# Homework 5 Solution

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Create a file named “hw6.pl” and include definitions for the six predicates
described below. Your definitions should be as general as you can make them
without being incorrect.

In the definitions, parameters are marked with + or ?. If the parameter is +,
your definition must always terminate if the argument contains no variables.
If the parameter is ?, you must produce results if the argument is a term
or a variable.

By “terminate”, we mean produce an answer or false within a finite amount of
time.

If you are using SWI-Prolog (recommended), you have to include the CLP(FD)
library in order to use the convenient numeric predicates. To do this, include
this line near the top of your file:

:- use_module(library(clpfd)).

(Note that this line begins with “:-“.)

Problems
——–

tree(?Tree)

Tree is a binary tree, which may be nil or b(Left,Here,Right), where
Left and Right are binary trees and Here is an arbitrary term.

?- tree(nil).
true.
?- tree(b(nil,_,nil)).
true.
?- tree(b(b(nil,1,nil),x,nil)).
true.

mirror(+Tree1, ?Tree2)

Tree1 and Tree2 are mirror images; that is, swapped left for right

?- mirror(b(nil,1,b(nil,2,nil)), R).
R = b(b(nil,2,nil),1,nil).

echo(+L1, ?L2)
True if L1 and L2 are lists, and L2 contains each element in L1
twice in a row.

?- echo([],[]).
true.
?- echo([1],[1,1]).
true.
?- echo([1,2], L).
L = [1,1,2,2].

unecho(+L1, ?L2)
True if L1 and L2 are lists, and any consecutive repetitions in L1 are
single elements in L2.

?- unecho([1,2,2,3], [1,2,3]).
true.
?- unecho([1,2,2,3], X).
X = [1,2,3].

slist(?List)

List is a non-decreasing list of integers

?- slist([1,2,2]).
true.
?- slist([0,4,4,8).
true.
?- slist([1,0]).
false.

slist(List) should produce arbitrarily many lists

sselect(?Item, ?List0, ?List1)

List1 is the result of inserting Item into List0

?- sselect(2, [1,3], [1,2,3]).
true.
?- sselect(2, [1,2,3], [1,2,2,3]).
true.
?- sselect(2, [1,3], L).
L = [1,2,3].
?- sselect(2, L, [1,2,3]).
L = [1,3].
?- sselect(X, [1,3], [1,2,3]).
X = 2.
?- sselect(X, L, [1,2,3]).
X = 1, L = [2,3] ;
X = 2, L = [1,3] ;
X = 3, L = [1,2] .

sselect(X, Y, Z) should produce arbitrarily many answers

sselect/3 should only examine enough of List0 and List1 to determine
the placement of Item. In particular, sselect(2, [1,3|X], [1,2,3|X])
should not bind X.

?- sselect(2, [1,3|X], [1,2,3|X]).
true.
?- sselect(2, [1,3|X], L).
L = [1,2,3|X].

The prefix of List0 up to Item and the element following item must be
non-decreasing.

?- sselect(2, L, [1,0,2,3]).
false.

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