, underlying_category, constructor_name" Name="HandlePrecompiledTowers" />
<Description>
Handles the information stored in <Code><A>underlying_category</A>!.compiler_hints.precompiled_towers</Code> (if bound) which is a list of records with components:
<List>
<Item>
<Code>remaining_constructors_in_tower</Code>: a non-empty list of strings (names of category constructors)
</Item>
<Item>
<Code>precompiled_functions_adder</Code>: a function accepting a CAP category as input
</Item>
</List>
<P/>
If <A>constructor_name</A> is the only entry of <Code>remaining_constructors_in_tower</Code>, <Code>precompiled_functions_adder</Code> is applied to <A>category</A>
(except if the option <Code>no_precompiled_code</Code> is set to <Code>true</Code>) and should add precompiled code.
Else, if <A>constructor_name</A> is the first entry of <Code>remaining_constructors_in_tower</Code>, the information is attached to <Code><A>category</A>!.compiler_hints.precompiled_towers</Code>
after removing <A>constructor_name</A> from <Code>remaining_constructors_in_tower</Code>.
Note: Currently, there is no logic for finding the "optimal" code to install if <A>constructor_name</A> is the only entry of <Code>remaining_constructors_in_tower</Code> of multiple entries.
</Description>
</ManSection>
<ManSection>
<Func Arg="value" Name="CAP_JIT_INCOMPLETE_LOGIC" />
<Description>
Simply returns <A>value</A>. Used to signify that the argument is not fully run through all logic functions/templates by CompilerForCAP.
</Description>
</ManSection>
<ManSection>
<Func Arg="func" Name="CAP_JIT_EXPR_CASE_WRAPPER" />
<Description>
Simply returns <A>func</A>, which must be a literal function without arguments only containing an <Code>if-elif-else</Code> statement with each branch consisting of a single <Code>return</Code> statement.
Used to write expressions of the form <Code>function() if-elif-else end()</Code> as <Code>CAP_JIT_EXPR_CASE_WRAPPER(function() if-elif-else end)()</Code> because the former is not valid in Julia.
</Description>
</ManSection>
<ManSection>
<Func Arg="list, func" Name="ListWithKeys" />
<Returns>a list
</Returns>
<Description>
Same as <Code>List( <A>list</A>, <A>func</A> )</Code> but <A>func</A> gets both the key <Code>i</Code> and <Code><A>list</A>[i]</Code> as arguments.
</Description>
</ManSection>
<ManSection>
<Func Arg="list, func" Name="SumWithKeys" />
<Returns>a list
</Returns>
<Description>
Same as <Code>Sum( <A>list</A>, <A>func</A> )</Code> but <A>func</A> gets both the key <Code>i</Code> and <Code><A>list</A>[i]</Code> as arguments.
</Description>
</ManSection>
<ManSection>
<Func Arg="list, func" Name="ProductWithKeys" />
<Returns>a list
</Returns>
<Description>
Same as <Code>Product( <A>list</A>, <A>func</A> )</Code> but <A>func</A> gets both the key <Code>i</Code> and <Code><A>list</A>[i]</Code> as arguments.
</Description>
</ManSection>
<ManSection>
<Func Arg="list, func" Name="ForAllWithKeys" />
<Returns>a list
</Returns>
<Description>
Same as <Code>ForAll( <A>list</A>, <A>func</A> )</Code> but <A>func</A> gets both the key <Code>i</Code> and <Code><A>list</A>[i]</Code> as arguments.
</Description>
</ManSection>
<ManSection>
<Func Arg="list, func" Name="ForAnyWithKeys" />
<Returns>a list
</Returns>
<Description>
Same as <Code>ForAny( <A>list</A>, <A>func</A> )</Code> but <A>func</A> gets both the key <Code>i</Code> and <Code><A>list</A>[i]</Code> as arguments.
</Description>
</ManSection>
<ManSection>
<Func Arg="list, func" Name="NumberWithKeys" />
<Returns>a list
</Returns>
<Description>
Same as <Code>Number( <A>list</A>, <A>func</A> )</Code> but <A>func</A> gets both the key <Code>i</Code> and <Code><A>list</A>[i]</Code> as arguments.
</Description>
</ManSection>
<ManSection>
<Func Arg="list, func" Name="FilteredWithKeys" />
<Returns>a list
</Returns>
<Description>
Same as <Code>Filtered( <A>list</A>, <A>func</A> )</Code> but <A>func</A> gets both the key <Code>i</Code> and <Code><A>list</A>[i]</Code> as arguments.
</Description>
</ManSection>
<ManSection>
<Func Arg="list, func" Name="FirstWithKeys" />
<Returns>a list
</Returns>
<Description>
Same as <Code>First( <A>list</A>, <A>func</A> )</Code> but <A>func</A> gets both the key <Code>i</Code> and <Code><A>list</A>[i]</Code> as arguments.
</Description>
</ManSection>
<ManSection>
<Func Arg="list, func" Name="LastWithKeys" />
<Returns>a list
</Returns>
<Description>
Same as <Code>Last( <A>list</A>, <A>func</A> )</Code> but <A>func</A> gets both the key <Code>i</Code> and <Code><A>list</A>[i]</Code> as arguments.
</Description>
</ManSection>
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