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    prolog assignment help

     Prolog Arithmetic and Operators

    a) Write a predicate to determine if a given integer is prime or not.
    You do not need to worry about efficiency for this question. There are many sophisticated ways to find prime numbers but a simple brute force check will suffice.
    ?- prime(2). true. ?- prime(4). false. ?- prime(7). true. ?- prime(987). false. ?- prime(997). true. b) Write a predicate that finds the greatest common divisor of two positive integers.
    Hint: Use Euclid’s algorithm. ?- gcd(6, 12, D). D = 6. ?- gcd(14, 21, D). D = 7. ?- gcd(1071, 462, D). D = 21. c) Write an infix operator =>> that returns true if one of its operands is double the other operand.
    ?- 40 =>> 20. true. ?- (-4) =>> (-8). true. ?- 1 =>> 0. false. ?- 3 =>> 7. false. d) Write a unary prefix operator isSingleton that determines if a list has exactly one element in it.
    ?- isSingleton []. false. ?- isSingleton [8]. true. ?- isSingleton [a,b]. false.   e) Write two predicates isort and msort that sort a list of integers. The predicate isort should use the insertion sort method; this method starts with an empty list and inserts items one at a time into the correct position. The predicate msort should use the merge sort method. Merge sort splits a list into two halves, recursively sorts each half and then merges them back together. You should expect to write a number of support predicates for this question. ?- isort([7,3,5,4,1,2,6],[1,2,3,4,5,6,7]). true. ?- isort([7,3,5,4,1,2,6],I). I = [1, 2, 3, 4, 5, 6, 7]. ?- msort([4,5,3,2,2], M). M = [2, 2, 3, 4, 5].

    2)You must put the following comments at the top of your program code and provide the appropriate information.
    % Assignment number, 159.202, 2016 S2 % Family Name, Given Name, Student ID, % Explain what the program is doing . . . Hand-in: Submit your script electronically through stream

    % Assignment number, 159.202, 2016 S2
    % Family Name, Given Name, Student ID,

    % Check if the number is prime
    prime(X) :-
    X \= 1, X \= 0,
    X1 is X – 1,
    prime(X, X1).

    prime(_X, 1).
    prime(_X, 0).

    prime(X, N) :-
    Mod is X mod N,
    Mod \= 0,
    N1 is N – 1,
    prime(X, N1).

    % test
    :- include(prime, [1,2,3,4,5,6,7,8,9, 10,11,12,13,14,15,16,17,18,19,20], Xs)
    , Xs = [2, 3, 5, 7, 11, 13, 17, 19].

    % find greatest common divisor
    gcd(A, A, A).
    gcd(A, B, D) :-
    A > B,
    A1 is A – B,
    gcd(A1, B, D).

    gcd(A, B, D) :-
    A < B,
    B1 is B – A,
    gcd(A, B1, D).

    :- gcd(6, 12, 6).
    :- gcd(14, 21, 7).
    :- gcd(1071, 462, 21).

    :- op(500, xfx, =>>).

    % Check if one arg is twice as big as another
    X =>> Y :-
    X is Y * 2.

    X =>> Y :-
    Y is X * 2.

    :- 40 =>> 20.
    :- (-4) =>> (-8).

    :- \+ (1 =>> 0).
    :- \+ (3 =>> 7).

    :- op(500, fx, isSingleton).

    % check if list is a singleton
    isSingleton [_].

    :- \+ isSingleton [].
    :- isSingleton [8].
    :- \+ isSingleton [a,b].

    % insertion sort
    isort(Src, Dst) :-
    % we insert each elem of Src into resulting list (which is initially [])
    foldl(insert_ord, Src, [], Dst).

    % trivial case
    insert_ord(X, [], [X]).

    % if current inserted X <= top Y, just prepend X to the list
    insert_ord(X, [Y | Rest], [X, Y | Rest]) :-
    X =< Y.

    % otherwise insert X into the Rest producing Rest1 and prepend Y back
    insert_ord(X, [Y | Rest], [Y | Rest1]) :-
    X > Y,
    insert_ord(X, Rest, Rest1).

    :- isort([7,3,5,4,1,2,6],[1,2,3,4,5,6,7]).

    % merge sort
    %
    % idea is: split list on two, recursively merge-sort both and merge the results
    %
    msort([], []).
    msort([X], [X]).
    msort(List, Sorted) :-
    split(List, A, B), % split
    maplist(msort, [A, B], [A1, B1]), % recure
    merge(A1, B1, Sorted), % merge
    !.

    % split: [a,b,c,d,e,f,…] -> ([a,c,e,…], [b,d,f,…])
    split(List, A, B) :- split(List, [], [], A, B).
    split([], A, B, A, B).
    split([X], A, B, [X | A], B).
    split([X, Y | Rest], A, B, [X | AN], [Y | BN]) :-
    split(Rest, A, B, AN, BN).

    % merge two sorted lists into one sorted
    merge(L, R, X) :- merge(L, R, [], X).

    % if one or another is empty, the result is nonempty one
    merge([], R, X, XN) :-
    append(X, R, XN).
    merge(L, [], X, XN) :-
    append(X, L, XN).

    % if one top is less than other, it goes first
    merge([A | L], [B | R], X, XN) :-
    A < B,
    append(X, [A], X1),
    merge(L, [B | R], X1, XN).

    merge([A | L], [B | R], X, XN) :-
    B =< A,
    append(X, [B], X1),
    merge([A | L], R, X1, XN).

    :- msort([7,3,5,4,1,2,6],[1,2,3,4,5,6,7]).

    Project Details

    • Date November 3, 2016
    • Tags Programming, Prolog and Clisp

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