Advanced Tabling Mechanisms

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Advanced tabling mechanisms

Advanced tabling mechanismsA call subsumption based tabling engine for Yap Prolog

Flavio Cruz <[email protected]>Advisor: Ricardo Rocha <[email protected]>

1Center for Research in Advanced Computing Systems2Faculdade de Ciencias da Universidade do Porto

February 1, 2010

CRACS Flavio Cruz February 1, 2010 1 / 17

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Advanced tabling mechanisms Outline

1 Prolog and SLDLimitations

2 TablingEvaluationVariant Tabling

3 Subsumptive TablingEvaluation

4 Table SpaceVariant Table SpaceSubsumptive Table Space

5 Objectives

6 Work Plan


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Advanced tabling mechanisms Prolog and SLD

Prolog and SLD evaluation

In Logic Programming, Selective Linear Definite (SLD) is a top-downresolution mechanism.

SLD is inherently non-deterministic and does not force any specificsearch strategy.

The Prolog language uses depth first search.

Despite being widely used, the current evaluation method has a fewshortcomings.


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Advanced tabling mechanisms Prolog and SLD

SLD shortcomings

?- path(1, Z)

1. path(1, Z)

2. path(1, Y), edge(Y, Z)

3. path(1, Y)

Infinite Loop

Program

path(X, Z) :- path(X, Y),

edge(Y, Z).

path(X, Z) :- edge(X, Z).

edge(1, 2).

edge(2, 3).

1 2 3


Ad d bli h i T bli

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Advanced tabling mechanisms Tabling

Tabling

Tabling is a refinement of the SLD resolution.

Consists in storing intermediate answers for subgoals so that they can

be reused when a repeated subgoal appears in the resolution process.Tabling evaluation reduces the search space, prunes redundantcomputations and has better termination properties.

Enables more expressive logic programs.


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Tabled Evaluation

Example

1. path(1, Z)

2. path(1, Y), edge(Y, Z) 3. edge(1, Z)

4. Z = 2 5. fail6. edge(2, Z)

7. Z = 3

9. edge(3, Z)

10. fail8. fail

Y = 2 Y = 3

11. complete

Answers: { (4) Z = 2, (7) Z = 3 }.



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Variant Tabling

In the previous example, when a subgoal is called, we verify if avariant subgoal is already in the table space .

A subgoal G is variant of subgoal G �, when G and G � represent the

same subgoal by variable renaming.path(X, Y) is variant of path(A, B), because both representpath(VAR0, VAR1).

While this is a simple approach, more sophisticated techniques areknown.

The YapTab tabling engine from Yap only supports variant checking.


Advanced tabling mechanisms Subsumptive Tabling

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Subsumptive Tabling

Tabling by call subsumption aims to reuse answer computations bysharing answers from more general goals.

Theorem

If two subgoals G and G � exist, such that S and S � are the respective

answer sets and G � subsumes G, then S ⊆ S �.

Example: path(X, Z) subsumes path(1, Z).

Subsumptive checking is implemented in SLG-WAM from XSB.

In the past, a technique called Dynamic Threaded Sequential

Automata (DTSA) was used, currently they use Time Stamped Tries

(TST).



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Subsumptive Evaluation

Answerspath(X, Z): {(3) X=1 Z=2, (4) X=2Z=3, (9) X=1 Z=3}

path(2, Z) {(9) Z=3}

path(3, Z): ∅

Programpath(X, Z) :- edge(X, Z).path(X, Z) :- edge(X, Y), path(Y, Z).

edge(1, 2). edge(2, 3).

Example1. path(X, Z)

2. edge(X, Z)

3. X = 1

Z = 2

4. X = 2

Z = 35. fail

7. edge(X, Y), path(Y, Z)

8. path(2, Z) 10. path(3, Z)

9. Z = 3

11. fail

12. complete

X=1,Y=2X=2,Y=3


Advanced tabling mechanisms Table Space

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Variant Table Space

Tries are used to index terms.

Tries are a tree-structured automaton where common term prefixesare represented only once.

Two levels of tries:� Call Trie : stores subgoals for a specific predicate, like path/2.� Answer Trie : where answers are stored.

Only the values of variables are stored in the answer trie, in amechanism called substitution factoring .

A leaf state in a subgoal trie points to a subgoal frame where stateabout the subgoal evaluation is kept.



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g p

Variant Table Space

Example

Table entry for path/2

Subgoal trie for path/2

root

a

VAR0

b

VAR0

VAR0

VAR1

Subgoal Frame forpath(a, VAR0)

Subgoal Frame forpath(b, VAR0)

Subgoal Frame forpath(VAR0, VAR1)

Answer trie for path(a, VAR0)

root

ba



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g p

Time Stamped Tries

A subsumptive approach to tabling.

Instead of using an answer trie, in this technique we use a timestamped trie.

Whenever a new answer is found, the timestamps along the answerpath are updated to the incremented maximum time stamp .

Each subsumed goal keeps track of the last time stamp used, thus itcan retrieve only the new answers by unification when consuming.

The main objective is to avoid repeated answers.



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g

Time Stamped Tries

Time stamped trie for subgoal p(X, Y, Z):

Example (before)

root node

a, 5

a, 5

a, 1c, 3d, 5

b, 4

b, 4

b, 2

a, 2

VAR0, 2

Example (new answer p(a, b, c))

root node

a, 6

a, 5

a, 1c, 3d, 5

b, 6

b, 4

b, 2

a, 2

VAR0, 2c, 6



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Finding subsuming goals

Another important component in call by subsumption deals withlocating more generals subgoals in the call trie.

Unification and backtracking are used by SLG-WAM.

The algorithm finds a minimally subsuming call , hence it can be usedto efficiently check wether the found subgoal is a variant or not.


Advanced tabling mechanisms Objectives

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Objectives

Implement a subsumptive tabling engine in Yap, using theSLG-WAM’s time stamped tries approach.

Work on new approaches and optimizations using the previous work.We are trying to reuse as much code from XSB as possible to enablenovel features to be used by both Prolog systems.

Produce original work.


Advanced tabling mechanisms Work Plan

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Work Plan

Until the end of February: complete a prototype version using timestamped tries.

March, April, May: implement a few optimizations and try some new

approaches.

May, June: write the dissertation.

Lots of testing!

Produce one or two papers.


Advanced tabling mechanisms Work Plan

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Some useful links

http://github.com/flavioc/yap/

http://cracs.fc.up.pt/http://www.dcc.fc.up.pt/~vsc/Yap/

http://flaviocruz.net/



http://cracs.fc.up.pt/

http://www.dcc.fc.up.pt/~vsc/Yap/






http://cracs.fc.up.pt/


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