Fact Bases and Querying

As well as offering a high-level interface for mapping ASP facts to Python objects, Clorm also provides facilities for dealing with collections of facts. An ASP application typically does not simply deal with individual facts in isolation, but instead needs to deal in a collection of facts; whether they are the set of facts that make up the problem instance or, alternatively, the facts that constitute the model of a problem,

A Container for Facts

Clorm provides the FactBase class as a container for storing and querying facts. A FactBase behaves much like a normal Python set object with two caveats: firstly, it can only contain instances of Predicate sub-classes, and secondly, it provides an interface to a database-like query mechanism.

from clorm import Predicate, ConstantField, StringField, FactBase

class Person(Predicate):
   id = ConstantField
   address = StringField

class Pet(Predicate):
   owner = ConstantField
   petname = StringField

dave = Person(id="dave", address="UNSW")
morri = Person(id="morri", address="UNSW")
dave_cat = Pet(owner="dave", petname="Frank")

fb = FactBase([dave,morri,dave_cat])

# The "in" and "len" operators work as expected
assert dave in fb
assert len(fb) == 3

A fact base can be populated at object construction time or later. It can also be manipulated using the standard Python set operators and member functions. Like a Python set object it has an FactBase.add() member function for adding facts. However, because it can only store Predicate instances this function is able to be more flexible and has been overloaded to accept either a single fact or a collection of facts.

dave_dog = Pet(owner="dave", petname="Bob")
morri_cat = Pet(owner="morri", petname="Fido")
morri_cat2 = Pet(owner="morri", petname="Dusty")

fb.add(dave_dog)
fb.add([morri_cat, morri_cat2])

assert dave_dog in fb
assert morri_cat in fb
assert morri_cat2 in fb

Querying

An important motivation for providing a specialised FactBase container class for storing facts, as opposed to simply using a Python list or set object, is to support a rich mechanism for querying the contents of a collection.

When an ASP model is returned by the solver the application developer needs to process the model in order to extract the relevant information. The simplest mechanism to do this is to simply loop through the facts in the model. This loop will typically contain a number of conditional statements to determine what action to take for the given fact; and to store it if some sort of matching needs to take place.

However, this loop-and-test approach leads to unnecessary boilerplate code as well as making the purpose of the code more obscure. FactBase is intended to alleviate this problem by offering a database-like query mechanism for extracting information from a model.

Note

The following highlights the operations of the new Query API. As of Clorm 1.2.1 this new API should be the preferred search mechanism. It provides all the functionality of the old query interface and much more; including SQL-like joins between predicates and controlling how the query results are presented.

Simple Queries

Continuing the running example above the FactBase.query() method can be used to create Query objects.

query1=fb.query(Pet).where(Pet.owner == "dave")
query2=fb.query(Person).where(Person.id == "dave")

The queries are defined by chaining over the member functions of a Query object. Each function call returns a modified copy of the Query object. Here the member function Query.where() returns a modified copy of itself. This chaining technique will be be familiar to users of Python ORM’s such as SQLAlchemy or Peewee, where it is used as a generator for SQL statements.

A query object needs to be executed in order to return the search results. There are number of end-points that can be used to execute the search. The Query.all() member function returns a generator to iterate over all matching search results:

assert set(query1.all()) == set([dave_cat,dave_dog])

The Query.singleton() member function returns the single matching item (and raises an exception if there is not exactly one match):

assert query2.singleton() == dave

The Query.first() member function returns the first matching item, and only raises an exception if there no matching items:

assert query2.first() == dave

The Query.count() member function returns the number of matching entries:

assert query1.count() == 2

Note

For comparison the following shows how these queries and results can be encoded using the legacy query API. The FactBase.select() method is used to create clorm.Select objects. Note: there is no matching member function for Query.first().

query1_legacy=fb.select(Pet).where(Pet.owner == "dave")
query2_legacy=fb.select(Person).where(Person.id == "dave")

assert set(query1_legacy.get()) == set([dave_cat,dave_dog])
assert query2_legacy.get_unique() == dave
assert query1_legacy.count() == 2

An important difference between the old and new interfaces is that the call to Select.get() executes the query and returns the list of results. In contrast the call to Query.all() returns a generator and the query is executed by the generator during its iteration.

Queries with Joins

It is often useful to match instances of different predicates in the same way that you would join multiple database tables in an SQL query. To perform a search across multiple predicates it is first necessary to specify the predicates in the call to FactBase.query() and then specify to how these predicates are to be joined in the chained member function Query.join()

query3=fb.query(Person,Pet).join(Person.id == Pet.owner)

When a query contains multiple predicates the result will consist of tuples, where each tuple contains the facts matching the signature of predicates in the query clause. Mathematically, the tuples are a subset of the cross-product over instances of the predicates; where the subset is determined by the join clause.

assert set(query3.all()) == set([(dave,dave_cat),(dave,dave_dog),
                                 (morri,morri_cat),(morri,morri_cat2)])

Projections

Returning tuples of facts may not be convenient and a more usable output format may be desired. In such a case it is possible to specify a Query.select() specification to provide the projection of the results. This is much like the use of the SQL SELECT clause.

Note

Instead of formulating the query from scratch a new query can be defined as a refinement of an existing query.

query4=query3.select(Pet.petname, Person.address)

assert set(query4.all()) == set([("Bob","UNSW"),("Frank","UNSW"),
                                 ("Fido","UNSW"),("Dusty","UNSW")])

In the general case the query result is returned as a tuple consisting of the instances of the signature matching the FactBase.query() specification. However, if the result signature is for a single item, for example you only want to return the name of the pet, then returning a singleton tuple is not very intuitive. So, instead, when the result signature consists only of a single item then the API default behaviour is for the query result to return the items themselves rather than being wrapped in a singleton tuple.

query5=query3.select(Pet.petname)

assert set(query5.all()) == set(["Bob","Frank","Fido","Dusty"])

One important point to note when using projections is that the uniqueness of the output is no longer guaranteed. While the combinations of the cross-product of tuples being joined are guaranteed to be unique, once a Query.select() signature is specified this may no longer be the case. For example, if in the above query we only want to output the addresses of the owners of the different pets, the projection will lead to duplicate elements. These duplicates can be removed from the search by specifying the Query.distinct() modifier. In terms of SQL this is similar to specfying a SELECT DISTINCT query.

query6=query3.select(Person.address)
query7=query6.distinct()

assert query6.count() == 4
assert set(query6.all()) == set(["UNSW"])
assert list(query7.all()) == ["UNSW"]

Finally, for greatest flexibility the Query.select() member function can be passed a single Python callable object such as a function or lambda expression. The call signature of this object must match the signature specified in the FactBase.query() specification. The output of this callable are then presented as the results of the query.

query7=fb.query(Person,Pet).join(Person.id == Pet.owner)\
         .select(lambda pn,pt: f"{pt.petname} from {pn.address}")

Queries with Ordered Results

The Query.order_by() member function allows for the ordering of results similar to an SQL ORDER BY clause. Multiple fields can be listed as well as being able to specify ascending or descending sort order; with ascending order being the default and descending order specified by the desc() function.

from clorm import desc

query8=fb.query(Pet).order_by(Pet.owner, desc(Pet.petname))\
         .select(Pet.owner,Pet.petname)

assert list(query8.all()) == [("dave","Frank"),("dave","Bob"),
                              ("morri","Fido"),("morri","Dusty")]

Grouping the Query Results

Query results can be grouped in a similarly to an SQL GROUP BY clause using the Query.group_by() member function . An important distinction between SQL and Clorm’s grouping mechanism is that Clorm does not support query aggregate functions, so any aggregating needs to be performed outside the query specification itself.

The Query.group_by() clause modifies the behaviour of the output of the generator returned Query.all(). Instead of simply iterating over the individual items, the iterator returns pairs where the first element of the pair is the group identifier (based on the group_by specification) and the second element is an iterator over the matching elements within the group.

query9=fb.query(Pet).group_by(Pet.owner)\
         .order_by(desc(Pet.petname)).select(Pet.petname)

result = [(oname, list(petnames)) for oname,petnames in query9.all()]
assert result == [("dave",["Frank","Bob"]),("morri",["Fido","Dusty"])]

Querying by Positional Arguments

As well as querying by field name (or sub-field name) it is also possible to query by the field (sub-field) position.

query10=fb.query(Pet).where(Pet[0] == "dave").order_by(Pet[1])

However, earlier warnings still hold; use positional arguments sparingly and only in cases where the order of elements will not change as the ASP code evolves.

Querying Predicates with Complex Terms

Querying Predicates with complex terms is no different to the simple case. A chain of “.” notation expressions and positional arguments can be used to identify the appropriate field. For example we can replace the Person definition earlier to something containing a tuple:

from clorm import Predicate, ConstantField, StringField, FactBase

class PersonAlt(Predicate):
   id = ConstantField
   address = (StringField,StringField)

dave = PersonAlt(id="dave", address=("Newcastle","UNSW"))
morri = PersonAlt(id="morri", address=("Sydney","UNSW"))
torsten = PersonAlt(id="torsten", address=("Potsdam","UP"))

fb2 = FactBase([dave,morri,torsten])

query11=fb2.query(PersonAlt)\
           .where(PersonAlt.address[1] == "UNSW")\
           .select(PersonAlt.address[0])\
           .order_by(PersonAlt.address[1])

assert list(query11.all()) == ["Newcastle","Sydney"]

Complex Query Expressions

So far we have only seen Clorm’s support for queiries with a single where clause, such as:

query12=fb.query(Pet).where(Pet.owner == "dave")

However, more complex queries can be specified. Firstly, a where clause can consist of a comma seperated list of clauses. These are treated as a conjunction:

# Search for pets named Bob that are owned by dave

query13=fb.query(Pet).where(Pet.petname == "Bob", Pet.owner == "dave")

assert query13.singleton() == dave_dog

It is also possible to specify more complex queries using the overloaded logical operators &, |, and ~.

# Find the Person with id "torsten" or whose university address is not "UP"
query14=fb2.query(PersonAlt)\
           .where((PersonAlt.id == "torsten") | ~(PersonAlt.address[1] == "UP"))

assert set(query14.all()) == set([dave,morri,torsten])

# Find the Person with id "dave" and with address "UNSW"
query15=fb2.query(PersonAlt)\
           .where((PersonAlt.id == "dave") & (PersonAlt.address[1] == "UNSW"))

assert query15.singleton() == dave

Clorm also provides the explicit functions and_(), or_(), and not_() for these logical operators, but the overloaded syntax is arguably more intuitive. With the explicit functions the above could also be written as:

query14alt=fb2.query(PersonAlt)\
              .where(or_(PersonAlt.id == "torsten", not_(PersonAlt.address[1] == "UP")))
query15alt=fb2.query(PersonAlt)\
              .where(and_(PersonAlt.id == "dave", PersonAlt.address[1] == "UNSW"))

Finally, it is also possible to test for membership of a collection using the in_() and notin_() functions.

query16=fb2.query(PersonAlt).where(in_(PersonAlt.id, ["dave","bob","sam"])

assert query16.singleton() == dave

Queries with Parameters

To support more flexible queries Clorm provides placeholders as a means of parameterising queries. Placeholders are named ph1_ to ph4_ and correspond to the positional parameters. These parameters are bounds to actual values by calling Query.bind() where the input parameter to the function call must match the declared placeholders.

from clorm import ph1_, ph2_

query12=fb.query(Pet).where((Pet.owner == ph1_) & (Pet.petname == ph2_))

assert query12.bind("dave","Bob").singleton() == dave_dog
assert query12.bind("dave","Fido").count() == 0

Additional placeholders can be defined using the ph_() function. For example, ph_(5) will create a placeholder for the 5th positional argument.

Clorm also supports named placeholders, which may be preferable if there are a larger number of parameters. A named placeholder is created by calling the ph_() function with a non-numeric first parameter, and are referenced in the call to Query.bind() using keyword function parameters. An advantange of named placeholders is that they allow for a default value to be set.

from clorm import ph_

query13=fb.query(Pet).where(Pet.owner == ph_("owner","dave"))

assert set(query13.all()) == set([dave_dog,dave_cat])
assert set(query13.bind(owner="morri").all()) == set([morri_cat,morri_cat2])

Querying Negative Facts/Complex-Terms

ASP problems can often by compactly modelled using only default negation instead of strong negation. Because of this the use of explicitly negated literals is not particularly common in ASP programs.

Nevertheless Clorm does support negated facts and the Clorm query mechanism support querying based on the sign of a fact or complex term.

from clorm import IntegerField

class P(Predicate):
    a = IntegerField

p1 = P(1)
neg_p2 = P(2,sign=False)

fb3 = FactBase([p1,neg_p2])
assert fb3.query(P).where(P.sign == True).singleton() == p1
assert fb3.query(P).where(P.sign == False).singleton() == neg_p2

Querying the Predicate Itself

While it is possible to query fields (and sub-fields) of a predicate using the intutive “.” syntax (eg., Pet.owner == ph1_), unfortunately, it is not possible to provide this intuitive syntax for querying the predicate itself (e.g., a query of Pet < ph1_ will fail).

Instead a helper function path() is provided for this special case.

from clorm import path

query14=fb.query(Pet).where(path(Pet) == dave_dog)
assert query14.count() == 1

Note, querying by the predicate itself is a boundary case. While testing for equality or inequality makes sense semantically, the semantics of a query based on an ordering operator doesn’t always make sense (eg., path(Pet) < dave_dog).

Furthermore, when testing for equality or inequality it is usually simpler to not use the query mechanism and instead to use the basic Python set inclusion operation:

assert dave_dog in fb

FactBases with Indexes

A typical ASP program has models that contain relatively small numbers of facts (e.g., 10-100 facts). With such small numbers of facts, querying these facts from a FactBase can often be done without regard to performance considerations, since the solving of the combinatorial ASP problem will often dominate.

However, as the number of the number of facts increases so to does the cost of querying these facts from a FactBase. Eventually this can lead to a noticeable impact of performance.

In order to alleviate this problem a FactBase can be defined with indexes for one of more fields.

To highlight this the following example creates a simple test predicate that has two fields. Instances are created where the two fields have identical values, and these instances are added to a FactBase where one field is indexed and the other is not.

class Num(Predicate):
    to_idx=IntegerField
    not_to_idx=IntegerField

fb4 = FactBase([Num(to_idx=n,not_to_idx=n) for n in range(0,100000)], indexes=[Num.to_idx])

We can now compare the timing differences between searching for a value where one query searches for a value based on the indexed field and the other query searches for the same value based on the non-indexed field.

import time

query15=fb4.query(Num).where(Num.to_idx == 50000)
query16=fb4.query(Num).where(Num.not_to_idx == 50000)


start_q15 = time.time()
assert query15.count() == 1
q15_time = time.time() - start_q15

start_q16 = time.time()
assert query16.count() == 1
q16_time = time.time() - start_q16

assert q15_time < q16_time
print("Indexed search {} vs non-indexed search {}".format(q15_time,q16_time))

To confirm that these two queries are indeed behaving differently we can examine the query plans for the respective queries by calling the Query.query_plan() methods.

print("Querying without indexing:\n{}\n".format(query15.query_plan()))
print("Query with indexing:\n{}\n".format(query16.query_plan()))

Note, currently, there is no official API for a query plan object so it is only possible to print the object for manual examination. The key aspect to notice here is that the search on the indexed field appears as a keyed search whereas the search on the non-indexed field appears as a filter clause. Essentially the non-indexed search has to examine every fact in the fact base while the indexed search doesn’t.

Querying without indexing:
------------------------------------------------------
QuerySubPlan:
        Input Signature: ()
        Root path: Num
        Indexes: (Num.to_idx,)
        Prejoin keyed search: [ Num.to_idx == 50000 ]
        Prejoin filter clauses: None
        Prejoin order_by: None
        Join key: None
        Post join clauses: None
        Post join order_by: None
------------------------------------------------------

Query with indexing:
------------------------------------------------------
QuerySubPlan:
        Input Signature: ()
        Root path: Num
        Indexes: (Num.to_idx,)
        Prejoin keyed search: None
        Prejoin filter clauses: ( [ Num.not_to_idx == 50000 ] )
        Prejoin order_by: None
        Join key: None
        Post join clauses: None
        Post join order_by: None
------------------------------------------------------

A final note. As with indexing in databases, the use of indexes should be monitored carefully. The speed up in search must always be balanced the cost of constructing and maintaining the index.