By following these steps, you can define the sorted/1 relation in Prolog to determine if a list of integers is in non-decreasing order.
In Prolog, we can define the relation sorted/1 to determine whether a list of integers is in non-decreasing order. Here's how you can define this relation:
1. The base case: An empty list is considered sorted.
sorted([]).
2. Recursive case: For a list with at least one element, we need to check if the first element is less than or equal to the second element, and then recursively check the rest of the list.
```
sorted([X]) :- !.
sorted([X,Y|Rest]) :- X =< Y, sorted([Y|Rest]).
```
Let's break down the steps:
1. The base case states that an empty list is considered sorted. This is because there are no elements to compare.
2. The recursive case checks if the first element (`X`) of the list is less than or equal to the second element (`Y`). If this condition holds, the predicate `sorted([X,Y|Rest])` is true. Then, we recursively call `sorted([Y|Rest])` to check the rest of the list.