Constructors are a basic building block of object-oriented programming (OOP). They expose ways to build specific types of objects consistently, using arbitrary rules to validate properties. Still, constructors are odd beasts in the OOP world. In Java, this is usually the first case of function overloading that learning programmers meet, often without knowing the term. An overloaded constructor is shown in the following example:

class Car {
    private Motor motor;

    public Car(Motor m) {
        this.motor = m;
    }
    public Car() {
        this.motor = new Motor();
    }
}

Scala and Kotlin, which are both languages on the Java Virtual Machine designed after and learning from Java, made the design choice of imposing a primary constructor, which all other constructors have to call. Constructors are weird beasts because they act partly as a function, partly as a method. Moreover, they expose a special use of this as a method call instead of being a pointer to the current object:

class Car {
    private Motor motor;

    public Car(Motor m) {
        // 'this' as an object reference
        this.motor = m;
    }
    public Car(int power) {
        Motor m = new Motor(power);
        // this as a method
        this(m);
    }
}

This has been in my experience confusing and harder to teach on my side because it forces the learner to get a grasp of many specific tricks at the same time. Another hard-to-grasp point is this(motor), which has never been defined has such. The definition it corresponds to is Car(Motor m), the required mental load here is just unnecessary. This is why I appreciate Kotlin and Scala having made constructors more restrictive, removing the need for hand-wavy explanations for bad design. This great blog post gives an overview of constructors in different mainstream languages and compare them with the trait-based system of Rust.

Constructors outside class-based OOP

I will focus here on composite types or struct. There is a whole section of the Julia docs on constructors, but I would summarize things as:

1. There is a primary constructor which must provide values for all fields.
2. All other constructors are just functions, no magic is involved, and constructors are just multiple methods in the context of multiple dispatch.

This way of building objects as simple structures holding data in different fields is not new, Kotlin and Scala have a similar pattern as we mentioned above. Languages like Rust and Go take a different path by having structures being plain structures, initialized by providing all fields directly:

// rust example

struct Motor {
    pub power: u8,
}

struct Car {
    pub motor : Motor
}
// let m = Motor{power : 33};

// go example

type Motor struct {
	Power uint
}
// m := Motor{33}

Both languages have conventions for calling a standard constructing function, namely fn new(args) -> T and func NewT(args) for Rust and Go respectively, but those are not special and remain a simple convention without additional language complexity.

Two lessons learned

Two interesting Pull Requests are about to be merged in Distributions.jl, which is the main package for working with probability distributions in Julia. Both revolve around a revision of the work of constructors. I will use them to make a point which I believe generalizes well to other systems. No probability theory should be needed here, it is merely a motivating example.

Lesson 1: product distributions and constructor promises

Given multiple random variables: $ X_{i}, i = 1..n $ we define a **product distribution** as the vector random variable built by stacking the different $ X_i $:

$$ X = [ X_i | i \in 1..n ] $$

They arrived in Distributions.jl in this PR if you are curious. One thing to be careful about is that the term “product distribution” does not correspond with the eponymous Wikipedia entry. What we refer to here is the product type in the sense of tuple construction and not the arithmetic product. EDIT: the correct corresponding Wikipedia entry is the one on Product measure, thanks Chad for pointing it out. One important property is that the entries of the product type are independent distributions, which helps a great deal deducing properties of the product distribution.

An example product type could be the product of two univariate Gaussian distributions:

$$ X_1 \sim \mathcal{N}(0, 1)$$ $$ X_2 \sim \mathcal{N}(0, 2)$$ $$ X = [X_1, X_2]$$

The implementation of the Product type stores the vector of univariate distributions, sampling and computing the PDF/CDF is done on a per-entry basis. The corresponding code would look like this:

using Distributions: Normal, Product, pdf

Xs = [Normal(0, 1), Normal(0, 2)]
p = Product(Xs)

# sample from p
rand(p)

# compute PDF at (x1 = 0, x2 = 1)
pdf(p, [0.0, 1.0])

One problem we have here is that we know some specialized, faster techniques can be used in specific cases. Our product here for example, is nothing more than a multivariate Gaussian distribution with independent components: $$ X \sim \mathcal{N}([0, 0], diag([1, 2]))$$ with $diag(\cdot)$ constructing a diagonal matrix from a vector.

Sampling and computing quantities of interest for such multivariate would be much faster by using a multivariate directly. Our new design can leverage multiple dispatch, and would look as follows:

function Product(distributions::Vector{<:Gaussian})
	# construct multivariate gaussian
end

function Product(distributions::Vector{<:Uniform})
	# construct multivariate uniform
end

function Product(distributions::Vector{<:UnivariateDistribution})
	# construct generic Product
end

It is all fine and type-stable; if you don’t know what it means, just think sound from a type perspective. One issue here though is that we break the promise of a constructor. A constructor of Product is supposed to return a Product and exactly this. If you work in a language that uses algebraic data types for possible failures and absence as Maybe/Either/Result/Option, the constructor should return the type and not one of these.

struct T
	# type fields
end

"""
T constructor
"""
T(args) = # ...

value = T(args)

# the following should always be true
typeof(value) <: T

In our cases, a more efficient implementation cannot be returned from a constructor. This means the construction of our type must be left to another method which could return it or something else. In the case of product distributions, it was done in this PR, adding the function product_distribution in Distributions.jl, which can have various methods returning a Product or something else. With this design, it is left possible for a distribution to define a special product type, while the default Product will work reasonably well.

The lesson learned here is to be wary of exposing constructors when many paths are possible, and a dispatch system might be preferable. Constructors should always return the same type and are not ideal for a specialization system.

Lesson 2: main constructors should remain lean

Many constructors for probability distributions include a verification of the parameters. When constructing a uniform distribution $\mathcal{U}(a, b)$, one would want to verify that $a \leq b$. For a Gaussian distribution, one would verify that the standard deviation is positive. These checks are fine, but have a runtime cost and may interrupt the construction of the object. There are many cases in which the parameters are guaranteed to be valid, two of them being:

1. Constructing an object by copy.
2. Constructing an object with default parameters.

struct T
	# fields
end

function T()
	# default parameters are valid
end

function T(t::T)
	# t is already constructed, and is therefore valid
end

Throwing errors in a constructor is ill-advised, because again, the promise of a constructor is to construct the object. In languages where throwing is not advised, it means the constructor would return a Maybe{T} / Either{_, T}, which again breaks the promise. The problem is that if checking is not the default, users are less likely to call the checking function. The solution found here is to use a keyword in all constructors:

struct D{T <: Real} <: Distribution
	param::T
end

function D(p::T; check_arg = true) where {T}
	if check_arg
		verify_parameter(p)
	end
	return D{T}(p)
end

The default is still to check the validity of parameters, but objects of type D can now be constructed with opt-out checking. Another way to do it is with multiple dispatch:

"""
A flag structure to avoid checking arguments.
"""
struct NoArgCheck end

struct D{T <: Real} <: Distribution
	param::T
end

# standard constructor, validates the parameter
function D(p::T) where {T <: Real}
	verify_parameter(p)
	return D{T}(p)
end

# faster constructor, no argument checking
function D(p::T, ::NoArgCheck) where {T}
	return D{T}(p)
end

In either cases, users can now take the responsibility of checking parameters themselves. In recent Julia version, the compiler optimization of boolean constants will make the two roughly equivalent. One general rule to highlight here for scientific programming work is that the constructor is a fixed cost imposed on all users, treat additional checks and operations carefully.

If you found this post useful (or not) or want to react in some way, feel free to reach out on Twitter and/or Reddit.

Edit: thanks Alec for spotting redundant code. Another blog post on the subject was posted on Reddit (thanks Paul for pointing it out).