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....stack is used for scheduling. The choice point stack thus serves as a scheduling stack for both returning answers and resolving program clauses. Accordingly, we call this scheduling strategy Single Stack Scheduling. The operational semantics of this scheduling strategy was described in detail in [Swi94] and it forms the basis of the SLG WAM as described in [SW94a] The following example demonstrates how this strategy works. Example 3.1 Consider the program and query of Example 2.1.1. table p 2. p(X,Y) p(X,Z) p(Z,Y) p(X,Y) a(X,Y) a(1,2) a(1,3) a(2,3) p(1,Y) The forest of SLG ....

.... p(3,Y) a(3,Y) Figure 7: SLG evaluation under Batched Scheduling In Single Stack Scheduling, since answers are returned eagerly, whenever the engine backtracks over the generator choice point for a subgoal, that subgoal is guaranteed to be completely evaluated (Swift discusses this in detail in [Swi94] Since the return of answers is delayed in Batched Scheduling, this fact no longer holds, and extra checks are required in Batched Scheduling to ensure all answers are returned to consuming nodes. CHAPTER 4. BATCHED SCHEDULING 38 Generator 1. p(1,Y) Generator 1. p(1,Y) a) Generator 1. ....

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T. Swift. Efficient Evaluation of Normal Logic Programs. PhD thesis, Department of Computer Science, State University of New York at Stony Brook, 1994.

....stack is used for scheduling. The choice point stack thus serves as a scheduling stack for both returning answers and resolving program clauses. Accordingly, we call this scheduling strategy Single Stack Scheduling. The operational semantics of this scheduling strategy was described in detail in [Swi94] and it forms the basis of the SLG WAM as described in [SW94a] The following example demonstrates how this strategy works. Example 3.1 Consider the program and query of Example 2.1.1. table p 2. p(X,Y) p(X,Z) p(Z,Y) p(X,Y) a(X,Y) a(1,2) a(1,3) a(2,3) p(1,Y) The forest of ....

.... a(3,Y) Figure 7: SLG evaluation under Batched Scheduling In Single Stack Scheduling, since answers are returned eagerly, whenever the engine backtracks over the generator choice point for a subgoal, that subgoal is guaranteed to be completely evaluated (Swift discusses this in detail in [Swi94] Since the return of answers is delayed in Batched Scheduling, this fact no longer holds, and extra checks are required in Batched Scheduling to ensure all answers are returned to consuming nodes. CHAPTER 4. BATCHED SCHEDULING 24 Generator 1. p(1,Y) Generator 1. p(1,Y) a) Generator 1. ....

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T. Swift. Efficient Evaluation of Normal Logic Programs. PhD thesis, Department of Computer Science, State University of New York at Stony Brook, 1994.

....then used for scheduling. The choice point stack thus serves as a scheduling stack for both returning answers and resolving program clauses. Accordingly, we may call this scheduling strategy single stack scheduling. The operational semantics of this scheduling strategy was described in detail in [6], and forms the basis of the XSB SLG WAM as described in [7] The following example demonstrates how this strategy works. 5. tc(1,4) 4. tc(1,2) a(2,Y) 0. tc(1,Y) 6. tc(1,4) a(4,Y) 8. tc(1,5) a(5,Y) 11. tc(1,3) a(3,Y) 7. tc(1,5) 12. tc(1,6) 14. tc(1,7) 13. tc(1,6) a(6,Y) 1. tc(1,Z) a(Z,Y) 10. ....

....created, the failure continuation will cause backtracking over two environments and choice points to return the derived answer to the active node. Furthermore, provision must be made so that the choice points for r(n,Z) a(Z,Y) and r(n,Z) b(Z,Y) can be reactivated at a later time. As described in [6], the SLG WAM freezes the stacks beneath the choice point for r(n,Z) a(Z,Y) along with the corresponding environment stack, heap, and trail. DRAFT c(n,Y) r(n,Z) b(Z,Y) b(n,Y) r(n,Z) a(Z,Y) a(n,Y) r(n,n) r(n,n) tc(1,Y) tc(1,Z) c(Z,Y) tc(1,n) c(X,Y) r(X,X) b(X,Y) b(X,Y) ....

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T. Swift. Efficient Evaluation of Normal Logic Programs. PhD thesis, SUNY at Stony Brook, 1994.

....sections provide a brief introduction to SLG resolution as it is implemented in XSB. For interested users, the ftp directory and web site contain papers covering in detail various aspects of tabling. An overview of SLG resolution, and a practical evaluation strategy for it are provided in [7, 28] [30, 29, 24, 15, 34, 26] describe fully the SLG WAM as it is implemented in Version 1.7.1, and [35, 6] analyze its performance. 5.1 SLG Evaluation 5.1.1 Tabling Consider the Prolog program ancestor(X,Y) parent(X,Y) ancestor(X,Y) ancestor(X,Z) parent(Z,Y) together with the query ancestor(1,Y) This ....

T. Swift. Efficient Evaluation of Normal Logic Programs. PhD thesis, SUNY at Stony Brook, 1994.

....is then used for scheduling. The choice point stack thus serves as a scheduling stack for both returning answers and resolving program clauses. Accordingly, we call this scheduling strategy Single Stack Scheduling. The operational semantics of this scheduling strategy was described in detail in [14] and forms the basis of XSB s SLG WAM as described in [15] The following example demonstrates how this strategy works. Example 1. Consider the following double recursive transitive closure : table p 2. a(1,2) a(1,3) a(2,3) p(X,Y) p(X,Z) p(Z,Y) p(X,Y) a(X,Y) and the query ....

T. Swift. Efficient Evaluation of Normal Logic Programs. PhD thesis, Department of Computer Science, State University of New York at Stony Brook, 1994. 17 DRAFT

....explore Knowledge Representation. Tabling as defined below for WFS has polynomial data completity. 5 Motivation ffl There has been a lot of research into it. Tabling and Related Research Formulation [41] 17] 108] 38] 60] 98] 115] 120] 15] 14] 20] 22] 33] 19] [105], 34] 94] 54] 110] 23] 27] Implementation and Systems [6] 116] 64] 42] 2] 55] 82] 84] 106] 107] 93] 7] 21] 43] 44] 96] 121] 45] 83] 95] 92] Optimizations [30] 6 Motivation Magic Sets and Related Research (e.g. Alexander Method) ....

T. Swift. Efficient Evaluation of Normal Logic Programs. PhD thesis, SUNY at Stony Brook, 1994.

....is then used for scheduling. The choice point stack thus serves as a scheduling stack for both returning answers and resolving program clauses. Accordingly, we call this scheduling strategy Single Stack Scheduling. The operational semantics of this scheduling strategy was described in detail in [18], and forms the basis of the SLG WAM as described in [19] The following example demonstrates how this strategy works. Generator 1. p(1,Y) Generator 1. p(1,Y) a) Generator 1. p(1,Y) freeze 2. p(1,Z) Answer Return 4. a(1,Y) p(1,2) Consuming Interior (b) Generator 1. p(1,Y) freeze freeze freeze ....

....Local Scheduling. Figure 6 illustrates the actions of a local evaluation of the program and query of Example 2.1. Note that the answer generated for subgoal p(2,Y) in node 10 is only returned to its calling environment (in node 5) after the tree for p(2,Y) is completely evaluated. It was shown in [18] that the SLG WAM s completion stack maintains exact dependencies for local evaluations. Maintaining exact dependencies allows the engine to verify whether loops through negation exist, and to delay literals (to break these loops [5] only when it is necessary. Even though negation handling and ....

T. Swift. Efficient Evaluation of Normal Logic Programs. PhD thesis, Department of Computer Science, State University of New York at Stony Brook, 1994.

....is then used for scheduling. The choice point stack thus serves as a scheduling stack for both returning answers and resolving program clauses. Accordingly, we call this scheduling strategy Single Stack Scheduling. The operational semantics of this scheduling strategy was described in detail in [17], and forms the basis of the SLG WAM as described in [18] The following example demonstrates how this strategy works. Example 3.1 The node numbers in Figure 1 represent the actions of Single Stack Scheduling on the program of Example 2.1, while Figure 3 represents the choice point stack at ....

....Local Scheduling. Figure 6 illustrates the actions of a local evaluation of the program and query of Example 2.1. Note that the answer generated for subgoal p(2,Y) in node 10 is only returned to its calling environment (in node 5) after the tree for p(2,Y) is completely evaluated. It was shown in [17] that the SLG WAM s completion stack maintains exact dependencies for local evaluations. Maintaining exact dependencies allows to engine to verify whether loops through negation exist, and to delay literals (to break these loops [4] only when it is necessary. Even though negation handling and ....

T. Swift. Efficient Evaluation of Normal Logic Programs. PhD thesis, Department of Computer Science, State University of New York at Stony Brook, 1994.

....is then used for scheduling. The choice point stack thus serves as a scheduling stack for both returning answers and resolving program clauses. Accordingly, we call this scheduling strategy Single Stack Scheduling. The operational semantics of this scheduling strategy was described in detail in [14] and forms the basis of XSB s SLG WAM as described in [15] The following example demonstrates how this strategy works. Example 1. Consider the following double recursive transitive closure : table p 2. a(1,2) a(1,3) a(2,3) p(X,Y) p(X,Z) p(Z,Y) p(X,Y) a(X,Y) and the query ....

T. Swift. Efficient Evaluation of Normal Logic Programs. PhD thesis, Department of Computer Science, State University of New York at Stony Brook, 1994.

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