Programming techniques
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Programming Techniques. [email protected] http://www.knoesis.org/tkprasad/. 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)). Application.

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Programming Techniques

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Programming techniques

Programming Techniques

[email protected]

http://www.knoesis.org/tkprasad/

L17ProgTech


Generalization abstraction

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))

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Application

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*/

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Enhancing efficiency

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

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    Cont d

    (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.

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    Optimizing fibonacci number computation

    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

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    Fibonacci call tree with parameter value

    Fibonacci Call Tree with Parameter Value

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    Cont d1

    (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)

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    Last call optimization

    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.

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    Caching intermediate results

    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!

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    Different lists motivation

    Different Lists : Motivation

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    Cont d2

    (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.

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    Difference lists details

    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.

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    Benefit

    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]).

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    Append using difference lists

    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

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    Cont d3

    (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

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    Restriction

    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.

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    Interpreter based semantics vs declarative semantics

    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.

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    Relational algebra operations on relations

    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.

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    Deductive databases datalog function free finite domain prolog

    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

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    Middle ground top down vs bottom up

    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.

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    Heuristics for rearranging rules and body literals for efficiency

    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

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    Backtracking

    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).

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    Data dependency graph

    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).

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    Indexing

    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]) :- …, …

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    Programming techniques

    Robert Kowalski

    • Algorithm = Logic + Control

      Niklaus Wirth

    • Programs = Data Structures + Algorithms

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