8 Managing Derived Methods

8.2 Derivation Objects

8.2-1 IsDerivedMethod

8.2-2 MakeDerivation

8.2-3 DerivationName

8.2-4 DerivationWeight

8.2-5 DerivationFunction

8.2-6 CategoryFilter

8.2-7 IsApplicableToCategory

8.2-8 TargetOperation

8.2-9 UsedOperationsWithMultiplesAndCategoryGetters

8.2-10 InstallDerivationForCategory

8.2-11 FunctionCalledBeforeInstallation

8.2-1 IsDerivedMethod

8.2-2 MakeDerivation

8.2-3 DerivationName

8.2-4 DerivationWeight

8.2-5 DerivationFunction

8.2-6 CategoryFilter

8.2-7 IsApplicableToCategory

8.2-8 TargetOperation

8.2-9 UsedOperationsWithMultiplesAndCategoryGetters

8.2-10 InstallDerivationForCategory

8.2-11 FunctionCalledBeforeInstallation

8.4 Managing Derivations in a Category

8.4-1 IsOperationWeightList

8.4-2 MakeOperationWeightList

8.4-3 DerivationGraph

8.4-4 CategoryOfOperationWeightList

8.4-5 CurrentOperationWeight

8.4-6 OperationWeightUsingDerivation

8.4-7 DerivationOfOperation

8.4-8 InstallDerivationsUsingOperation

8.4-9 Reevaluate

8.4-10 Saturate

8.4-11 AddPrimitiveOperation

8.4-12 PrintDerivationTree

8.4-13 PrintTree

8.4-14 PrintTreeRec

8.4-1 IsOperationWeightList

8.4-2 MakeOperationWeightList

8.4-3 DerivationGraph

8.4-4 CategoryOfOperationWeightList

8.4-5 CurrentOperationWeight

8.4-6 OperationWeightUsingDerivation

8.4-7 DerivationOfOperation

8.4-8 InstallDerivationsUsingOperation

8.4-9 Reevaluate

8.4-10 Saturate

8.4-11 AddPrimitiveOperation

8.4-12 PrintDerivationTree

8.4-13 PrintTree

8.4-14 PrintTreeRec

`‣ DerivationInfo` | ( info class ) |

Info class for derivations.

`‣ ActivateDerivationInfo` ( arg ) | ( function ) |

`‣ DeactivateDerivationInfo` ( arg ) | ( function ) |

`‣ IsDerivedMethod` ( arg ) | ( filter ) |

Returns: `true`

or `false`

A derivation object describes a derived method. It contains information about which operation the derived method implements, and which other operations it relies on.

`‣ MakeDerivation` ( name, target_op, used_ops_with_multiples, weight, func, category_filter ) | ( operation ) |

Creates a new derivation object. The argument `name` is an arbitrary name used to identify this derivation, and is useful only for debugging purposes. The argument `target_op_name` is the name of the operation which the derived method implements. The argument `used_ops_with_multiples` contains

the name of each operation used by the derived method,

together with a positive integer specifying how many times that operation is used and

either a category getter or

`fail`

.

This is given as a list of lists, where each sublist has as first entry the name of an operation, as second entry an integer and as third entry either a function or `fail`

. This function should accept the category for which this derivation will be installed, and return a category for which the operation in the first entry must be installed for the derivation to be considered applicable. The argument `weight` is an additional number to add when calculating the resulting weight of the target operation using this derivation. Unless there is any particular reason to regard the derivation as exceedingly expensive, this number should be `1`

. The argument `func` contains the actual implementation of the derived method. The argument `category_filter` is a filter (or function) describing which categories the derivation is valid for. If it is valid for all categories, then this argument should have the value `IsCapCategory`

. The output of `category_filter` must not change during the installation of operations. In particular, it must not rely on `CanCompute`

to check conditions.

`‣ DerivationName` ( d ) | ( attribute ) |

The name of the derivation. This is a name identifying this particular derivation, and normally not the same as the name of the operation implemented by the derivation.

`‣ DerivationWeight` ( d ) | ( attribute ) |

Extra weight for the derivation.

`‣ DerivationFunction` ( d ) | ( attribute ) |

The implementation of the derivation.

`‣ CategoryFilter` ( d ) | ( attribute ) |

Filter describing which categories the derivation is valid for.

`‣ IsApplicableToCategory` ( d, C ) | ( operation ) |

Returns: `true`

if the category `C` is known to satisfy the category filter of the derivation `d`.

Checks if the derivation is known to be valid for a given category.

`‣ TargetOperation` ( d ) | ( attribute ) |

Returns: The name (as a string) of the operation implemented by the derivation `d`

`‣ UsedOperationsWithMultiplesAndCategoryGetters` ( d ) | ( attribute ) |

Returns: The names of the operations used by the derivation `d`, together with their multiplicities and category getters. The result is a list consisting of lists of the form `[op_name, mult, getter]`

, where `op_name`

is a string, `mult`

a positive integer and `getter`

is a function or `fail`

.

`‣ InstallDerivationForCategory` ( d, weight, C ) | ( operation ) |

Install the derived method `d` for the category `C`. The integer `weight` is the computed weight of the operation implemented by this derivation.

`‣ FunctionCalledBeforeInstallation` ( d ) | ( attribute ) |

Input is a derived method. Output is a unary function that takes as an input a category and does not output anything. This function is always called before the installation of the derived method for a concrete instance of a category.

`‣ IsDerivedMethodGraph` ( arg ) | ( filter ) |

Returns: `true`

or `false`

A derivation graph consists of a set of operations and a set of derivations specifying how some operations can be implemented in terms of other operations.

`‣ MakeDerivationGraph` ( operations ) | ( operation ) |

Make a derivation graph containing the given set of operations and no derivations. The argument `operations` should be a list of strings, the names of the operations. The set of operations is fixed once the graph is created. Derivations can be added to the graph by calling `AddDerivation`

.

`‣ AddOperationsToDerivationGraph` ( graph, operations ) | ( operation ) |

Adds a list of operation names `operations` to a given derivation graph `graph`. This is used in extensions of CAP which want to have their own basic operations, but do not want to pollute the CAP kernel any more. Please use it with caution. If a weight list/category was created before it will not be aware of the operations.

`‣ AddDerivation` ( graph, target_op, description, used_ops_with_multiples_and_category_getters, func, weight, category_filter, loop_multiplier, category_getters, function_called_before_installation ) | ( function ) |

Add a derivation to a derivation graph.

`‣ AddDerivationToCAP` ( arg ) | ( function ) |

`‣ Operations` ( G ) | ( attribute ) |

Gives the operations in the graph `G`, as a list of strings.

`‣ DerivationsUsingOperation` ( G, op_name ) | ( operation ) |

Finds all the derivations in the graph `G` that use the operation named `op_name`, and returns them as a list.

`‣ DerivationsOfOperation` ( G, op_name ) | ( operation ) |

Finds all the derivations in the graph `G` targeting the operation named `op_name` (that is, the derivations that provide implementations of this operation), and returns them as a list.

`‣ IsOperationWeightList` ( arg ) | ( filter ) |

Returns: `true`

or `false`

An operation weight list manages the use of derivations in a single category \(C\). For every operation, it keeps a weight value which indicates how costly it is to perform that operation in the category \(C\). Whenever a new operation is implemented in \(C\), the operation weight list should be notified about this and given a weight to assign to this operation. It will then automatically install all possible derived methods for \(C\) in such a way that every operation has the smallest possible weight (the weight of a derived method is computed by using the weights of the operations it uses).

`‣ MakeOperationWeightList` ( C, G ) | ( operation ) |

Create the operation weight list for a category. This should only be done once for every category, and the category should afterwards remember the returned object. The argument `C` is the CAP category this operation weight list is associated to, and the argument `G` is a derivation graph containing operation names and derivations.

`‣ DerivationGraph` ( owl ) | ( attribute ) |

Returns the derivation graph used by the operation weight list `owl`.

`‣ CategoryOfOperationWeightList` ( owl ) | ( attribute ) |

Returns the CAP category associated to the operation weight list `owl`.

`‣ CurrentOperationWeight` ( owl, op_name ) | ( operation ) |

Returns the current weight of the operation named `op_name`.

`‣ OperationWeightUsingDerivation` ( owl, d ) | ( operation ) |

Finds out what the weight of the operation implemented by the derivation `d` would be if we had used that derivation.

`‣ DerivationOfOperation` ( owl, op_name ) | ( operation ) |

Returns the derivation which is currently used to implement the operation named `op_name`. If the operation is not implemented by a derivation (that is, either implemented directly or not implemented at all), then `fail`

is returned.

`‣ InstallDerivationsUsingOperation` ( owl, op_name ) | ( operation ) |

Performs a search from the operation `op_name`, and installs all derivations that give improvements over the current state. This is used internally by `AddPrimitiveOperation`

and `Reevaluate`

. It should normally not be necessary to call this function directly.

`‣ Reevaluate` ( owl ) | ( operation ) |

Reevaluate the installed derivations, installing better derivations if possible. This should be called if new derivations become available for the category, either because the category has acquired more knowledge about itself (e.g. it is told that it is abelian) or because new derivations have been added to the graph.

`‣ Saturate` ( owl ) | ( operation ) |

Saturates the derivation graph, i.e., calls reevaluate until no more changes in the derivation graph occur.

`‣ AddPrimitiveOperation` ( owl, op_name, weight ) | ( operation ) |

Add the operation named `op_name` to the operation weight list `owl` with weight `weight`. This causes all operations that can be derived, directly or indirectly, from the newly added operation to be installed as well (unless they are already installed with the same or lower weight).

`‣ PrintDerivationTree` ( owl, op_name ) | ( operation ) |

Print a tree representation of the way the operation named `op_name` is implemented in the category of the operation weight list `owl`.

`‣ PrintTree` ( arg1, arg2, arg3 ) | ( operation ) |

Prints a tree structure.

`‣ PrintTreeRec` ( arg1, arg2, arg3, arg4 ) | ( operation ) |

This section describes an implementation of min heaps for storing strings with associated integer keys, used internally by operation weight lists.

`‣ IsStringMinHeap` ( arg ) | ( filter ) |

Returns: `true`

or `false`

A string min heap is a min heap where every node contains a string label and an integer key.

`‣ StringMinHeap` ( arg ) | ( function ) |

Create an empty string min heap.

`‣ Add` ( H, string, key ) | ( operation ) |

Add a new node containing the label `string` and the key `key` to the heap `H`.

`‣ ExtractMin` ( H ) | ( operation ) |

Remove a node with minimal key value from the heap `H`, and return it. The return value is a list `[ label, key ]`

, where `label`

is the extracted node's label (a string) and `key`

is the node's key (an integer).

`‣ DecreaseKey` ( H, string, key ) | ( operation ) |

Decrease the key value for the node with label `string` in the heap `H`. The new key value is given by `key` and must be smaller than the node's current value.

`‣ IsEmptyHeap` ( H ) | ( operation ) |

Returns `true`

if the heap `H` is empty, `false`

otherwise.

`‣ HeapSize` ( H ) | ( operation ) |

Returns the number of nodes in the heap `H`.

`‣ Contains` ( H, string ) | ( operation ) |

Returns `true`

if the heap `H` contains a node with label `string`, and `false`

otherwise.

`‣ Swap` ( H, i, j ) | ( operation ) |

Swaps two elements in the list used to implement the heap, and updates the heap's internal mapping of labels to list indices. This is an internal function which should only be called from the functions that implement the heap functionality.

`‣ Heapify` ( H, i ) | ( operation ) |

Heapify the heap `H`, starting from index `i`. This is an internal function.

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