Catch the fire starter¶

Learn about QL predicates and classes to solve your second mystery as a QL detective.

Just as you’ve successfully found the thief and returned the golden crown to the castle, another terrible crime is committed. Early in the morning, a few people start a fire in a field in the north of the village and destroy all the crops!

You now have the reputation of being an expert QL detective, so you are once again asked to find the culprits.

This time, you have some additional information. There is a strong rivalry between the north and south of the village and you know that the criminals live in the south.

Read the examples below to learn how to define predicates and classes in QL. These make the logic of your queries easier to understand and will help simplify your detective work.

Select the southerners¶

This time you only need to consider a specific group of villagers, namely those living in the south of the village. Instead of writing getLocation() = "south" in all your queries, you could define a new predicate isSouthern:

predicate isSouthern(Person p) {
  p.getLocation() = "south"
}

The predicate isSouthern(p) takes a single parameter p and checks if p satisfies the property p.getLocation() = "south".

Note

The name of a predicate always starts with a lowercase letter.

You can also define predicates with a result. In that case, the keyword predicate is replaced with the type of the result. This is like introducing a new argument, the special variable result. For example, int getAge() { result = ... } returns an int.

You can now list all southerners using:

/* define predicate `isSouthern` as above */

from Person p
where isSouthern(p)
select p

This is already a nice way to simplify the logic, but we could be more efficient. Currently, the query looks at every Person p, and then restricts to those who satisfy isSouthern(p). Instead, we could define a new class Southerner containing precisely the people we want to consider.

class Southerner extends Person {
  Southerner() { isSouthern(this) }
}

A class in QL represents a logical property: when a value satisfies that property, it is a member of the class. This means that a value can be in many classes—being in a particular class doesn’t stop it from being in other classes too.

The expression isSouthern(this) defines the logical property represented by the class, called its characteristic predicate. It uses a special variable this and indicates that a Person “this” is a Southerner if the property isSouthern(this) holds.

Note

If you are familiar with object-oriented programming languages, you might be tempted to think of the characteristic predicate as a constructor. However, this is not the case—it is a logical property which does not create any objects.

You always need to define a class in QL in terms of an existing (larger) class. In our example, a Southerner is a special kind of Person, so we say that Southerner extends (“is a subset of”) Person.

Using this class you can now list all people living in the south simply as:

from Southerner s
select s

You may have noticed that some predicates are appended, for example p.getAge(), while others are not, for example isSouthern(p). This is because getAge() is a member predicate, that is, a predicate that only applies to members of a class. You define such a member predicate inside a class. In this case, getAge() is defined inside the class Person. In contrast, isSouthern is defined separately and is not inside any classes. Member predicates are especially useful because you can chain them together easily. For example, p.getAge().sqrt() first gets the age of p and then calculates the square root of that number.

Travel restrictions¶

Another factor you want to consider is the travel restrictions imposed following the theft of the crown. Originally there were no restrictions on where villagers could travel within the village. Consequently the predicate isAllowedIn(string region) held for any person and any region. The following query lists all villagers, since they could all travel to the north:

from Person p
where p.isAllowedIn("north")
select p

However, after the recent theft, the villagers have become more anxious of criminals lurking around the village and they no longer allow children under the age of 10 to travel out of their home region.

This means that isAllowedIn(string region) no longer holds for all people and all regions, so you should temporarily override the original predicate if p is a child.

Start by defining a class Child containing all villagers under 10 years old. Then you can redefine isAllowedIn(string region) as a member predicate of Child to allow children only to move within their own region. This is expressed by region = this.getLocation().

class Child extends Person {
  /* the characteristic predicate */
  Child() { this.getAge() < 10 }

  /* a member predicate */
  override predicate isAllowedIn(string region) {
    region = this.getLocation()
  }
}

Now try applying isAllowedIn(string region) to a person p. If p is not a child, the original definition is used, but if p is a child, the new predicate definition overrides the original.

You know that the fire starters live in the south and that they must have been able to travel to the north. Write a query to find the possible suspects. You could also extend the select clause to list the age of the suspects. That way you can clearly see that all the children have been excluded from the list.

➤ Check your answer

You can now continue to gather more clues and find out which of your suspects started the fire…

Identify the bald bandits¶

You ask the northerners if they have any more information about the fire starters. Luckily, you have a witness! The farmer living next to the field saw two people run away just after the fire started. He only saw the tops of their heads, and noticed that they were both bald.

This is a very helpful clue. Remember that you wrote a QL query to select all bald people:

from Person p
where not exists (string c | p.getHairColor() = c)
select p

To avoid having to type not exists (string c | p.getHairColor() = c) every time you want to select a bald person, you can instead define another new predicate isBald.

predicate isBald(Person p) {
  not exists (string c | p.getHairColor() = c)
}

The property isBald(p) holds whenever p is bald, so you can replace the previous query with:

from Person p
where isBald(p)
select p

The predicate isBald is defined to take a Person, so it can also take a Southerner, as Southerner is a subtype of Person. It can’t take an int for example—that would cause an error.

You can now write a query to select the bald southerners who are allowed into the north.

➤ Check your answer

You have found the two fire starters! They are arrested and the villagers are once again impressed with your work.

Answers¶

In these answers, we use /* and */ to label the different parts of the query. Any text surrounded by /* and */ is not evaluated as part of the QL code, but is treated as a comment.

Exercise 1¶

import tutorial

predicate isSouthern(Person p) { p.getLocation() = "south" }

class Southerner extends Person {
  /* the characteristic predicate */
  Southerner() { isSouthern(this) }
}

class Child extends Person {
  /* the characteristic predicate */
  Child() { this.getAge() < 10 }

  /* a member predicate */
  override predicate isAllowedIn(string region) { region = this.getLocation() }
}

from Southerner s
where s.isAllowedIn("north")
select s, s.getAge()

Exercise 2¶

import tutorial

predicate isSouthern(Person p) { p.getLocation() = "south" }

class Southerner extends Person {
  /* the characteristic predicate */
  Southerner() { isSouthern(this) }
}

class Child extends Person {
  /* the characteristic predicate */
  Child() { this.getAge() < 10 }

  /* a member predicate */
  override predicate isAllowedIn(string region) { region = this.getLocation() }
}

predicate isBald(Person p) { not exists(string c | p.getHairColor() = c) }

from Southerner s
where s.isAllowedIn("north") and isBald(s)
select s