Methods

Until now, we have, in our examples, defined only functions with a single method having unconstrained argument types. Such functions behave just like they would in traditional dynamically typed languages. Nevertheless, we have used multiple dispatch and methods almost continually without being aware of it: all of Julia’s standard functions and operators, like the aforementioned + function, have many methods defining their behavior over various possible combinations of argument type and count.

When defining a function, one can optionally constrain the types of parameters it is applicable to, using the :: type-assertion operator, introduced in the section on Composite Types:

This function definition applies only to calls where x and y are both values of type Float64:

Applying it to any other types of arguments will result in a MethodError:

As you can see, the arguments must be precisely of type Float64. Other numeric types, such as integers or 32-bit floating-point values, are not automatically converted to 64-bit floating-point, nor are strings parsed as numbers. Because Float64 is a concrete type and concrete types cannot be subclassed in Julia, such a definition can only be applied to arguments that are exactly of type Float64. It may often be useful, however, to write more general methods where the declared parameter types are abstract:

This method definition applies to any pair of arguments that are instances of Number. They need not be of the same type, so long as they are each numeric values. The problem of handling disparate numeric types is delegated to the arithmetic operations in the expression 2x - y.

To define a function with multiple methods, one simply defines the function multiple times, with different numbers and types of arguments. The first method definition for a function creates the function object, and subsequent method definitions add new methods to the existing function object. The most specific method definition matching the number and types of the arguments will be executed when the function is applied. Thus, the two method definitions above, taken together, define the behavior for f over all pairs of instances of the abstract type Number — but with a different behavior specific to pairs of Float64 values. If one of the arguments is a 64-bit float but the other one is not, then the f(Float64,Float64) method cannot be called and the more general f(Number,Number) method must be used:

The 2x + y definition is only used in the first case, while the 2x - y definition is used in the others. No automatic casting or conversion of function arguments is ever performed: all conversion in Julia is non-magical and completely explicit. Conversion and Promotion, however, shows how clever application of sufficiently advanced technology can be indistinguishable from magic. ^[2]

For non-numeric values, and for fewer or more than two arguments, the function f remains undefined, and applying it will still result in a MethodError:

You can easily see which methods exist for a function by entering the function object itself in an interactive session:

This output tells us that f is a function object with two methods. To find out what the signatures of those methods are, use the methods function:

which shows that f has two methods, one taking two Float64 arguments and one taking arguments of type Number. It also indicates the file and line number where the methods were defined: because these methods were defined at the REPL, we get the apparent line number none:1.

In the absence of a type declaration with ::, the type of a method parameter is Any by default, meaning that it is unconstrained since all values in Julia are instances of the abstract type Any. Thus, we can define a catch-all method for f like so:

This catch-all is less specific than any other possible method definition for a pair of parameter values, so it will only be called on pairs of arguments to which no other method definition applies.

Note that in the signature of the third method, there is no type specified for the arguments x and y. This is a shortened way of expressing f(x::Any, y::Any).

Although it seems a simple concept, multiple dispatch on the types of values is perhaps the single most powerful and central feature of the Julia language. Core operations typically have dozens of methods:

Multiple dispatch together with the flexible parametric type system give Julia its ability to abstractly express high-level algorithms decoupled from implementation details.

When you create multiple methods of the same function, this is sometimes called "specialization." In this case, you’re specializing the function by adding additional methods to it: each new method is a new specialization of the function. As shown above, these specializations are returned by methods.

There’s another kind of specialization that occurs without programmer intervention: Julia’s compiler can automatically specialize the method for the specific argument types used. Such specializations are not listed by methods, as this doesn’t create new Methods, but tools like @code_typed allow you to inspect such specializations.

For example, if you create a method

you’ve given the function mysum one new method (possibly its only method), and that method takes any pair of Real number inputs. But if you then execute

Julia will compile mysum twice, once for x::Int, y::Int and again for x::Float64, y::Float64. The point of compiling twice is performance: the methods that get called for + (which mysum uses) vary depending on the specific types of x and y, and by compiling different specializations Julia can do all the method lookup ahead of time. This allows the program to run much more quickly, since it does not have to bother with method lookup while it is running. Julia’s automatic specialization allows you to write generic algorithms and expect that the compiler will generate efficient, specialized code to handle each case you need.

In cases where the number of potential specializations might be effectively unlimited, Julia may avoid this default specialization. See Be aware of when Julia avoids specializing for more information.

It is possible to define a set of function methods such that there is no unique most specific method applicable to some combinations of arguments:

Here the call g(2.0, 3.0) could be handled by either the g(Float64, Any) or the g(Any, Float64) method, and neither is more specific than the other. In such cases, Julia raises a MethodError rather than arbitrarily picking a method. You can avoid method ambiguities by specifying an appropriate method for the intersection case:

It is recommended that the disambiguating method be defined first, since otherwise the ambiguity exists, if transiently, until the more specific method is defined.

In more complex cases, resolving method ambiguities involves a certain element of design; this topic is explored further below.

Method definitions can optionally have type parameters qualifying the signature:

The first method applies whenever both arguments are of the same concrete type, regardless of what type that is, while the second method acts as a catch-all, covering all other cases. Thus, overall, this defines a boolean function that checks whether its two arguments are of the same type:

Such definitions correspond to methods whose type signatures are UnionAll types (see UnionAll Types).

This kind of definition of function behavior by dispatch is quite common — idiomatic, even — in Julia. Method type parameters are not restricted to being used as the types of arguments: they can be used anywhere a value would be in the signature of the function or body of the function. Here’s an example where the method type parameter T is used as the type parameter to the parametric type Vector{T} in the method signature:

As you can see, the type of the appended element must match the element type of the vector it is appended to, or else a MethodError is raised. In the following example, the method type parameter T is used as the return value:

Just as you can put subtype constraints on type parameters in type declarations (see Parametric Types), you can also constrain type parameters of methods:

The same_type_numeric function behaves much like the same_type function defined above, but is only defined for pairs of numbers.

Parametric methods allow the same syntax as where expressions used to write types (see UnionAll Types). If there is only a single parameter, the enclosing curly braces (in where {T}) can be omitted, but are often preferred for clarity. Multiple parameters can be separated with commas, e.g. where {T, S<:Real}, or written using nested where, e.g. where S<:Real where T.

When redefining a method or adding new methods, it is important to realize that these changes don’t take effect immediately. This is key to Julia’s ability to statically infer and compile code to run fast, without the usual JIT tricks and overhead. Indeed, any new method definition won’t be visible to the current runtime environment, including Tasks and Threads (and any previously defined @generated functions). Let’s start with an example to see what this means:

In this example, observe that the new definition for newfun has been created, but can’t be immediately called. The new global is immediately visible to the tryeval function, so you could write return newfun (without parentheses). But neither you, nor any of your callers, nor the functions they call, or etc. can call this new method definition!

But there’s an exception: future calls to newfun from the REPL work as expected, being able to both see and call the new definition of newfun.

However, future calls to tryeval will continue to see the definition of newfun as it was at the previous statement at the REPL, and thus before that call to tryeval.

You may want to try this for yourself to see how it works.

The implementation of this behavior is a "world age counter". This monotonically increasing value tracks each method definition operation. This allows describing "the set of method definitions visible to a given runtime environment" as a single number, or "world age". It also allows comparing the methods available in two worlds just by comparing their ordinal value. In the example above, we see that the "current world" (in which the method newfun exists), is one greater than the task-local "runtime world" that was fixed when the execution of tryeval started.

Sometimes it is necessary to get around this (for example, if you are implementing the above REPL). Fortunately, there is an easy solution: call the function using Base.invokelatest:

Finally, let’s take a look at some more complex examples where this rule comes into play. Define a function f(x), which initially has one method:

Start some other operations that use f(x):

Now we add some new methods to f(x):

Compare how these results differ:

While complex dispatch logic is not required for performance or usability, sometimes it can be the best way to express some algorithm. Here are a few common design patterns that come up sometimes when using dispatch in this way.

Function parameters can also be used to constrain the number of arguments that may be supplied to a "varargs" function (Varargs Functions). The notation Vararg{T,N} is used to indicate such a constraint. For example:

More usefully, it is possible to constrain varargs methods by a parameter. For example:

would be called only when the number of indices matches the dimensionality of the array.

When only the type of supplied arguments needs to be constrained Vararg{T} can be equivalently written as T.... For instance f(x::Int...) = x is a shorthand for f(x::Vararg{Int}) = x.

As mentioned briefly in Functions, optional arguments are implemented as syntax for multiple method definitions. For example, this definition:

translates to the following three methods:

This means that calling f() is equivalent to calling f(1,2). In this case the result is 5, because f(1,2) invokes the first method of f above. However, this need not always be the case. If you define a fourth method that is more specialized for integers:

then the result of both f() and f(1,2) is -3. In other words, optional arguments are tied to a function, not to any specific method of that function. It depends on the types of the optional arguments which method is invoked. When optional arguments are defined in terms of a global variable, the type of the optional argument may even change at run-time.

Keyword arguments behave quite differently from ordinary positional arguments. In particular, they do not participate in method dispatch. Methods are dispatched based only on positional arguments, with keyword arguments processed after the matching method is identified.

Methods are associated with types, so it is possible to make any arbitrary Julia object "callable" by adding methods to its type. (Such "callable" objects are sometimes called "functors.")

For example, you can define a type that stores the coefficients of a polynomial, but behaves like a function evaluating the polynomial:

Notice that the function is specified by type instead of by name. As with normal functions there is a terse syntax form. In the function body, p will refer to the object that was called. A Polynomial can be used as follows:

This mechanism is also the key to how type constructors and closures (inner functions that refer to their surrounding environment) work in Julia.

Occasionally it is useful to introduce a generic function without yet adding methods. This can be used to separate interface definitions from implementations. It might also be done for the purpose of documentation or code readability. The syntax for this is an empty function block without a tuple of arguments:

Julia’s method polymorphism is one of its most powerful features, yet exploiting this power can pose design challenges. In particular, in more complex method hierarchies it is not uncommon for ambiguities to arise.

Above, it was pointed out that one can resolve ambiguities like

by defining a method

This is often the right strategy; however, there are circumstances where following this advice mindlessly can be counterproductive. In particular, the more methods a generic function has, the more possibilities there are for ambiguities. When your method hierarchies get more complicated than this simple example, it can be worth your while to think carefully about alternative strategies.

Below we discuss particular challenges and some alternative ways to resolve such issues.

You can define methods within a local scope, for example

However, you should not define local methods conditionally or subject to control flow, as in

as it is not clear what function will end up getting defined. In the future, it might be an error to define local methods in this manner.

For cases like this use anonymous functions instead: