Scientific computing

(for the rest of us)

Multiple dispatch in practice

In this module, we will expand on the previous content (understanding dispatch) to get familiar with a central design paradigm of Julia: multiple dispatch. We will do so by writing code to simulate the growth of a population in space.

The difference between dispatch and multiple dispatch is, essentially, that under multiple dispatch (what Julia does), the methods that gets called is a function of all of the types of the arguments in the signature. The practical consequence is that in Julia, types matter. A lot.

To start our simulations, we will create an abstract type to store organisms:

abstract type Organism end

We will specifically focus on two types of organisms: Rabbits and Foxes. These will be defined by a population size, which is an integer.

Base.@kwdef mutable struct Rabbit <: Organism
    population::Integer = 1
end

Main.var"##338".Rabbit

Note that we have prefaced the declaration of our struct with Base.@kwdef. This is a strange little macro, which is very useful, and also very undocumented. What it does is let us put default values in the fields, and call them by their names:

🐰 = Rabbit(; population = 4)

Main.var"##338".Rabbit(4)

We can do the same work for foxes:

Base.@kwdef mutable struct Fox <: Organism
    population::Integer = 1
end

Main.var"##338".Fox
Notice how the types are almost the same? We could solve this problem in a dozen different ways, including making Organism a concrete parametric type, or using metaprogramming to write the struct definitions for us. Do not hesitate to look for these keywords in the Julia manual when you have mastered the content of this module; for now, explicit and verbose is better than fancy and concise.
🦊 = Fox()

Main.var"##338".Fox(1)

Even if we do not specify a value for population, it will take the default value. Also, yes, emojis are valid variable names. And function names. And it’s a curse and a blessing.

What we will do is write a function called sight, which will establish a set of rules for what happens when an organism sees another organism.

function sight!(fox::Fox, rabbit::Rabbit)
    if iszero(rabbit.population)
        fox.population -= 1
    else
        fox.population += 1
        rabbit.population -= 1
    end
end

sight! (generic function with 1 method)
The ! at the end of the sight function means nothing in terms of the language, but is part of the social contract of using Julia, and signifies that the function will mutate (this means “change”) its arguments. It is an exclamation mark because mutation is a side-effect, and there are situations where we care about side-effects and so-called pure functions a lot, and we will revisit mutating functions in the next section.

We can try to apply this function now:

sight!(🦊, 🐰)

3

Because the fox has sighted the rabbit first, the rabbit population loses one individual, and the fox population grows by one.

This is, and we cannot emphasize this enough, not how any of this works.

Let’s check the status of our populations:

🦊, 🐰

(Main.var"##338".Fox(2), Main.var"##338".Rabbit(3))

So far, so good. How do we add more complexity to this? Well, let’s add a version of sight! that accounts for the fact that foxes are hunting during sunset, at night, and very early in the morning. Let’s say that they hunt from 9pm to 5am. To represent this, we will load the Dates package from the standard library:

using Dates

It is going to let us do a little bit of interesting date arithmetic, and its documentation is worth reading a couple times over if you have the misfortune of needing to manipulate dates and times. Specifically, the thing we want to express is that foxes are hunting between 9pm yesterday and 5am today, which are respectively

Hour(21) - Day(1)

-1 day, 21 hours

and

Hour(5)

5 hours

We can check that this is covering the correct timespan of 8 hours:

Hour(5) - (Hour(21) - Day(1))

1 day, -16 hours

Now, to add this to a method for sight!

function sight!(fox::Fox, rabbit::Rabbit, time::DateTime)
    if (Hour(21) - Day(1)) <= Hour(time) <= Hour(5)
        sight!(fox, rabbit)
    else
        @info "Foxes are currently closed for business"
    end
end

sight! (generic function with 2 methods)

Let’s try this at different moments – for example, at 4:58pm on the first day of August, 2018:

sight!(🦊, 🐰, DateTime(2018, 8, 1, 16, 58, 00))

[ Info: Foxes are currently closed for business

We can check that the population size has not changed:

🦊, 🐰

(Main.var"##338".Fox(2), Main.var"##338".Rabbit(3))

Alternatively, if the same encounter happens a bit later:

sight!(🦊, 🐰, DateTime(2018, 8, 2, 01, 35, 21))
🦊, 🐰

(Main.var"##338".Fox(3), Main.var"##338".Rabbit(2))

This is an illustration of the things we can do when dispatching on the types of multiple arguments. In the next modules, this will become standard practice, and so it is worth spending a bit of time trying to experiment with the concepts here. For example, we have not defined a situation in which the rabbit is the one sighting the fox first – this is a good example to implement yourself!