Introduction

The dlvhex reasoner evaluates Answer Set Programs with external atoms. One important design principle was to provide a mechanism to easily add further external atoms without having to recompile the main application. A plugin is a shared library that provides functions to realise custom external atoms. Furthermore, a plugin can supply rewriting facilities, which may alter the input logic program prior to evaluation. Plugins can be written in Python as described below or in C++ as described here; the former does not have all features of the C++ version but should be sufficient in almost all cases.

This Section gives an overview of dlvhex Python plugins and external atoms.

The External Atom Function

Formally, an external atom is defined to evaluate to true or false, depending on a number of parameters:

An interpretation (a set of facts)
A list of input constants
A list of output constants

However, it is more intuitive and convenient to think of an external atom not as being boolean, but rather functional: Depending on a given interpretation and a list of input constants, it returns output tuples. For instance, the external atom to import triples from RDF files has this form:

   &rdf[uri](X,Y,Z)

where uri stands for a string denoting the RDF-source and X, Y, and Z are variables that represent an RDF-triple. The function associated with this atom simply returns all RDF-triples from the specified source. Obviously, in this case the interpretation is ignored.

Information Flow

The interface that is used by dlvhex to access a plugin follows very closely these semantics. For each atom, a retrieval function has to be implemented, which receives a query-object and has to return an an answer-object. The query-object carries the input interpretation as well as the ground input parameters of the external atom call, while the answer object is a container for the output tuples of the external atom's function.

Types of Input Parameters

Theoretically, it is completely up to the atom function how to process the interpretation together with the input constants, which are basically only names. In practice however, only parts of the interpretation might be needed (if at all). Considering this as well as for efficiency reasons, we created two (in the implementation three, see below) categories of input parameters:

the Constant parameter and
the Predicate parameter. A third category called Tuple exists, which is a meta category standing for an arbitrary mount of Constant input parameters. This is useful, e.g., for &concat[s1,s2,...](Out).

A parameter of type "Constant" is not related to the interpretation at all, like in the previous example of the RDF-atom. A parameter is of type "Predicate" means that all facts in the interpretation with this predicate are necessary for the atom. Let's assume, we have an external atom that calculates the overall price of a number of books given by their ISBN number:

   &overallbookprice[isbn](X)

The single input parameter of this atom would be of type "Predicate", meaning that not the constant itself is necessary for the atom's function, but the part of the interpretation with this predicate. So if we have, e.g.,

$I=\{{\rm isbn}({\rm 0{-}19{-}824183{-}6}), {\rm isbn}({\rm 0{-}201{-}99954{-}4}), p(a), q(b),\ldots\}$

the atom's function will be called with a "reduced" interpretation:

$I=\{{\rm isbn}({\rm 0{-}19{-}824183{-}6}), {\rm isbn}({\rm 0{-}201{-}99954{-}4})\}$

Specifying the type of input parameters not only helps to single out the relevant part of the interpretation, but also supports dlvhex in calculating the dependencies within a HEX-program.

Writing a Python Plugin

We wanted to keep the interface between dlvhex and the plugins as lean as possible. Necessary tasks are:

Write a new Python script which contains a register function and imports the package dlvhex
Write another function for each external atom, and export this function using the register function

The register function has the following form:

 def register():
   dlvhex.addAtom ("concat", (dlvhex.CONSTANT, dlvhex.CONSTANT), 1) )

It adds one entry for each external atom. Each entry is again a tuple of arity 3: the first element is the external predicate name, the third element is the output arity, and the second is another tuple of input parameter types (dlvhex.CONSTANT, dlvhex.PREDICATE, dlvhex.TUPLE).

Each external predicate name (e.g. concat) needs to be implemented in form of another Python function with an appropriate number of input parameters.

Example:

 def concat(a, b):
   dlvhex.output((dlvhex.getValue(a) + dlvhex.getValue(b), ))

The function just takes the values of these parameters and outputs their string concatenation. Here, a and b are the input parameters (of type constant). If an external atom specifies an input parameter of type TUPLE, the elements will be passed as a Python tuple.

Example:

 def concat(tup):
   ret = ""
   for x in tup:
     ret = reg + x
   dlvhex.output((ret, ))

Note that akin to the C++ API, terms and atoms are represented by IDs and the retrieval of the value behind usually requires the use of the getValue method; some methods combine this with other functionalities (see method list below).

If an external atom specifies that it provides partial answers (see below), it further must add all tuples which can become true if currently unassigned input atoms are defined using

 dlvhex.outputUnknown((ret, ))

. As this might be the case for infinitely many tuples, the (finite) set of relevant ones can be retrieved from the output atoms returned by

 dlvhex.getRelevantOutputAtoms()

.

In addition to the actual semantics of an external atom, the Python API can also be used for defining custom learning techniques (described in the following list). Advanced plugin features, such as providing converters, rewriters and dependency graph optimizations. are, however, only possible with the C++ API.

In more detail, the dlvhex Python module provides the methods described in the following paragraphs.

Management of dlvhex IDs

```
 {.txt}tuple getTuple(aID)
```
Return the IDs of the elements of a dlvhex atom identified by ID aID.
```
 {.txt}tuple getTupleValues(aID)
```
Return the values of the elements of a dlvhex atom identified by ID aID.
```
 {.txt}string getValue(id)
```
Return the value of an atom or term ID id.
```
 {.txt}int getIntValue(id)
```
Return the value of an integer term ID id as integer.
```
 {.txt}string getValue(tup)
```
Print the tuple tup recursively, i.e., the elements of the tuple can be further tuples or IDs. IDs id are printed by calling dlvhex.getValue(id), they are delimited by , and the output is enclosed in curly braces.
```
 {.txt}tuple getExtension(id)
```
Returns all tuples tup in the extension of the predicate represented by id (wrt. the input interpretation).
```
 {.txt}dlvhex.ID storeString(str)
```
Stores a string str as dlvhex object and returns its ID.
```
 {.txt}dlvhex.ID storeInteger(int)
```
Stores an integer int as dlvhex object and returns its ID.
```
 {.txt}dlvhex.ID storeAtom(args)
```
Transforms a sequence of terms or values args into a dlvhex atom.
```
 {.txt}dlvhex.ID negate(aID)
```
Negates an atom ID aID.
```
 {.txt}void addAtom(name, args, ar, [prop])
```
Add external atom name with arguments args (see above), output arity ar and external source properties prop ("prop" is optional).
```
 {.txt}void storeExternalAtom(pred, input, output)
```
Stores an external atom with predicate pred, input parameters input and output parameters output (can be terms or their IDs) and returns its ID.

Basic Plugin Functionality

```
 {.txt}void output(args)
```
Adds a tuple of IDs or values args to the external source output.
```
 {.txt}void outputUnknown(args)
```
Adds a tuple of IDs or values args to the external source possible output under more complete input (only needed if the external atom provides partial answers, see below). The external source is expected to decide for all tuples from output atoms returned by
```
 dlvhex.getRelevantOutputAtoms() 
```
whether they might become true (if not true yet).
```
 {.txt}ID getExternalAtomID()
```
Returns the ID of the currently evaluated external atom; the changed information (cf. hasChanged) is relative to the last call for the same external atom
```
 {.txt}tuple getInputAtoms([pred])
```
Returns a tuple of all input atoms (not only true ones!) to this external atom; pred is an optional predicate ID, which allows for restricting the tuple to atoms over this predicate.
```
 {.txt}tuple getRelevantOutputAtoms([pred])
```
Returns a set of all relevant output atoms of this external atom ; this is relevant for answering queries partially (see
```
 prop.providesPartialAnswer() \code): the external atom is expected to mark all tuples of the output atoms as unknown if they might become true under a more complete input.</li>
   <li>\code{.txt}tuple getTrueInputAtoms([pred])
```
Returns a tuple of all input atoms to this external atom which are currently true; pred is an optional predicate ID, which allows for restricting the tuple to atoms over this predicate.
```
 {.txt}int getInputAtomCount()
```
Returns the number of input atoms (not only true ones!).
```
 {.txt}int getTrueInputAtomCount()
```
Returns the number of input atoms which are currently true.
```
 {.txt}bool isInputAtom(id)
```
Checks if atom id belongs to the input of the current external atom.
```
 {.txt}bool isTrue(id)
```
Checks if an input atom identified by ID id is assigned to true.
```
 {.txt}bool isFalse(id)
```
Checks if an input atom identified by ID id is assigned to false.
```
 {.txt}void resetCacheOfPlugins()
```
Empties all caches of external atom evaluation results and all cached nogoods from external learning.

Conflict-driven Learning

Usually, learned nogoods consist of 1. a set of positive or negated input atoms, and 2. a negative output atom, where 1. is the justification for the (positive) output atom to be true. Note that a nogood is a set of atoms which must not be all simultanously true. Therefore, this encodes that whenever all atoms from 1. are true, then the output atom must not be false (this is why the negative output atom is added).

```
 {.txt}bool learn(tup)
```
Learns a nogood as a tuple of atom IDs or their negations tup; returns if learning was enabled.
```
 {.txt}bool learnSupportSets()
```
Returns True if the plugin was called for support set learning, and False if it was called for query answering. If the external source provides a complete set support sets (declared via properties) and it was called for support set learning, then it must return all support sets. If it was called for query answering, then it must answer the query. However, it may also answer the query if it was called for support set learning and it may also return support sets if it was called for query answering (although this is not necessary and not suggested for efficiency reasons).
```
 {.txt}ID storeOutputAtom(args, [sign])
```
Constructs an external atom output atom from IDs or values args (for learning purposes) and its sign, where true (default) means positive and false means negative, and returns its ID.

For instance, the nogood { p(a), -q(a), -&diff[p,q](a) } encodes that whenever the atom p(a) is true and the atom q(a) is false, then the atom &diff[p,q](a) must be true (i.e. must not be false) since constant a will be in the output of the set difference of p and q.

Inremental External Query Answering

```
 {.txt}bool isAssignmentComplete()
```
Returns true if the external source is evaluated over an interpretation which is complete for sure (if it returns false, then the assignment is possibly partial but it might still be complete).
```
 {.txt}bool isAssigned(id)
```
Provided that the source declared that it is interested in this property (cf. setCaresAboutAssigned), the method checks if an input atom identified by ID id is assigned.
```
 {.txt}bool hasChanged(id)
```
Provided that the source declared that it is interested in this property (cf. setCaresAboutChanged), the method checks if an input atom has possibly changes since the last call (if the method returns false, then it has not changed for sure).
```
 {.txt}ID storeRule(head, pbody, nbody)
```
Stores a rule with head atoms head, positive body atoms pbody and negative body atoms nbody and returns its ID; all parameters need to be a tuples of IDs.

Subprogram Evaluation

```
 {.txt}tuple evaluateSubprogram(tup)
```
Evaluates the subprogram specified by a tuple
```
 {.txt}facts, rules
```
consisting of facts facts (tuple of IDs of ground atoms) and rules rules (tuple of rule IDs) and returns the number of answer sets; the result is a tuple of answer sets, where each answer set is again a tuple of the ground atom IDs which are true in the respective answer set.
```
 {.txt}tuple loadSubprogram(filename)
```
Loads the program stored in file filename and returns a pair
```
 {.txt}(edb, idb)
```
consisting of a tuple edb of facts (ground atom IDs) and a tuple idb of rule IDs.

External Source Properties Declaration

An instance of dlvhex.ExtSourceProperties can be passed to the addAtom method as last parameter to specify properties of the external atom, which might help the reasoner to speed up evaluation. The structure can be configured using the following methods:

 {.txt}void prop.addMonotonicInputPredicate(index)

Declare argument index as monotonic predicate parameter.

 {.txt}void prop.addAntimonotonicInputPredicate(index)

Declare argument index as antimonotonic predicate parameter.

```
 {.txt}void prop.addPredicateParameterNameIndependence(index)
```
Declare argument index as independent of the predicate name (only its extension is relevant).
```
 {.txt}void prop.addFiniteOutputDomain(index)
```
Declare that output argument index has a finite domain.
```
 {.txt}void prop.addRelativeFiniteOutputDomain(index1, index2)
```
Declare that output argument index2 has a finite domain wrt. input argument index1.
```
 {.txt}void prop.setFunctional(value)
```
Declare the source as functional.
```
 {.txt}void prop.setFunctionalStart(index)
```
Declare the source as functional beginning at term index + 1.
```
 {.txt}void prop.setOnlySafeSupportSets(value)
```
Declare that the source provides only safe support sets, i.e., all variables in support sets occur in positive input atoms (atoms other than output atoms).
```
 {.txt}void prop.setSupportSets(value)
```
Declare that the source provides support sets.
```
 {.txt}void prop.setCompletePositiveSupportSets(value)
```
Declare that the source provides complete positive support sets.
```
 {.txt}void prop.setCompleteNegativeSupportSets(value)
```
Declare that the source provides complete negative support sets.
```
 {.txt}void prop.setVariableOutputArity(value)
```
Declare that the source has a variable output arity.
```
 {.txt}void prop.setCaresAboutAssigned(value)
```
Declare that the sources wants to know the assigned values.
```
 {.txt}void prop.setCaresAboutChanged(value)
```
Declare that the sources wants to know the values which potentially changed since the previous call.
```
 {.txt}void prop.setAtomlevellinear(value)
```
Declare the source as linear on the atom level.
```
 {.txt}void prop.setUsesEnvironment(value)
```
Declare the source as linear on the tuple level.
```
 {.txt}void prop.setFiniteFiber(value)
```
Declare that the source has a finite fiber.
```
 {.txt}void prop.addWellorderingStrlen(index1, index2)
```
Declare that output argument index1 has a string length wellordering wrt. input argument index2.
```
 {.txt}void prop.addWellorderingNatural(index1, index2)
```
Declare that output argument index1 has a natural wellordering wrt. input argument index2.
```
 {.txt}void prop.providesPartialAnswer(values)
```
Declare that the external atom provies a partial answer under partial input using a 3-valued logic (true, false, unknown); in that case the implementation must add positive answer tuples using
```
 dlvhex.output 
```
and currently unknown ones using
```
 dlvhex.outputUnknown 
```
(others are false), whereas without this property the unassigned input atoms should be assumed to be false and a complete answer wrt. this assumption should be delivered.

Moreover, for an ID object id, there are the following shortcuts:

id.value() for dlvhex.getValue(id)
id.extension() for dlvhex.getExtension(id)
id.intValue() for dlvhex.getIntValue(id)
id.tuple() for dlvhex.getTuple(id)
id.tupleValues() for dlvhex.getTupleValues(id)
id.negate() for dlvhex.negate(id)
id.isInputAtom() for dlvhex.isInputAtom(id)
id.isAssigned() for dlvhex.isAssigned(id)
id.hasChanged() for dlvhex.hasChanged(id)
id.isTrue() for dlvhex.isTrue(id)
id.isFalse() for dlvhex.isFalse(id)

Using a Python Plugin

In order to load a Python-implemented plugin stored in file PATH, pass the additional option

 --pythonplugin=PATH

to dlvhex.