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Julia 构造函数

# Constructors

Constructors [^1] are functions that create new objects -- specifically, instances of Composite Types. In Julia, type objects also serve as constructor functions: they create new instances of themselves when applied to an argument tuple as a function. This much was already mentioned briefly when composite types were introduced. For example:

julia> struct Foo

julia> foo = Foo(1, 2)
Foo(1, 2)

julia> foo.bar

julia> foo.baz

For many types, forming new objects by binding their field values together is all that is ever
needed to create instances. However, in some cases more functionality is required when
creating composite objects. Sometimes invariants must be enforced, either by checking arguments
or by transforming them. Recursive data structures,
especially those that may be self-referential, often cannot be constructed cleanly without first
being created in an incomplete state and then altered programmatically to be made whole, as a
separate step from object creation. Sometimes, it's just convenient to be able to construct objects
with fewer or different types of parameters than they have fields. Julia's system for object construction
addresses all of these cases and more.

Nomenclature: while the term "constructor" generally refers to the entire function which constructs objects of a type, it is common to abuse terminology slightly and refer to specific constructor methods as "constructors". In such situations, it is generally clear from the context that the term is used to mean "constructor method" rather than "constructor function", especially as it is often used in the sense of singling out a particular method of the constructor from all of the others.

# Outer Constructor Methods

A constructor is just like any other function in Julia in that its overall behavior is defined
by the combined behavior of its methods. Accordingly, you can add functionality to a constructor
by simply defining new methods. For example, let's say you want to add a constructor method for
Foo objects that takes only one argument and uses the given value for both the bar and baz
fields. This is simple:

julia> Foo(x) = Foo(x,x)

julia> Foo(1)
Foo(1, 1)

You could also add a zero-argument Foo constructor method that supplies default values for both
of the bar and baz fields:

julia> Foo() = Foo(0)

julia> Foo()
Foo(0, 0)

Here the zero-argument constructor method calls the single-argument constructor method, which
in turn calls the automatically provided two-argument constructor method. For reasons that will
become clear very shortly, additional constructor methods declared as normal methods like this
are called outer constructor methods. Outer constructor methods can only ever create a new instance
by calling another constructor method, such as the automatically provided default ones.

# Inner Constructor Methods

While outer constructor methods succeed in addressing the problem of providing additional convenience
methods for constructing objects, they fail to address the other two use cases mentioned in the
introduction of this chapter: enforcing invariants, and allowing construction of self-referential
objects. For these problems, one needs inner constructor methods. An inner constructor method
is like an outer constructor method, except for two differences:

  1. It is declared inside the block of a type declaration, rather than outside of it like normal methods.
  2. It has access to a special locally existent function called new that creates objects of the
    block's type.

For example, suppose one wants to declare a type that holds a pair of real numbers, subject to
the constraint that the first number is not greater than the second one. One could declare it
like this:

julia> struct OrderedPair
           OrderedPair(x,y) = x > y ? error("out of order") : new(x,y)

Now OrderedPair objects can only be constructed such that x <= y:

julia> OrderedPair(1, 2)
OrderedPair(1, 2)

julia> OrderedPair(2,1)
ERROR: out of order
 [1] error at ./error.jl:33 [inlined]
 [2] OrderedPair(::Int64, ::Int64) at ./none:4
 [3] top-level scope

If the type were declared mutable, you could reach in and directly change the field values to
violate this invariant. Of course, messing around with an object's internals uninvited is bad practice.
You (or someone else) can also provide additional outer constructor methods at any later point, but
once a type is declared, there is no way to add more inner constructor methods. Since outer constructor
methods can only create objects by calling other constructor methods, ultimately, some inner constructor
must be called to create an object. This guarantees that all objects of the declared type must come into
existence by a call to one of the inner constructor methods provided with the type, thereby giving
some degree of enforcement of a type's invariants.

If any inner constructor method is defined, no default constructor method is provided: it is presumed
that you have supplied yourself with all the inner constructors you need. The default constructor
is equivalent to writing your own inner constructor method that takes all of the object's fields
as parameters (constrained to be of the correct type, if the corresponding field has a type),
and passes them to new, returning the resulting object:

julia> struct Foo
           Foo(bar,baz) = new(bar,baz)

This declaration has the same effect as the earlier definition of the Foo type without an explicit
inner constructor method. The following two types are equivalent -- one with a default constructor,
the other with an explicit constructor:

julia> struct T1

julia> struct T2
           T2(x) = new(x)

julia> T1(1)

julia> T2(1)

julia> T1(1.0)

julia> T2(1.0)

It is good practice to provide as few inner constructor methods as possible: only those
taking all arguments explicitly and enforcing essential error checking and transformation. Additional
convenience constructor methods, supplying default values or auxiliary transformations, should
be provided as outer constructors that call the inner constructors to do the heavy lifting. This
separation is typically quite natural.

# Incomplete Initialization

The final problem which has still not been addressed is construction of self-referential objects,
or more generally, recursive data structures. Since the fundamental difficulty may not be immediately
obvious, let us briefly explain it. Consider the following recursive type declaration:

julia> mutable struct SelfReferential

This type may appear innocuous enough, until one considers how to construct an instance of it.
If a is an instance of SelfReferential, then a second instance can be created by the call:

julia> b = SelfReferential(a)

But how does one construct the first instance when no instance exists to provide as a valid value
for its obj field? The only solution is to allow creating an incompletely initialized instance
of SelfReferential with an unassigned obj field, and using that incomplete instance as a valid
value for the obj field of another instance, such as, for example, itself.

To allow for the creation of incompletely initialized objects, Julia allows the new function
to be called with fewer than the number of fields that the type has, returning an object with
the unspecified fields uninitialized. The inner constructor method can then use the incomplete
object, finishing its initialization before returning it. Here, for example, is another attempt
at defining the SelfReferential type, this time using a zero-argument inner constructor returning instances
having obj fields pointing to themselves:

julia> mutable struct SelfReferential
           SelfReferential() = (x = new(); x.obj = x)

We can verify that this constructor works and constructs objects that are, in fact, self-referential:

julia> x = SelfReferential();

julia> x === x

julia> x === x.obj

julia> x === x.obj.obj

Although it is generally a good idea to return a fully initialized object from an inner constructor,
it is possible to return incompletely initialized objects:

julia> mutable struct Incomplete
           Incomplete() = new()

julia> z = Incomplete();

While you are allowed to create objects with uninitialized fields, any access to an uninitialized
reference is an immediate error:

julia> z.data
ERROR: UndefRefError: access to undefined reference

This avoids the need to continually check for null values. However, not all object fields are
references. Julia considers some types to be "plain data", meaning all of their data is self-contained
and does not reference other objects. The plain data types consist of primitive types (e.g. Int)
and immutable structs of other plain data types. The initial contents of a plain data type is

julia> struct HasPlain
           HasPlain() = new()

julia> HasPlain()

Arrays of plain data types exhibit the same behavior.

You can pass incomplete objects to other functions from inner constructors to delegate their completion:

julia> mutable struct Lazy
           Lazy(v) = complete_me(new(), v)

As with incomplete objects returned from constructors, if complete_me or any of its callees
try to access the data field of the Lazy object before it has been initialized, an error will
be thrown immediately.

# Parametric Constructors

Parametric types add a few wrinkles to the constructor story. Recall from Parametric Types
that, by default, instances of parametric composite types can be constructed either with explicitly
given type parameters or with type parameters implied by the types of the arguments given to the
constructor. Here are some examples:

julia> struct Point{T<:Real}

julia> Point(1,2) ## implicit T ##
Point{Int64}(1, 2)

julia> Point(1.0,2.5) ## implicit T ##
Point{Float64}(1.0, 2.5)

julia> Point(1,2.5) ## implicit T ##
ERROR: MethodError: no method matching Point(::Int64, ::Float64)
Closest candidates are:
  Point(::T<:Real, ::T<:Real) where T<:Real at none:2

julia> Point{Int64}(1, 2) ## explicit T ##
Point{Int64}(1, 2)

julia> Point{Int64}(1.0,2.5) ## explicit T ##
ERROR: InexactError: Int64(Int64, 2.5)

julia> Point{Float64}(1.0, 2.5) ## explicit T ##
Point{Float64}(1.0, 2.5)

julia> Point{Float64}(1,2) ## explicit T ##
Point{Float64}(1.0, 2.0)

As you can see, for constructor calls with explicit type parameters, the arguments are converted
to the implied field types: Point{Int64}(1,2) works, but Point{Int64}(1.0,2.5) raises an
InexactError when converting 2.5 to Int64. When the type is implied
by the arguments to the constructor call, as in Point(1,2), then the types of the
arguments must agree -- otherwise the T cannot be determined -- but any pair of real
arguments with matching type may be given to the generic Point constructor.

What's really going on here is that Point, Point{Float64} and Point{Int64} are all different
constructor functions. In fact, Point{T} is a distinct constructor function for each type T.
Without any explicitly provided inner constructors, the declaration of the composite type Point{T<:Real}
automatically provides an inner constructor, Point{T}, for each possible type T<:Real, that
behaves just like non-parametric default inner constructors do. It also provides a single general
outer Point constructor that takes pairs of real arguments, which must be of the same type.
This automatic provision of constructors is equivalent to the following explicit declaration:

julia> struct Point{T<:Real}
           Point{T}(x,y) where {T<:Real} = new(x,y)

julia> Point(x::T, y::T) where {T<:Real} = Point{T}(x,y);

Notice that each definition looks like the form of constructor call that it handles.
The call Point{Int64}(1,2) will invoke the definition Point{T}(x,y) inside the
struct block.
The outer constructor declaration, on the other hand, defines a
method for the general Point constructor which only applies to pairs of values of the same real
type. This declaration makes constructor calls without explicit type parameters, like Point(1,2)
and Point(1.0,2.5), work. Since the method declaration restricts the arguments to being of the
same type, calls like Point(1,2.5), with arguments of different types, result in "no method"

Suppose we wanted to make the constructor call Point(1,2.5) work by "promoting" the integer
value 1 to the floating-point value 1.0. The simplest way to achieve this is to define the
following additional outer constructor method:

julia> Point(x::Int64, y::Float64) = Point(convert(Float64,x),y);

This method uses the convert function to explicitly convert x to Float64
and then delegates construction to the general constructor for the case where both arguments are
Float64. With this method definition what was previously a MethodError now
successfully creates a point of type Point{Float64}:

julia> Point(1,2.5)
Point{Float64}(1.0, 2.5)

julia> typeof(ans)

However, other similar calls still don't work:

julia> Point(1.5,2)
ERROR: MethodError: no method matching Point(::Float64, ::Int64)
Closest candidates are:
  Point(::T<:Real, !Matched::T<:Real) where T<:Real at none:1

For a more general way to make all such calls work sensibly, see [Conversion and Promotion](@ref conversion-and-promotion).
At the risk of spoiling the suspense, we can reveal here that all it takes is the following outer
method definition to make all calls to the general Point constructor work as one would expect:

julia> Point(x::Real, y::Real) = Point(promote(x,y)...);

The promote function converts all its arguments to a common type -- in this case Float64.
With this method definition, the Point constructor promotes its arguments the same way that
numeric operators like + do, and works for all kinds of real numbers:

julia> Point(1.5,2)
Point{Float64}(1.5, 2.0)

julia> Point(1,1//2)
Point{Rational{Int64}}(1//1, 1//2)

julia> Point(1.0,1//2)
Point{Float64}(1.0, 0.5)

Thus, while the implicit type parameter constructors provided by default in Julia are fairly strict,
it is possible to make them behave in a more relaxed but sensible manner quite easily. Moreover,
since constructors can leverage all of the power of the type system, methods, and multiple dispatch,
defining sophisticated behavior is typically quite simple.

# Case Study: Rational

Perhaps the best way to tie all these pieces together is to present a real world example of a
parametric composite type and its constructor methods. To that end, we implement our own rational number type
OurRational, similar to Julia's built-in Rational type, defined in

julia> struct OurRational{T<:Integer} <: Real
           function OurRational{T}(num::T, den::T) where T<:Integer
               if num == 0 && den == 0
                    error("invalid rational: 0//0")
               g = gcd(den, num)
               num = div(num, g)
               den = div(den, g)
               new(num, den)

julia> OurRational(n::T, d::T) where {T<:Integer} = OurRational{T}(n,d)

julia> OurRational(n::Integer, d::Integer) = OurRational(promote(n,d)...)

julia> OurRational(n::Integer) = OurRational(n,one(n))

julia> ⊘(n::Integer, d::Integer) = OurRational(n,d)
⊘ (generic function with 1 method)

julia> ⊘(x::OurRational, y::Integer) = x.num ⊘ (x.den*y)
⊘ (generic function with 2 methods)

julia> ⊘(x::Integer, y::OurRational) = (x*y.den) ⊘ y.num
⊘ (generic function with 3 methods)

julia> ⊘(x::Complex, y::Real) = complex(real(x) ⊘ y, imag(x) ⊘ y)
⊘ (generic function with 4 methods)

julia> ⊘(x::Real, y::Complex) = (x*y') ⊘ real(y*y')
⊘ (generic function with 5 methods)

julia> function ⊘(x::Complex, y::Complex)
           xy = x*y'
           yy = real(y*y')
           complex(real(xy) ⊘ yy, imag(xy) ⊘ yy)
⊘ (generic function with 6 methods)

The first line -- struct OurRational{T<:Integer} <: Real -- declares that OurRational takes one
type parameter of an integer type, and is itself a real type. The field declarations num::T
and den::T indicate that the data held in a OurRational{T} object are a pair of integers of type
T, one representing the rational value's numerator and the other representing its denominator.

Now things get interesting. OurRational has a single inner constructor method which checks that
both of num and den aren't zero and ensures that every rational is constructed in "lowest
terms" with a non-negative denominator. This is accomplished by dividing the given numerator and
denominator values by their greatest common divisor, computed using the gcd function. Since
gcd returns the greatest common divisor of its arguments with sign matching the first argument
(den here), after this division the new value of den is guaranteed to be non-negative. Because
this is the only inner constructor for OurRational, we can be certain that OurRational objects are
always constructed in this normalized form.

OurRational also provides several outer constructor methods for convenience. The first is the "standard"
general constructor that infers the type parameter T from the type of the numerator and denominator
when they have the same type. The second applies when the given numerator and denominator values
have different types: it promotes them to a common type and then delegates construction to the
outer constructor for arguments of matching type. The third outer constructor turns integer values
into rationals by supplying a value of 1 as the denominator.

Following the outer constructor definitions, we defined a number of methods for the
operator, which provides a syntax for writing rationals (e.g. 1 ⊘ 2). Julia's Rational
type uses the // operator for this purpose. Before these definitions,
is a completely undefined operator with only syntax and no meaning. Afterwards, it behaves just
as described in Rational Numbers -- its entire behavior is defined in these few lines.
The first and most basic definition just makes a ⊘ b construct a OurRational by applying the
OurRational constructor to a and b when they are integers. When one of the operands of
is already a rational number, we construct a new rational for the resulting ratio slightly differently;
this behavior is actually identical to division of a rational with an integer.
Finally, applying
to complex integral values creates an instance of Complex{OurRational} -- a complex
number whose real and imaginary parts are rationals:

julia> z = (1 + 2im) ⊘ (1 - 2im);

julia> typeof(z)

julia> typeof(z) <: Complex{OurRational}

Thus, although the operator usually returns an instance of OurRational, if either
of its arguments are complex integers, it will return an instance of Complex{OurRational} instead.
The interested reader should consider perusing the rest of rational.jl:
it is short, self-contained, and implements an entire basic Julia type.

# Outer-only constructors

As we have seen, a typical parametric type has inner constructors that are called when type parameters
are known; e.g. they apply to Point{Int} but not to Point. Optionally, outer constructors
that determine type parameters automatically can be added, for example constructing a Point{Int}
from the call Point(1,2). Outer constructors call inner constructors to actually
make instances. However, in some cases one would rather not provide inner constructors, so
that specific type parameters cannot be requested manually.

For example, say we define a type that stores a vector along with an accurate representation of
its sum:

julia> struct SummedArray{T<:Number,S<:Number}

julia> SummedArray(Int32[1; 2; 3], Int32(6))
SummedArray{Int32,Int32}(Int32[1, 2, 3], 6)

The problem is that we want S to be a larger type than T, so that we can sum many elements
with less information loss. For example, when T is Int32, we would like S to
be Int64. Therefore we want to avoid an interface that allows the user to construct
instances of the type SummedArray{Int32,Int32}. One way to do this is to provide a
constructor only for SummedArray, but inside the struct definition block to suppress
generation of default constructors:

julia> struct SummedArray{T<:Number,S<:Number}
           function SummedArray(a::Vector{T}) where T
               S = widen(T)
               new{T,S}(a, sum(S, a))

julia> SummedArray(Int32[1; 2; 3], Int32(6))
ERROR: MethodError: no method matching SummedArray(::Array{Int32,1}, ::Int32)
Closest candidates are:
  SummedArray(::Array{T,1}) where T at none:5

This constructor will be invoked by the syntax SummedArray(a). The syntax new{T,S} allows
specifying parameters for the type to be constructed, i.e. this call will return a SummedArray{T,S}.
new{T,S} can be used in any constructor definition, but for convenience the parameters
to new{} are automatically derived from the type being constructed when possible.