2018-01-19 00:30:58 +00:00
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%% Chapter 5 practical session
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%%
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%% The purpose of Practical Session 5 is to help you get familiar with Prolog’s
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%% arithmetic capabilities, and to give you some further practice in list
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%% manipulation. To this end, we suggest the following programming exercises:
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%%
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%% 1. In the text we discussed the 3-place predicate accMax which returned the
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%% maximum of a list of integers. By changing the code slightly, turn this into
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%% a 3-place predicate accMin which returns the minimum of a list of integers.
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min([], N, N).
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min([H|T], N, M) :-
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H < N,
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min(T, H, M).
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min([H|T], N, M) :-
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H >= N,
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min(T, N, M).
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min([H|T], N) :-
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min(T, H, N).
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%% 2. In mathematics, an n-dimensional vector is a list of numbers of length n.
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%% For example, [2,5,12] is a 3-dimensional vector, and [45,27,3,-4,6] is a
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%% 5-dimensional vector. One of the basic operations on vectors is scalar
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%% multiplication . In this operation, every element of a vector is multiplied
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%% by some number. For example, if we scalar multiply the 3-dimensional vector
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%% [2,7,4] by 3 the result is the 3-dimensional vector [6,21,12] .
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%%
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%% Write a 3-place predicate scalarMult whose first argument is an integer,
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%% whose second argument is a list of integers, and whose third argument is the
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%% result of scalar multiplying the second argument by the first. For example,
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%% the query
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%% ?- scalarMult(3,[2,7,4],Result).
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%% should yield
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%% Result = [6,21,12]
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scalarMult(_, [], []).
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2018-01-19 02:01:08 +00:00
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scalarMult(K, [H|T], [V|R]) :-
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V is K * H,
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scalarMult(K, T, R).
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2018-01-19 00:30:58 +00:00
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%% 3. Another fundamental operation on vectors is the dot product. This
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%% operation combines two vectors of the same dimension and yields a
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%% number as a result. The operation is carried out as follows: the
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%% corresponding elements of the two vectors are multiplied, and the
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%% results added. For example, the dot product of [2,5,6] and [3,4,1] is
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%% 6+20+6 , that is, 32 . Write a 3-place predicate dot whose first
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%% argument is a list of integers, whose second argument is a list of
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%% integers of the same length as the first, and whose third argument is
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%% the dot product of the first argument with the second. For example,
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%% the query
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%% ?- dot([2,5,6],[3,4,1],Result).
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%% should yield
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2018-01-19 02:01:08 +00:00
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%% Result = 32
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dot([], [], 0).
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dot([X|TX], [Y|TY], R) :-
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dot(TX, TY, R2),
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V is X * Y,
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R is R2 + V.
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