Define and test the Prolog predicates described below. Each of your predicates must have the same name and signature as the examples below. Your predicates must behave properly on all instances of valid input types.

Your submission should consist of a single source code text file that includes all facts, predicate definitions, and propositions. Your file should be named <your_net_id>.pro, then subsequently archived using zip, gzip, or tar and named <your_net_id>.<archive_extension>.

You may find additional Prolog language help at the following links:

- SWI-Prolog manual
- SWI-Prolog documentation
- Learn Prolog Now!

1) Odd Multiple of 3 [10 points]

Define a predicate oddMultOf3/1 that determines whether an integer is an odd multiple of 3. A user should be able to enter the predicate with an integer, e.g. oddMultOf3(42) and evaluate to either true or false. If the given parameter is not an integer, your predicate should display the message “ERROR: The given parameter is not an integer”.

Examples:

?- oddMultOf3(171). true.

?- oddMultOf3(100). false.

?- oddMultOf3(12). false.

?- oddMultOf3(4.2). ERROR: The given parameter is not an integer

?- oddMultOf3(-9). true.

2) Product List

Define a predicate prod_list/2 that takes a list of numbers as a first parameter and determines the product of all of the list elements in the second parameter. Your predicate should have the signature prod_list(List, Product).

Examples:

?- prod_list([4,3], Product). Product = 12.

?- prod_list([7,8,0,13], Product). Product = 0.

?- prod_list([6,2,5,10], Product). Product = 600.

?- prod_list([], Product). Product = 0.

3) Palindrome

Define a predicate palindrome/1 that takes a list of numbers as a single parameter and evaluates whether the list is the same both backward and forward, i.e. a “palindrome” list. Your predicate should have the signature palindrome(List). Note that the list to be tested may be heterogenous data types.

Examples:

?- palindrome([4,3,4]). true.

?- palindrome([7,2,5,7]). false.

?- palindrome([d,4,4,d]). true.

?- palindrome([]). true.

?- palindrome([a]). true.

4) Second Minimum [10 points]

Define a predicate secondMin/2 with the signature secondMin(List, Min2) where Min2 is the second lowest unique valued element in some list of numbers, List. If the list has fewer than two unique elements, then your predicate should display the following, “ERROR: List has fewer than two unique elements.” If one more elements of List is not a number, then your predicate should display the following for the first encounter of a non-number element, “ERROR: "element" is not a number.”, where element is the value of the non-number element.

Examples:

?- secondMin([17,29,11,62,37,53], M2). M2 = 17

?- secondMin([512], M2). ERROR: List has fewer than two unique elements.

?- secondMin([7,5.2,3,6,-3.6,9,-2], M2). M2 = -2

?- secondMin([12,2,b,7], M2). ERROR: "b" is not a number.

?- secondMin([3,3,3], M2). ERROR: List has fewer than two unique elements.

5) Segregate

Define a predicate segregate/3 that takes a list of integers as an argument and generates two lists, the first containing containing the even numbers from the original list and the second sublist containing the odd numbers from the original list. Your predicate should have the signature segregate(List, Even, Odd).

Examples:

?- segregate([8,7,6,5,4,3], Even, Odd). Even = [8,6,4] Odd = [7,5,3]

?- segregate([7,2,3,5,8], Even, Odd). Even = [2,8] Odd = [7,3,5]

?- segregate([-4,11,-7,9,0], Even, Odd). Even = [-4,0] Odd = [11,-7,9]

?- segregate([5,13,29], Even, Odd). Even = [] Odd = [5,13,29]

?- segregate([], Even, Odd). Even = [] Odd = []

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6) Bookends

Design a predicate bookends/3 whose parameters are all lists. It tests if the first list parameter is a prefix of the third and if the second list parameter is a suffix of the third. Note that the lists in the first and second arguments may overlap.

Examples:

?- bookends([1],[3,4,5],[1,2,3,4,5]). true.

?- bookends([],[4],[1,2,3,4]). true.

?- bookends([8,7,3],[3,4],[8,7,3,4]). true.

?- bookends([6],[9,3],[6,9,3,7]). false.

?- bookends([],[],[2,4,6]). true.

?- bookends([23],[23],[23]). true.

7) Subslice

Design a predicate subslice/2 that tests if the first list argument is a contiguous series of elements anywhere within in the second list argument.

Examples:

?- subslice([2,3,4],[1,2,3,4]). true.

?- subslice([8,13],[3,4,8,13,7]). true.

?- subslice([3],[1,2,4]). false.

?- subslice([],[1,2,4]). true.

?- subslice([1,2,4],[]). false.

8) Shift

Design a predicate shift/3 that “shifts” or “rotates” a list N places to the left. N may be a negative number, i.e. rotate to the right. Your predicate should have the signature shift(List, N, Shifted).

Examples:

?- shift([a,b,c,d,e,f,g,h],3,Shifted). Shifted = [d,e,f,g,h,a,b,c]

?- shift([1,2,3,4,5],1,Shifted). Shifted = [2,3,4,5,1]

?- shift([a,b,c,d,e,f,g,h],-2,Shifted). Shifted = [g,h,a,b,c,d,e,f]

8) Luhn Algorithm

Design a predicate luhn/3 that is an implementation of the Luhn Algorithm and returns true if the parameter is an integer that passes the Luhn test and false otherwise.

Examples:

?- luhn(799273987104). true.

?- luhn(49927398717). false.

?- luhn(49927398716). true.

10) Graph

Design two predicates path/2 and cycle/1 that determine structures within a graph whose directed edges are encoded with given instances of edge/2. For example, path(x,y) should evaluate to true if a path exists from vertex x to vertex y, and false otherwise. And cycle(x) should evaluate to true if a cycle exists which includes vertex x.

Note: All edges are directional.

Note: Your solution should avoid infinite recursion.

Note: The Knowledge Base of edges below is for example only. You are just responsible for the definitions of path/2 and cycle/1. The Knowledge Base used for grading will be different.

Examples:

% Knowledge Base edge(a,b). edge(b,c). edge(c,d). edge(d,a). edge(d,e). edge(b,a).

?- path(b,d) true.

?- path(e,b). false.

?- path(c,a).CS-4337.0u1 Project #2 (Logic Progrmming) 16Su

?- cycle(b). true.

?- cycle(e). false.

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