Expressions

Intro to Expressions

Expressions are a specific type of object in Julia. You can think of an expression as representing a piece of Julia code that has not yet been evaluated (i.e. executed). There are then specific functions and operations, like eval() which will evaluate the expression.

For instance, we could write a script or enter into the interpreter the following: julia> 1+1 2

One way to create an expression is using the :() syntax. For example:

julia> MyExpression = :(1+1)
:(1 + 1)
julia> typeof(MyExpression)
Expr

We now have an Expr type object. Having just been formed, it doesn’t do anything - it just sits around like any other object until it is acted upon. In this case, we can evaluate that expression using the eval() function:

julia> eval(MyExpression)
2

Thus, we see that the following two are equivalent:

1+1
eval(:(1+1))

Why would we want to go through the much more complicated syntax in eval(:(1+1)) if we just want to find what 1+1 equals? The basic reason is that we can define an expression at one point in our code, potentially modify it later on, and then evaluate it at a later point still. This can potentially open up powerful new capabilities to the Julia programmer. Expressions are a key component of metaprogramming in Julia.

Creating Expressions

There are a number of different methods that can be used to create the same type of expression. The expressions intro mentioned the :() syntax. Perhaps the best place to start, however is with strings. This helps to reveal some of the fundamental similarities between expressions and strings in Julia.

Create Expression from String

From the Julia documentation:

Every Julia program starts life as a string

In other words, any Julia script is simply written in a text file, which is nothing but a string of characters. Likewise, any Julia command entered into an interpreter is just a string of characters. The role of Julia or any other programming language then is to interpret and evaluate strings of characters in a logical, predictable way so that those strings of characters can be used to describe what the programmer wants the computer to accomplish.

Thus, one way to create an expression is to use the parse() function as applied to a string. The following expression, once it is evaluated, will assign the value of 2 to the symbol x.

MyStr = "x = 2"
MyExpr = parse(MyStr)
julia> x
ERROR: UndefVarError: x not defined
eval(MyExpr)
julia> x
2

Create Expression Using :() Syntax

MyExpr2 = :(x = 2)
julia> MyExpr == MyExpr2
true

Note that with this syntax, Julia will automatically treat the names of objects as referring to symbols. We can see this if we look at the args of the expression. (See Fields of Expression Objects for more details on the args field in an expression.)

julia> MyExpr2.args
2-element Array{Any,1}:
  :x
 2

Create Expression using the Expr() Function

MyExpr3 = Expr(:(=), :x, 2)
MyExpr3 == MyExpr

This syntax is based on prefix notation. In other words, the first argument of the specified to the Expr() function is the head or prefix. The remaining are the arguments of the expression. The head determines what operations will be performed on the arguments.

For more details on this, see Fields of Expression Objects

When using this syntax, it is important to distinguish between using objects and symbols for objects. For instance, in the above example, the expression assigns the value of 2 to the symbol :x, a perfectly sensible operation. If we used x itself in an expression such as that, we would get the nonsensical result:

julia> Expr(:(=), x, 5)
:(2 = 5)

Similarly, if we examine the args we see:

julia> Expr(:(=), x, 5).args
2-element Array{Any,1}:
 2
 5

Thus, the Expr() function does not perform the same automatic transformation into symbols as the :() syntax for creating expressions.

Create multi-line Expressions using quote...end

MyQuote = 
quote
    x = 2
    y = 3
end
julia> typeof(MyQuote)
Expr

Note that with quote...end we can create expressions that contain other expressions in their args field:

julia> typeof(MyQuote.args[2])
Expr

See Fields of Expression Objects for more on this args field.

More on Creating Expressions

This Example just gives the basics for creating expressions. See also, for example, Interpolation and Expressions and Fields of Expression Objects for more information on creating more complex and advanced expressions.

Fields of Expression Objects

As mentioned in the Intro to Expressions expressions are a specific type of object in Julia. As such, they have fields. The two most used fields of an expression are its head and its args. For instance, consider the expression

MyExpr3 = Expr(:(=), :x, 2)

discussed in Creating Expressions. We can see the head and args as follows:

julia> MyExpr3.head
:(=)

julia> MyExpr3.args
2-element Array{Any,1}:
  :x
 2

Expressions are based on prefix notation. As such, the head generally specifies the operation that is to be performed on the args. The head must be of Julia type Symbol.

When an expression is to assign a value (when it gets evaluated), it will generally use a head of :(=). There are of course obvious variations to this that can be employed, e.g.:

ex1 = Expr(:(+=), :x, 2)

:call for expression heads

Another common head for expressions is :call. E.g.

ex2 = Expr(:call, :(*), 2, 3)
eval(ex2) ## 6

Following the conventions of prefix notation, operators are evaluated from left to right. Thus, this expression here means that we will call the function that is specified on the first element of args on the subsequent elements. We similarly could have:

julia> ex2a = Expr(:call, :(-), 1, 2, 3)
:(1 - 2 - 3)

Or other, potentially more interesting functions, e.g.

julia> ex2b = Expr(:call, :rand, 2,2)
:(rand(2,2))

julia> eval(ex2b)
2x2 Array{Float64,2}:
 0.429397  0.164478
 0.104994  0.675745

Automatic determination of head when using :() expression creation notation

Note that :call is implicitly used as the head in certain constructions of expressions, e.g.

julia> :(x + 2).head
:call

Thus, with the :() syntax for creating expressions, Julia will seek to automatically determine the correct head to use. Similarly:

julia> :(x = 2).head
:(=)

In fact, if you aren’t certain what the right head to use for an expression that you are forming using, for instance, Expr() this can be a helpful tool to get tips and ideas for what to use.

Interpolation and Expressions

Creating Expressions mentions that expressions are closely related to strings. As such, the principles of interpolation within strings are also relevant for Expressions. For instance, in basic string interpolation, we can have something like:

n = 2
julia> MyString = "there are $n ducks"
"there are 2 ducks"

We use the $ sign to insert the value of n into the string. We can use the same technique with expressions. E.g.

a = 2
ex1 = :(x = 2*$a)  ##     :(x = 2 * 2)
a = 3
eval(ex1)
x # 4

Contrast this this:

a = 2
ex2 = :(x = 2*a) # :(x = 2a)
a = 3
eval(ex2)
x # 6

Thus, with the first example, we set in advance the value of a that will be used at the time that the expression is evaluated. With the second example, however, the Julia compiler will only look to a to find its value at the time of evaluation for our expression.

External References on Expressions

There are a number of useful web resources that can help further your knowledge of expressions in Julia. These include:

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