Programming Techniques

1. Programming Techniques t.k.prasad@wright.edu http://www.knoesis.org/tkprasad/ L17ProgTech

2. Generalization/Abstraction Analogy: [a,b,c]  [f(a),f(b),f(c)] maplist(_,[],[]). maplist(P,[X|T],[NX|NT]) :- G =.. [P,X,NX], call(G), maplist(P,T,NT). (G  p(N,NX)) L17ProgTech

3. Application transpose([],[]). transpose([[]|_],[]) :- !. transpose([R|Rs],[C|Cs]) :- maplist(first,[R|Rs],C), maplist(rest,[R|Rs],RC), transpose(RC,Cs). first([H|T],H). rest([H|T],T). /* Built-in maplist exists*/ L17ProgTech

4. Enhancing Efficiency • Interpreted vs Compiled code (order of magnitude improvement observed) • Improving data structures and algorithm • 8-Queens problem, Heuristic Search, Quicksort, etc • Tail-recursive optimization • Memoization • storing partial results / caching intermediate results • Difference lists • DCGs L17ProgTech

5. (cont’d) • Prolog implementations that index on the first argument of a predicate improve determinism. • Cuts and other meta-programming primitives can be used to program in new search strategies for controlled backtracking. L17ProgTech

6. Optimizing Fibonacci Number Computation fib(0,0) :- !. fib(1,1) :- !. fib(N,F) :- N1 is N - 1, N2 is N1 -1, fib(N1,F1), fib(N2,F2), F is F1 + F2. ?-fib(5,F). Complexity: Exponential time algorithm L17ProgTech

7. Fibonacci Call Tree with Parameter Value L17ProgTech

8. (cont’d) f(0,F,_,F). f(1,_,F,F). f(N,Fpp,Fp,F) :- N >= 2, N1 is N – 1, F0 is Fp + Fpp, f(N1,Fp,F0,F). fib(N,F) :- f(N,0,1,F). ?-fib(5,F). Complexity: Linear time algorithm (tail-recursive version) L17ProgTech

9. Last call optimization • Activation record normally stores a continuation and a backtrack point, to be used when the goal succeeds or fails respectively. p :- q, r. p :- s. • LCO avoids allocating a new activation record for s, but rather reuses one for p. L17ProgTech

10. Caching intermediate results • Instead of explicitly modifying the code to improve performance, XSB uses tabling to store intermediate results and avoids recomputing earlier goals. • Ironically, double-recursive (exponential-time) Fibonacci Number definition serves as a benchmark for testing efficiency of implementation of recursion! L17ProgTech

11. Different Lists : Motivation L17ProgTech

12. (cont’d) • In Prolog, pointers implementing list structures are not available for inspection/manipulation. Hence, complexity of enqueue (resp. dequeue) is O(1) and that of dequeue (resp. enqueue) is O(n). enqueue(Q,E,[E|Q]). dequeue([E],E). dequeue([_|F|T],E) :- dequeue([F|T],E). • Difference list is a techqniue to get O(1) complexity for both the operations. L17ProgTech

13. Difference Lists : Details • Represent list L as a difference of two lists L1 and L2 • E.g., consider L = [a,b,c] and various L1-L2 combinations given below. L17ProgTech

14. Benefit L = L1 – L2 • Both enqueue and dequeue are O(1) operations obtained by cons-ing an element to L1 and L2 respectively. enqueue(L1-L2, E, [E|L1] – L2). dequeue(L1-L2, E, L1 – [E|L2]). E.g., enqueue([a]-[], b, [b,a] – []). dequeue([a]-[], a, [a]–[a]). L17ProgTech

15. Append using Difference Lists append(X-Y, Y-Z, X-Z). • Ordinary append complexity = O(length of first list) • Difference list append complexity = O(1) X-Z X X-Y Y Y Y-Z Z Z Z L17ProgTech

16. (cont’d) append(X-Y, Y-Z, X-Z). ?-append([a,b,c|L]-L, [1,2|M]-M, N). X=[a,b,c|L] Y = L Y = [1,2|M] Z = M X – Z = N N= [a,b,c|[1,2|Z]]-Z N= [a,b,c,1,2|Z]]-Z L17ProgTech

17. Restriction append(X-Y, Y-Z, X-Z). ?-append([a,b,c|[d]]-[d], [1,2]-[], N). • Fails because the second lists must be a variable. Incomplete data structure is a necessity. L17ProgTech

18. Interpreter-based Semantics vs Declarative Semantics • IS is an over-specification but may provide an efficient implementation. • DS specifies correctness criteria and may permit further optimization. • Overall research goal: Characterize classes of programs for which the declarative and the procedural semantics coincide. L17ProgTech

19. Relational Algebra (Operations on Relations) • Select, Project, Join, Union, Intersection, difference • Transitive closure cannot be expressed in terms of these operations. • A query language is relationally complete if it can perform the above operations. L17ProgTech

20. Deductive Databases : Datalog (Function-free/Finite Domain Prolog) • Datalog + Negation is relationally complete. • What effects query evaluation efficiency? • Characteristics of data (cyclic vs acyclic) • Ordering of rules and body literals • Search strategy (top-down vs bottom-up) • Tuple-at-a-time vs Set-at-a-time L17ProgTech

21. Middle Ground:Top-down vs Bottom-up • Improve efficiency by caching. (cf. tabling) • Remove Incompleteness by loop detection. • Focused search. • Propagate bindings in the query. (cf. Magic sets) In general, the efficiency of query evaluation can be improved by sequencing goals on the basis of their bindings and dependencies among rule literals. L17ProgTech

22. Heuristics for rearranging rules and body literals for efficiency • Order body literals by decreasing values of failure probability • Order rules by decreasing values of success probability • Order body literals to maximize dependencies among adjacent literals. • Metric for comparison – e.g., extent of base relation graphs inspected L17ProgTech

23. Backtracking • Chronological • Dependency directed • focus on the reason for backtracking ans(X,Y) :- p(X), q(Y), r(X). p(1). p(2). p(3). q(1). q(2). q(3). r(3). L17ProgTech

24. Data Dependency Graph p(X), r(X), ans(X,Y) :- q(Y), If r(X) fails, then backtrack to p(X) rather than q(Y). L17ProgTech

25. Indexing • Prolog indexes on • predicate symbol and arity • principal functor of first argument (cf. constant -> hash) • Randomly accessed rule groups p(a) :- … p(22) :- … p(f(X)) :- … p([]) :- …, p([a]) :- …, … L17ProgTech

26. Robert Kowalski • Algorithm = Logic + Control Niklaus Wirth • Programs = Data Structures + Algorithms L17ProgTech