Julia Language

Tuples

Syntax#

  • a,
  • a, b
  • a, b = xs
  • ()
  • (a,)
  • (a, b)
  • (a, b…)
  • Tuple{T, U, V}
  • NTuple{N, T}
  • Tuple{T, U, Vararg{V}}

Remarks#

Tuples have much better runtime performance than arrays for two reasons: their types are more precise, and their immutability allows them to be allocated on the stack instead of the heap. However, this more precise typing comes with both more compile-time overhead and more difficulty achieving type stability.

Introduction to Tuples

Tuples are immutable ordered collections of arbitrary distinct objects, either of the same type or of different types. Typically, tuples are constructed using the (x, y) syntax.

julia> tup = (1, 1.0, "Hello, World!")
(1,1.0,"Hello, World!")

The individual objects of a tuple can be retrieved using indexing syntax:

julia> tup[1]
1

julia> tup[2]
1.0

julia> tup[3]
"Hello, World!"

They implement the iterable interface, and can therefore be iterated over using for loops:

julia> for item in tup
           println(item)
       end
1
1.0
Hello, World!

Tuples also support a variety of generic collections functions, such as reverse or length:

julia> reverse(tup)
("Hello, World!",1.0,1)

julia> length(tup)
3

Furthermore, tuples support a variety of higher-order collections operations, including any, all, map, or broadcast:

julia> map(typeof, tup)
(Int64,Float64,String)

julia> all(x -> x < 2, (1, 2, 3))
false

julia> all(x -> x < 4, (1, 2, 3))
true

julia> any(x -> x < 2, (1, 2, 3))
true

The empty tuple can be constructed using ():

julia> ()
()

julia> isempty(ans)
true

However, to construct a tuple of one element, a trailing comma is required. This is because the parentheses (( and )) would otherwise be treated as grouping operations together instead of constructing a tuple.

julia> (1)
1

julia> (1,)
(1,)

For consistency, a trailing comma is also allowed for tuples with more than one element.

julia> (1, 2, 3,)
(1,2,3)

Tuple types

The typeof a tuple is a subtype of Tuple:

julia> typeof((1, 2, 3))
Tuple{Int64,Int64,Int64}

julia> typeof((1.0, :x, (1, 2)))
Tuple{Float64,Symbol,Tuple{Int64,Int64}}

Unlike other data types, Tuple types are covariant. Other data types in Julia are generally invariant. Thus,

julia> Tuple{Int, Int} <: Tuple{Number, Number}
true

julia> Vector{Int} <: Vector{Number}
false

This is the case because everywhere a Tuple{Number, Number} is accepted, so too would a Tuple{Int, Int}, since it also has two elements, both of which are numbers. That is not the case for a Vector{Int} versus a Vector{Number}, as a function accepting a Vector{Number} may wish to store a floating point (e.g. 1.0) or a complex number (e.g. 1+3im) in such a vector.

The covariance of tuple types means that Tuple{Number} (again unlike Vector{Number}) is actually an abstract type:

julia> isleaftype(Tuple{Number})
false

julia> isleaftype(Vector{Number})
true

Concrete subtypes of Tuple{Number} include Tuple{Int}, Tuple{Float64}, Tuple{Rational{BigInt}}, and so forth.

Tuple types may contain a terminating Vararg as their last parameter to indicate an indefinite number of objects. For instance, Tuple{Vararg{Int}} is the type of all tuples containing any number of Ints, possibly zero:

julia> isa((), Tuple{Vararg{Int}})
true

julia> isa((1,), Tuple{Vararg{Int}})
true

julia> isa((1,2,3,4,5), Tuple{Vararg{Int}})
true

julia> isa((1.0,), Tuple{Vararg{Int}})
false

whereas Tuple{String, Vararg{Int}} accepts tuples consisting of a string, followed by any number (possibly zero) of Ints.

julia> isa(("x", 1, 2), Tuple{String, Vararg{Int}})
true

julia> isa((1, 2), Tuple{String, Vararg{Int}})
false

Combined with co-variance, this means that Tuple{Vararg{Any}} describes any tuple. Indeed, Tuple{Vararg{Any}} is just another way of saying Tuple:

julia> Tuple{Vararg{Any}} == Tuple
true

Vararg accepts a second numeric type parameter indicating how many times exactly its first type parameter should occur. (By default, if unspecified, this second type parameter is a typevar that can take any value, which is why any number of Ints are accepted in the Varargs above.) Tuple types ending in a specified Vararg will automatically be expanded to the requested number of elements:

julia> Tuple{String,Vararg{Int, 3}}
Tuple{String,Int64,Int64,Int64}

Notation exists for homogenous tuples with a specified Vararg: NTuple{N, T}. In this notation, N denotes the number of elements in the tuple, and T denotes the type accepted. For instance,

julia> NTuple{3, Int}
Tuple{Int64,Int64,Int64}

julia> NTuple{10, Int}
NTuple{10,Int64}

julia> ans.types
svec(Int64,Int64,Int64,Int64,Int64,Int64,Int64,Int64,Int64,Int64)

Note that NTuples beyond a certain size are shown simply as NTuple{N, T}, instead of the expanded Tuple form, but they are still the same type:

julia> Tuple{Int,Int,Int,Int,Int,Int,Int,Int,Int,Int}
NTuple{10,Int64}

Dispatching on tuple types

Because Julia function parameter lists are themselves tuples, dispatching on various kinds of tuples is often easier done through the method parameters themselves, often with liberal usage for the “splatting” ... operator. For instance, consider the implementation of reverse for tuples, from Base:

revargs() = ()
revargs(x, r...) = (revargs(r...)..., x)

reverse(t::Tuple) = revargs(t...)

Implementing methods on tuples this way preserves type stability, which is crucial for performance. We can see that there is no overhead to this approach using the @code_warntype macro:

julia> @code_warntype reverse((1, 2, 3))
Variables:
  #self#::Base.#reverse
  t::Tuple{Int64,Int64,Int64}

Body:
  begin 
      SSAValue(1) = (Core.getfield)(t::Tuple{Int64,Int64,Int64},2)::Int64
      SSAValue(2) = (Core.getfield)(t::Tuple{Int64,Int64,Int64},3)::Int64
      return (Core.tuple)(SSAValue(2),SSAValue(1),(Core.getfield)(t::Tuple{Int64,Int64,Int64},1)::Int64)::Tuple{Int64,Int64,Int64}
  end::Tuple{Int64,Int64,Int64}

Although somewhat hard to read, the code here is simply getting creating a new tuple with values 3rd, 2nd, and 1st elements of the original tuple, respectively. On many machines, this compiles down to extremely efficient LLVM code, which consists of loads and stores.

julia> @code_llvm reverse((1, 2, 3))

define void @julia_reverse_71456([3 x i64]* noalias sret, [3 x i64]*) #0 {
top:
  %2 = getelementptr inbounds [3 x i64], [3 x i64]* %1, i64 0, i64 1
  %3 = getelementptr inbounds [3 x i64], [3 x i64]* %1, i64 0, i64 2
  %4 = load i64, i64* %3, align 1
  %5 = load i64, i64* %2, align 1
  %6 = getelementptr inbounds [3 x i64], [3 x i64]* %1, i64 0, i64 0
  %7 = load i64, i64* %6, align 1
  %.sroa.0.0..sroa_idx = getelementptr inbounds [3 x i64], [3 x i64]* %0, i64 0, i64 0
  store i64 %4, i64* %.sroa.0.0..sroa_idx, align 8
  %.sroa.2.0..sroa_idx1 = getelementptr inbounds [3 x i64], [3 x i64]* %0, i64 0, i64 1
  store i64 %5, i64* %.sroa.2.0..sroa_idx1, align 8
  %.sroa.3.0..sroa_idx2 = getelementptr inbounds [3 x i64], [3 x i64]* %0, i64 0, i64 2
  store i64 %7, i64* %.sroa.3.0..sroa_idx2, align 8
  ret void
}

Multiple return values

Tuples are frequently used for multiple return values. Much of the standard library, including two of the functions of the iterable interface (next and done), returns tuples containing two related but distinct values.

The parentheses around tuples can be omitted in certain situations, making multiple return values easier to implement. For instance, we can create a function to return both positive and negative square roots of a real number:

julia> pmsqrt(x::Real) = sqrt(x), -sqrt(x)
pmsqrt (generic function with 1 method)

julia> pmsqrt(4)
(2.0,-2.0)

Destructuring assignment can be used to unpack the multiple return values. To store the square roots in variables a and b, it suffices to write:

julia> a, b = pmsqrt(9.0)
(3.0,-3.0)

julia> a
3.0

julia> b
-3.0

Another example of this is the divrem and fldmod functions, which do an integer (truncating or floored, respectively) division and remainder operation at the same time:

julia> q, r = divrem(10, 3)
(3,1)

julia> q
3

julia> r
1
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